Re: [EM] MaxMinPA
If course the balloting for choosing between the 2 finalists need only be
rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would be
better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison to
the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in addition to
the MMPO count.
One argument against that variation is that a voter's inferred approvals
are likely to be more optimal for hir than the Score ratings on which
they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising voters
might approve lower than than necessary, if the approval were explicitly
voted. ...in comparison to their ratings-which tend to soften voting
errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The first
set of ballots is used to narrow down to two alternatives. It is expected
that these ballots will be voted with all possible manipulative strategy
... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives served
up by the first set.
A voter who doesn't like strategic burden need not contribute to the first
set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from blank
(=0) to 10, there would be enough resolution for all practical purposes.
Approval voters could simply specify their approvals with 10 and leave the
other candidates' scores blank.
There should be no consistency requirement between the two ballots. They
should be put in separate boxes and counted separately. Only that policy
can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect information
approval strategy may require you to approve out of order, i.e. approve X
and not Y even if you sincerely rate Y higher than X. [We're talking about
optimal in the sense of maximizing your expectation, meaning the
expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them are
sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit Approval,
respectively, applied to the first set of ballots. People's eyes would be
opened when they saw how often the Approval Winner was sincerely preferred
over the IRV winner.
Currently my first choice of methods for choosing the respective finalists
would be MMPO for one of them and Approval for the other, with the approval
cutoff at midrange (so scores of six through ten represent approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would be B,
unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would be A,
the CWs. The chicken defection was to no avail. Note that even though
this violates Plurality on the first set of ballots, it does not on the
sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt to
win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that are
immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of the
voters vote approval style in either or both sets of ballots, the Plurality
problem will automatically evaporate; on approval style ballots the
Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only top
and bottom votes are used, in particular when Condorcet methods allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval style
ballots.
Everything else (besides approval strategy) that we do seems to be an
effort to lift the strategical burden from the voter. We would like to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should do so.
- But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only votes
Approval style if he can coordinate with enough other voters to pass the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties (like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it all.
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my forwarding
an email with his private earlier input included. It was too late when I
realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest potential
problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the two
base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote at
the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can externalize
the paradoxes of voting. To a certain extent Approval avoids bad
properties by externalizing them. The cost is the "burden" of the voter
deciding whom to approve. As Ron LeGrand has so amply demonstrated, any
time you try to automate approval strategy in a semi-optimal way, you end
up with a non-monotone method. By the same token IRV can be thought of as
a rudimentary DSV approach to plurality voting, so it should be no surprise
that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff email9648742@gmail.com
wrote:
If course the balloting for choosing between the 2 finalists need only be
rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would be
better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison to
the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in addition
to the MMPO count.
One argument against that variation is that a voter's inferred approvals
are likely to be more optimal for hir than the Score ratings on which
they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The first
set of ballots is used to narrow down to two alternatives. It is expected
that these ballots will be voted with all possible manipulative strategy
... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives served
up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from blank
(=0) to 10, there would be enough resolution for all practical purposes.
Approval voters could simply specify their approvals with 10 and leave the
other candidates' scores blank.
There should be no consistency requirement between the two ballots. They
should be put in separate boxes and counted separately. Only that policy
can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit Approval,
respectively, applied to the first set of ballots. People's eyes would be
opened when they saw how often the Approval Winner was sincerely preferred
over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would be
B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would be
A, the CWs. The chicken defection was to no avail. Note that even though
this violates Plurality on the first set of ballots, it does not on the
sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt to
win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that are
immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only top
and bottom votes are used, in particular when Condorcet methods allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval style
ballots.
Everything else (besides approval strategy) that we do seems to be an
effort to lift the strategical burden from the voter. We would like to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should do
so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only votes
Approval style if he can coordinate with enough other voters to pass the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties (like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.
It should be MMPO, rather than Smith//MMPO, for one finalist-choosing
method, and Approval, Inferred-Approval, or Score for the other, because
MMPO, Approval, & Score meet FBC.
If Plain MMPO were replaced by anything else, Weak CD would be lost.
If, for the other finalist-choosing method, Approval, Inferred-Approval or
Score were replaced by MAM or Beatpath, then both finalist-choosing methods
would share the same strategic vulnerabilities.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my forwarding
an email with his private earlier input included. It was too late when I
realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest potential
problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the two
base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote
at the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can externalize
the paradoxes of voting. To a certain extent Approval avoids bad
properties by externalizing them. The cost is the "burden" of the voter
deciding whom to approve. As Ron LeGrand has so amply demonstrated, any
time you try to automate approval strategy in a semi-optimal way, you end
up with a non-monotone method. By the same token IRV can be thought of as
a rudimentary DSV approach to plurality voting, so it should be no surprise
that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <email9648742@gmail.com
wrote:
If course the balloting for choosing between the 2 finalists need only be
rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would be
better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison to
the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in addition
to the MMPO count.
One argument against that variation is that a voter's inferred approvals
are likely to be more optimal for hir than the Score ratings on which
they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The first
set of ballots is used to narrow down to two alternatives. It is expected
that these ballots will be voted with all possible manipulative strategy
... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives
served up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from blank
(=0) to 10, there would be enough resolution for all practical purposes.
Approval voters could simply specify their approvals with 10 and leave the
other candidates' scores blank.
There should be no consistency requirement between the two ballots.
They should be put in separate boxes and counted separately. Only that
policy can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit
Approval, respectively, applied to the first set of ballots. People's eyes
would be opened when they saw how often the Approval Winner was sincerely
preferred over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would be
B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would be
A, the CWs. The chicken defection was to no avail. Note that even though
this violates Plurality on the first set of ballots, it does not on the
sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt to
win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that are
immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only
top
and bottom votes are used, in particular when Condorcet methods allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval style
ballots.
Everything else (besides approval strategy) that we do seems to be an
effort to lift the strategical burden from the voter. We would like
to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should do
so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only votes
Approval style if he can coordinate with enough other voters to pass the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties (like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.
On 10/19/2016 8:10 AM, Michael Ossipoff wrote:
It should be MMPO, rather than Smith//MMPO, for one finalist-choosing
method, and Approval, Inferred-Approval, or Score for the other,
because MMPO, Approval, & Score meet FBC.
FBC won't survive any Push-over incentive (as I'm sure Kevin Venzke
would confirm).
Chris Benham
It should be MMPO, rather than Smith//MMPO, for one finalist-choosing
method, and Approval, Inferred-Approval, or Score for the other,
because MMPO, Approval, & Score meet FBC.
If Plain MMPO were replaced by anything else, Weak CD would be lost.
If, for the other finalist-choosing method, Approval,
Inferred-Approval or Score were replaced by MAM or Beatpath, then both
finalist-choosing methods would share the same strategic vulnerabilities.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" <fsimmons@pcc.edu
mailto:fsimmons@pcc.edu> wrote:
I appreciate all of the great insights from Kristofer, Chris
Benham, and Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my
forwarding an email with his private earlier input included. It
was too late when I realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest
potential problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for
the two base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method
that doesn't just reduce to Approval when all candidates are
ranked or rated at the extremes. I think that the other method
should be one that does reduce to Approval at the extremes, like
River, MAM/RankedPairs, or Beatpath/Tideman/Schulz. It could be a
Bucklin variant like MJ, Andy Jennings's Chiastic Approval, or
Jameson's MAS.
Like Michael I think that Range itself gives too much incentive
to vote at the extremes on the strategic ballots. Better to use
Approval or an approval variant so that the strategic ratings are
not unduly compressed for the other base method.
I like Kristofer's insights about the subtle differences between
the proposed "manual" version in contradistinction to a DSV
version that automates strategy for the two methods based on the
first set of (perhaps somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can
externalize the paradoxes of voting. To a certain extent Approval
avoids bad properties by externalizing them. The cost is the
"burden" of the voter deciding whom to approve. As Ron LeGrand
has so amply demonstrated, any time you try to automate approval
strategy in a semi-optimal way, you end up with a non-monotone
method. By the same token IRV can be thought of as a rudimentary
DSV approach to plurality voting, so it should be no surprise that
IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset
Voting. It externalizes everything, which makes it impossible to
contradict any nice ballot based property. Because of this there
is an extreme resulting strategic burden, but in this case that
burden is placed squarely onto the shoulders of the candidates,
not the voters. Presumably the candidates are up to that kind of
burden since they are, after all, politicians (in our contemplated
public applications).
But this brings up another intriguing idea. Let one of the two
base methods be Asset Voting, so that the sincere ballots decide
between (say) the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff
<email9648742@gmail.com <mailto:email9648742@gmail.com>> wrote:
If course the balloting for choosing between the 2 finalists
need only be rankings, to show preferences between the 2
finalists, whoever they turn out to be.
Some variations occurred to me. I'm not saying that any of
them would be better. I just wanted to mention them, without
any implication that they haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in
comparison to the initial proposal:
1. What if, for the initial 2 counts, it were a Score-count,
in addition to the MMPO count.
One argument against that variation is that a voter's inferred
approvals are likely to be more optimal for hir than the Score
ratings on which they're based.
2. For the 2 initial counts, what if the MMPO count used a
separate ranking, & the Approval count used a separate set of
Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that
overcompromising voters might approve lower than than
necessary, if the approval were explicitly voted. ...in
comparison to their ratings-which tend to soften voting errors.
So far, it appears that the initial proposal is probably the
best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" <fsimmons@pcc.edu
<mailto:fsimmons@pcc.edu>> wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each
voter. The first set of ballots is used to narrow down to
two alternatives. It is expected that these ballots will
be voted with all possible manipulative strategy ...
chicken defection, pushover, burial, etc.
The second set is used only to decide between the two
alternatives served up by the first set.
A voter who doesn't like strategic burden need not
contribute to the first set, or could submit the same
ballot to both sets.
If both ballots were Olympic Score style, with scores
ranging from blank (=0) to 10, there would be enough
resolution for all practical purposes. Approval voters
could simply specify their approvals with 10 and leave the
other candidates' scores blank.
There should be no consistency requirement between the two
ballots. They should be put in separate boxes and counted
separately. Only that policy can guarantee the sincerity
of the ballots in the second set.
In this regard it is important to realize that optimal
perfect information approval strategy may require you to
approve out of order, i.e. approve X and not Y even if you
sincerely rate Y higher than X. [We're talking about
optimal in the sense of maximizing your expectation,
meaning the expectation of your sincere ratings ballot,
(your contribution to the second set).]
Nobody expects sincerity on the first set of ballots. If
some of them are sincere, no harm done, as long as the
methods for choosing the two finalists are reasonable.
On the other hand, no rational voter would vote
insincerely on hir contribution to the second set. The
social scientist has a near perfect window into the
sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and
Implicit Approval, respectively, applied to the first set
of ballots. People's eyes would be opened when they saw
how often the Approval Winner was sincerely preferred over
the IRV winner.
Currently my first choice of methods for choosing the
respective finalists would be MMPO for one of them and
Approval for the other, with the approval cutoff at
midrange (so scores of six through ten represent approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval
finalist would be B, unless too many B ratings were below
midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of
ballots would be A, the CWs. The chicken defection was to
no avail. Note that even though this violates Plurality
on the first set of ballots, it does not on the sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C
faction attempt to win by truncation of B would have no
effect. A burial of B by the C faction would be no more
rewarding than their truncation of B.
So this idea seems to take care of the tension between
methods that are immune to burial and methods that are
immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates.
Even if all of the voters vote approval style in either or
both sets of ballots, the Plurality problem will
automatically evaporate; on approval style ballots the
Approval winner pairwise beats all other candidates,
including the MMPO candidate (if different from the
approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm
<km_elmet@t-online.de <mailto:km_elmet@t-online.de>> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem
waiting for formalization.
That reminds me that someone once pointed out that
almost all of the
methods favored by EM list enthusiasts reduce to
Approval when only top
and bottom votes are used, in particular when
Condorcet methods allow
equal top and multiple truncation votes they fall
into this category
because the Approval Winner is the pairwise winner
for approval style
ballots.
Everything else (besides approval strategy) that we
do seems to be an
effort to lift the strategical burden from the
voter. We would like to
remove that burden in all cases, but at least in the
zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you
could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style,
then you should do so.
- But figuring out the correct threshold to use is
tough (strategic burden)
- So you may err, which leads to a problem. And even
if you don't, if
the voters feel they have to burden their minds,
that's a bad thing.
Here, traditional game theory would probably pick some
kind of mixed
strategy, where you "exaggerate" (Approval-ize) only
to the extent that
you benefit even when taking your errors into account.
But such an
equilibrium is unrealistic (we'd have to find out why,
but probably
because it would in the worst case require everybody
to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results,
we're left with two
possibilities:
- Either suppose that the method is sufficiently
robust that most voters
won't use Approval strategy (e.g. the pro-MJ argument
that Approval
strategy only is a benefit if enough people use it, so
most people
won't, so we'll have a correlated equilibrium of sorts)
- That any admissible method must have a "bump in the
road" on the way
from a honest vote to an Approval vote, where moving
closer to
Approval-style harms the voter. Then a
game-theoretical voter only votes
Approval style if he can coordinate with enough other
voters to pass the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice
properties (like
monotonicity + FBC; if the proof is by contradiction,
then we'd know
some property combinations we'd have to violate). So
we can't have it all.
Election-Methods mailing list - see http://electorama.com/em for list info
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An example is needed.
On Oct 18, 2016 9:37 PM, "C.Benham" cbenham@adam.com.au wrote:
On 10/19/2016 8:10 AM, Michael Ossipoff wrote:
It should be MMPO, rather than Smith//MMPO, for one finalist-choosing
method, and Approval, Inferred-Approval, or Score for the other, because
MMPO, Approval, & Score meet FBC.
FBC won't survive any Push-over incentive (as I'm sure Kevin Venzke would
confirm).
Chris Benham
It should be MMPO, rather than Smith//MMPO, for one finalist-choosing
method, and Approval, Inferred-Approval, or Score for the other, because
MMPO, Approval, & Score meet FBC.
If Plain MMPO were replaced by anything else, Weak CD would be lost.
If, for the other finalist-choosing method, Approval, Inferred-Approval or
Score were replaced by MAM or Beatpath, then both finalist-choosing methods
would share the same strategic vulnerabilities.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my forwarding
an email with his private earlier input included. It was too late when I
realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest
potential problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the two
base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote
at the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can externalize
the paradoxes of voting. To a certain extent Approval avoids bad
properties by externalizing them. The cost is the "burden" of the voter
deciding whom to approve. As Ron LeGrand has so amply demonstrated, any
time you try to automate approval strategy in a semi-optimal way, you end
up with a non-monotone method. By the same token IRV can be thought of as
a rudimentary DSV approach to plurality voting, so it should be no surprise
that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <
email9648742@gmail.com> wrote:
If course the balloting for choosing between the 2 finalists need only
be rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would be
better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison to
the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in addition
to the MMPO count.
One argument against that variation is that a voter's inferred approvals
are likely to be more optimal for hir than the Score ratings on which
they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The first
set of ballots is used to narrow down to two alternatives. It is expected
that these ballots will be voted with all possible manipulative strategy
... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives
served up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from
blank (=0) to 10, there would be enough resolution for all practical
purposes. Approval voters could simply specify their approvals with 10 and
leave the other candidates' scores blank.
There should be no consistency requirement between the two ballots.
They should be put in separate boxes and counted separately. Only that
policy can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit
Approval, respectively, applied to the first set of ballots. People's eyes
would be opened when they saw how often the Approval Winner was sincerely
preferred over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would be
B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would be
A, the CWs. The chicken defection was to no avail. Note that even though
this violates Plurality on the first set of ballots, it does not on the
sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt
to win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that are
immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only
top
and bottom votes are used, in particular when Condorcet methods allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval style
ballots.
Everything else (besides approval strategy) that we do seems to be an
effort to lift the strategical burden from the voter. We would like
to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should do
so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most
voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only
votes
Approval style if he can coordinate with enough other voters to pass
the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties (like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.
Election-Methods mailing list - see http://electorama.com/em for list info
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Yes, saying that everyone ranked is approved would unnecessarily inhibit
people's MMPO rankings, as would a Score-count.
So an approval-cutoff inferred at the candidates rating-midrange would be
better. ...in the ratings from whose order the MMPO rankings are Inferred.
...or an explicitly-voted approval-cutoff in a ranked MMPO ballot. If
course it comes to the same thing, just different ballot-implementation.
If I'd introduced this best-appearing method, I'd want it named after me.
Beatpath is named after Markus. So: Simmons' method, in its various
variations.
...which, anyway, is lot less cumbersome than something like
MMPO/Approval-like Fnalist-Choice.
That is relevant because, when discussing something, it helps to have a
name by which to refer to it.
It avoids chicken dilemma, because, even if the A voters give an approval
to B, and B wins the Approval count, A (the MMPO winner) pairwise-beats B,
and so A wins & the defection fails.
Truncation of the CWs doesn't take away hir win in MMPO. Even if the
truncators' candidate wins the approval count, the CWs pairwise-beats hir,
& wins the runoff.
Burial of the CWs?:
Here, MMPO & wv need the CWs's voters to plump, or at least not rank the
buriers' candidate over the candidate insincerely ranked over hir.
So, too, Approval, Score & Bucklin need that plumping. It seems a universal
requirement.
So Simmons doesn't escape that requirement.
But, when done, that defensive plumping protects the CWs's win, in both
finalist-choosing counts.
...And, if the burial is deterred, as it often or usually will be in
MMPO, but the plumping isn't actually done, then the CWs still wins in
MMPO.
Even if the truncators' candidates wins in the Approval-like method, the
CWs pairbeats hir, & wins the runoff.
So Simmons has wv strategy.
But that means it also has the possibility of the perpetual burial fiasco,
which goes with it.
But that possibility doesn't keep wv from being one of the most popular
classes of methods.
Simmons, though using MMPO, doesn't have Kevin's MMPO bad-example:
C doesn't win in any Approval-like method. They give an A & B tie. A & B
pairbeat C, and would therefore win the runoff.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my forwarding
an email with his private earlier input included. It was too late when I
realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest potential
problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the two
base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote
at the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can externalize
the paradoxes of voting. To a certain extent Approval avoids bad
properties by externalizing them. The cost is the "burden" of the voter
deciding whom to approve. As Ron LeGrand has so amply demonstrated, any
time you try to automate approval strategy in a semi-optimal way, you end
up with a non-monotone method. By the same token IRV can be thought of as
a rudimentary DSV approach to plurality voting, so it should be no surprise
that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <email9648742@gmail.com
wrote:
If course the balloting for choosing between the 2 finalists need only be
rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would be
better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison to
the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in addition
to the MMPO count.
One argument against that variation is that a voter's inferred approvals
are likely to be more optimal for hir than the Score ratings on which
they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The first
set of ballots is used to narrow down to two alternatives. It is expected
that these ballots will be voted with all possible manipulative strategy
... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives
served up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from blank
(=0) to 10, there would be enough resolution for all practical purposes.
Approval voters could simply specify their approvals with 10 and leave the
other candidates' scores blank.
There should be no consistency requirement between the two ballots.
They should be put in separate boxes and counted separately. Only that
policy can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit
Approval, respectively, applied to the first set of ballots. People's eyes
would be opened when they saw how often the Approval Winner was sincerely
preferred over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would be
B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would be
A, the CWs. The chicken defection was to no avail. Note that even though
this violates Plurality on the first set of ballots, it does not on the
sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt to
win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that are
immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only
top
and bottom votes are used, in particular when Condorcet methods allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval style
ballots.
Everything else (besides approval strategy) that we do seems to be an
effort to lift the strategical burden from the voter. We would like
to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should do
so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only votes
Approval style if he can coordinate with enough other voters to pass the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties (like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.
On 10/20/2016 6:35 AM, Michael Ossipoff wrote:
An example is needed.
C: Not really. Logically it's impossible to have both any Push-over
incentive and FBC.
Whenever you're determining the winner by who is pairwise preferred out
of the winner of method A and the winner of method B,
there will always be situations where you do better by not equal-top
voting your sincere favourite F so as to keep F out of the final
where F would lose to your worst W.
Chris Benham
An example is needed.
On Oct 18, 2016 9:37 PM, "C.Benham" <cbenham@adam.com.au
mailto:cbenham@adam.com.au> wrote:
On 10/19/2016 8:10 AM, Michael Ossipoff wrote:
It should be MMPO, rather than Smith//MMPO, for one
finalist-choosing method, and Approval, Inferred-Approval, or
Score for the other, because MMPO, Approval, & Score meet FBC.
FBC won't survive any Push-over incentive (as I'm sure Kevin
Venzke would confirm).
Chris Benham
It should be MMPO, rather than Smith//MMPO, for one
finalist-choosing method, and Approval, Inferred-Approval, or
Score for the other, because MMPO, Approval, & Score meet FBC.
If Plain MMPO were replaced by anything else, Weak CD would be lost.
If, for the other finalist-choosing method, Approval,
Inferred-Approval or Score were replaced by MAM or Beatpath, then
both finalist-choosing methods would share the same strategic
vulnerabilities.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" <fsimmons@pcc.edu
<mailto:fsimmons@pcc.edu>> wrote:
I appreciate all of the great insights from Kristofer, Chris
Benham, and Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about
my forwarding an email with his private earlier input
included. It was too late when I realized I hadn't deleted
that part.
Intuitively, I think Chris is right that Pushover is the
biggest potential problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities
for the two base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one
method that doesn't just reduce to Approval when all
candidates are ranked or rated at the extremes. I think that
the other method should be one that does reduce to Approval
at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like
MJ, Andy Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much
incentive to vote at the extremes on the strategic ballots.
Better to use Approval or an approval variant so that the
strategic ratings are not unduly compressed for the other
base method.
I like Kristofer's insights about the subtle differences
between the proposed "manual" version in contradistinction to
a DSV version that automates strategy for the two methods
based on the first set of (perhaps somewhat pre-strategized)
ratings.
In particular he pointed out how certain procedural rules can
externalize the paradoxes of voting. To a certain extent
Approval avoids bad properties by externalizing them. The
cost is the "burden" of the voter deciding whom to approve.
As Ron LeGrand has so amply demonstrated, any time you try to
automate approval strategy in a semi-optimal way, you end up
with a non-monotone method. By the same token IRV can be
thought of as a rudimentary DSV approach to plurality voting,
so it should be no surprise that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset
Voting. It externalizes everything, which makes it
impossible to contradict any nice ballot based property.
Because of this there is an extreme resulting strategic
burden, but in this case that burden is placed squarely onto
the shoulders of the candidates, not the voters. Presumably
the candidates are up to that kind of burden since they are,
after all, politicians (in our contemplated public applications).
But this brings up another intriguing idea. Let one of the
two base methods be Asset Voting, so that the sincere ballots
decide between (say) the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff
<email9648742@gmail.com <mailto:email9648742@gmail.com>> wrote:
If course the balloting for choosing between the 2
finalists need only be rankings, to show preferences
between the 2 finalists, whoever they turn out to be.
Some variations occurred to me. I'm not saying that any
of them would be better. I just wanted to mention them,
without any implication that they haven't already
occurred to everyone.
Both of the following possibilities have disadvantages,
in comparison to the initial proposal:
1. What if, for the initial 2 counts, it were a
Score-count, in addition to the MMPO count.
One argument against that variation is that a voter's
inferred approvals are likely to be more optimal for hir
than the Score ratings on which they're based.
2. For the 2 initial counts, what if the MMPO count used
a separate ranking, & the Approval count used a separate
set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that
overcompromising voters might approve lower than than
necessary, if the approval were explicitly voted. ...in
comparison to their ratings-which tend to soften voting
errors.
So far, it appears that the initial proposal is probably
the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons"
<fsimmons@pcc.edu <mailto:fsimmons@pcc.edu>> wrote:
Kristofer,
Perhaps the way out is to invite two ballots from
each voter. The first set of ballots is used to
narrow down to two alternatives. It is expected that
these ballots will be voted with all possible
manipulative strategy ... chicken defection,
pushover, burial, etc.
The second set is used only to decide between the two
alternatives served up by the first set.
A voter who doesn't like strategic burden need not
contribute to the first set, or could submit the same
ballot to both sets.
If both ballots were Olympic Score style, with scores
ranging from blank (=0) to 10, there would be enough
resolution for all practical purposes. Approval
voters could simply specify their approvals with 10
and leave the other candidates' scores blank.
There should be no consistency requirement between
the two ballots. They should be put in separate
boxes and counted separately. Only that policy can
guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that
optimal perfect information approval strategy may
require you to approve out of order, i.e. approve X
and not Y even if you sincerely rate Y higher than
X. [We're talking about optimal in the sense of
maximizing your expectation, meaning the expectation
of your sincere ratings ballot, (your contribution to
the second set).]
Nobody expects sincerity on the first set of
ballots. If some of them are sincere, no harm done,
as long as the methods for choosing the two finalists
are reasonable.
On the other hand, no rational voter would vote
insincerely on hir contribution to the second set.
The social scientist has a near perfect window into
the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV
and Implicit Approval, respectively, applied to the
first set of ballots. People's eyes would be opened
when they saw how often the Approval Winner was
sincerely preferred over the IRV winner.
Currently my first choice of methods for choosing the
respective finalists would be MMPO for one of them
and Approval for the other, with the approval cutoff
at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval
finalist would be B, unless too many B ratings were
below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set
of ballots would be A, the CWs. The chicken defection
was to no avail. Note that even though this violates
Plurality on the first set of ballots, it does not on
the sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C
faction attempt to win by truncation of B would have
no effect. A burial of B by the C faction would be
no more rewarding than their truncation of B.
So this idea seems to take care of the tension
between methods that are immune to burial and methods
that are immune to chicken defection.
Furthermore, the plurality problem of MMPO
evaporates. Even if all of the voters vote approval
style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on
approval style ballots the Approval winner pairwise
beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer
Munsterhjelm <km_elmet@t-online.de
<mailto:km_elmet@t-online.de>> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk
theorem waiting for formalization.
That reminds me that someone once pointed out
that almost all of the
methods favored by EM list enthusiasts reduce
to Approval when only top
and bottom votes are used, in particular when
Condorcet methods allow
equal top and multiple truncation votes they
fall into this category
because the Approval Winner is the pairwise
winner for approval style
ballots.
Everything else (besides approval strategy)
that we do seems to be an
effort to lift the strategical burden from the
voter. We would like to
remove that burden in all cases, but at least
in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then
you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval
style, then you should do so.
- But figuring out the correct threshold to use
is tough (strategic burden)
- So you may err, which leads to a problem. And
even if you don't, if
the voters feel they have to burden their minds,
that's a bad thing.
Here, traditional game theory would probably pick
some kind of mixed
strategy, where you "exaggerate" (Approval-ize)
only to the extent that
you benefit even when taking your errors into
account. But such an
equilibrium is unrealistic (we'd have to find out
why, but probably
because it would in the worst case require
everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad
results, we're left with two
possibilities:
- Either suppose that the method is sufficiently
robust that most voters
won't use Approval strategy (e.g. the pro-MJ
argument that Approval
strategy only is a benefit if enough people use
it, so most people
won't, so we'll have a correlated equilibrium of
sorts)
- That any admissible method must have a "bump in
the road" on the way
from a honest vote to an Approval vote, where
moving closer to
Approval-style harms the voter. Then a
game-theoretical voter only votes
Approval style if he can coordinate with enough
other voters to pass the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few
nice properties (like
monotonicity + FBC; if the proof is by
contradiction, then we'd know
some property combinations we'd have to violate).
So we can't have it all.
----
Election-Methods mailing list - seehttp://electorama.com/em for list info
Very kind of you to suggest "Simmons" for this method, and I certainly
don't mind associating my name with it, although every idea in it owes much
to input from you all, especially Chris Benham, Michael Ossipoff, Kevin
Venzke, Kristofer M, Jameson Q, Andy Jennings, Jobst Heitzig, Joe
Weinstein, Craig Layton,Warren Smith, Toby Pereira, Rob LeGrand, Rob
Lanphier, Richard Moore, Bart Ingles, Rick Denman. Steven J Brams, Steve
Eppley, Francis Edward Su, Sylvia Owl, Adam Tarr, Alex Small, Stephane
Rouillon, Craig Carey, Dave Ketchum, Douglas Greene, Blake Cretney, James
Gilmour, Jan Kok, Josh Narins, Steve Barney, Joseph Malkevitch, Olli Salmi,
Gervase Lam, Elisabeth Varin, Mike Rouse, Donald E Davison, Markus Schulze,
Martin Harper, DEMOREP1, Buddha Buck, David Catchpole, Anthony Simmons, James
Green-Armytage, Kathy Dopp, Juho Laatu, and too many more to mention.
If it turns out to have a serious Achilles heel, I will disavow the whole
thing!
When Approval doesn't elect the CWs, there are several possible excuses,
among them ...
(1) lack of information
(2) too much disinformation
(3) poor approval strategy by the CW supporters
(4) sincere reflection of the intensity of support
To elaborate on (4), if the preference profile is
40 A=B>D(90%)
35 B=C>D(90%)
25 A=C>D(90%)
then D is the sincere Range winner, as well as the Sincere Approval winner,
but is the Condorcet Loser.
I have constructed an example that yields this profile based on three
neighborhoods whose centers form an equilateral triangle, and four proposed
sites for a deep well (into a pure aquifer far below the contaminated
surface water)
Site D is the center of the triangle. The other three sites (A, B, and C)
are exterior to the triangle on the perpendicular bisectors of the segments
connecting the neighborhood centers, but not quite as far from the
midpoints of those segments as the center of the triangle.
As for "sincere approval, " I have described it elsewhere. Basically, for
a score ballot divide the total score of the candidates on that ballot by
the max possible score. Take the integer part and approve that many
candidates. The fractional part left over determines the probability of
approving the next candidate in line. A spin of a spinner can make that
decision.
Or in the above case, community spirit can make the difference..
In this case Sincere Approval and Range give the same expected results:
D(90), A(65), B(75), and C(60)
In conclusion, I don't think we need to be embarrassed if Simmons doesn't
choose the CWs revealed by the second (sincere) set of ballots, especially
if the ballots in the second set are merely ranked preference ballots,
which are perfectly adequate for their purpose.
Thanks,
Forest
On Wed, Oct 19, 2016 at 2:24 PM, Michael Ossipoff email9648742@gmail.com
wrote:
Yes, saying that everyone ranked is approved would unnecessarily inhibit
people's MMPO rankings, as would a Score-count.
So an approval-cutoff inferred at the candidates rating-midrange would be
better. ...in the ratings from whose order the MMPO rankings are Inferred.
...or an explicitly-voted approval-cutoff in a ranked MMPO ballot. If
course it comes to the same thing, just different ballot-implementation.
If I'd introduced this best-appearing method, I'd want it named after me.
Beatpath is named after Markus. So: Simmons' method, in its various
variations.
...which, anyway, is lot less cumbersome than something like
MMPO/Approval-like Fnalist-Choice.
That is relevant because, when discussing something, it helps to have a
name by which to refer to it.
It avoids chicken dilemma, because, even if the A voters give an approval
to B, and B wins the Approval count, A (the MMPO winner) pairwise-beats B,
and so A wins & the defection fails.
Truncation of the CWs doesn't take away hir win in MMPO. Even if the
truncators' candidate wins the approval count, the CWs pairwise-beats hir,
& wins the runoff.
Burial of the CWs?:
Here, MMPO & wv need the CWs's voters to plump, or at least not rank the
buriers' candidate over the candidate insincerely ranked over hir.
So, too, Approval, Score & Bucklin need that plumping. It seems a
universal requirement.
So Simmons doesn't escape that requirement.
But, when done, that defensive plumping protects the CWs's win, in both
finalist-choosing counts.
...And, if the burial is deterred, as it often or usually will be in
MMPO, but the plumping isn't actually done, then the CWs still wins in
MMPO.
Even if the truncators' candidates wins in the Approval-like method, the
CWs pairbeats hir, & wins the runoff.
So Simmons has wv strategy.
But that means it also has the possibility of the perpetual burial fiasco,
which goes with it.
But that possibility doesn't keep wv from being one of the most popular
classes of methods.
Simmons, though using MMPO, doesn't have Kevin's MMPO bad-example:
C doesn't win in any Approval-like method. They give an A & B tie. A & B
pairbeat C, and would therefore win the runoff.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my forwarding
an email with his private earlier input included. It was too late when I
realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest
potential problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the two
base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote
at the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can externalize
the paradoxes of voting. To a certain extent Approval avoids bad
properties by externalizing them. The cost is the "burden" of the voter
deciding whom to approve. As Ron LeGrand has so amply demonstrated, any
time you try to automate approval strategy in a semi-optimal way, you end
up with a non-monotone method. By the same token IRV can be thought of as
a rudimentary DSV approach to plurality voting, so it should be no surprise
that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <
email9648742@gmail.com> wrote:
If course the balloting for choosing between the 2 finalists need only
be rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would be
better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison to
the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in addition
to the MMPO count.
One argument against that variation is that a voter's inferred approvals
are likely to be more optimal for hir than the Score ratings on which
they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The first
set of ballots is used to narrow down to two alternatives. It is expected
that these ballots will be voted with all possible manipulative strategy
... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives
served up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from
blank (=0) to 10, there would be enough resolution for all practical
purposes. Approval voters could simply specify their approvals with 10 and
leave the other candidates' scores blank.
There should be no consistency requirement between the two ballots.
They should be put in separate boxes and counted separately. Only that
policy can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit
Approval, respectively, applied to the first set of ballots. People's eyes
would be opened when they saw how often the Approval Winner was sincerely
preferred over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would be
B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would be
A, the CWs. The chicken defection was to no avail. Note that even though
this violates Plurality on the first set of ballots, it does not on the
sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt
to win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that are
immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only
top
and bottom votes are used, in particular when Condorcet methods allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval style
ballots.
Everything else (besides approval strategy) that we do seems to be an
effort to lift the strategical burden from the voter. We would like
to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should do
so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most
voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only
votes
Approval style if he can coordinate with enough other voters to pass
the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties (like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.
This is just a brief partial reply, addressing one topic.
Approval strategy is more important & interesting than most people think,
including most who discuss voting system.
...partly because, as I said, improvements in Approval are largely, if not
entirely, illusory.
So I'm interested in discussion of Approval strategy, & different views of
it.
Let me make a few comments on the example:
-
None of those voters should approve or give Score points to their last
choice (D). -
If they all vote as I suggest, and approve (only) their top-set, then of
course it's inevitable that the winner will be the candidate regarded as
top-set by the most voters. A social optimization achieved by people voting
purely strategically.
Each voter is voting to maximize hir Pt, Probability of electing from hir
top-set.
B wins then.
- Based on the sincere preferences, there's no CWs, and so CWs-protective
strategy doesn't apply.
Even if there were one, approving down to it, if it's in your bottom-set,
would be suboptimal, and un-tempting.
If the CWs is in your top-set, then should you refuse to Approval anyone
you like less, &, in particular, should you plump if that CWs is your
favorite?
No. As an individual strategy, it's best to approve your entire top-set, to
maximize Pt.
...even though you might be tempted to choose among your top-set.
But, as a group strategy, that might not be so. Say you aren't
majority-favored (MF), and maybe aren't in a mutual-majority (MM) at all.
Then (I'm assuming a 1D political spectrum) the CWs isn't your favorite,
and hir voters prefer someone you like less than hir to those you like more
than hir.
Say that the CWs is at the far edge of your top-set.
You'd like hir voters to plump, just as you'd like other voters on your
side of hir to not approve past hir.
But then you're asking them to vote suboptimally, if your request
contradicts my top-set voting advice.
But maybe it would be best, for the group (the voters on your side of the
CWs) as a whole, to have such an agreement.
Besides, though individually suboptimal, if the CWs's voters plump, they
get something for it, because they're helping their favorite against
their other top-set candidates.
Suboptimal, but not without some potential reward.
Part 2 will follow.
Michael Ossipoff
On Oct 20, 2016 12:52 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Very kind of you to suggest "Simmons" for this method, and I certainly
don't mind associating my name with it, although every idea in it owes much
to input from you all, especially Chris Benham, Michael Ossipoff, Kevin
Venzke, Kristofer M, Jameson Q, Andy Jennings, Jobst Heitzig, Joe
Weinstein, Craig Layton,Warren Smith, Toby Pereira, Rob LeGrand, Rob
Lanphier, Richard Moore, Bart Ingles, Rick Denman. Steven J Brams, Steve
Eppley, Francis Edward Su, Sylvia Owl, Adam Tarr, Alex Small, Stephane
Rouillon, Craig Carey, Dave Ketchum, Douglas Greene, Blake Cretney, James
Gilmour, Jan Kok, Josh Narins, Steve Barney, Joseph Malkevitch, Olli Salmi,
Gervase Lam, Elisabeth Varin, Mike Rouse, Donald E Davison, Markus Schulze,
Martin Harper, DEMOREP1, Buddha Buck, David Catchpole, Anthony Simmons, James
Green-Armytage, Kathy Dopp, Juho Laatu, and too many more to mention.
If it turns out to have a serious Achilles heel, I will disavow the whole
thing!
When Approval doesn't elect the CWs, there are several possible excuses,
among them ...
(1) lack of information
(2) too much disinformation
(3) poor approval strategy by the CW supporters
(4) sincere reflection of the intensity of support
To elaborate on (4), if the preference profile is
40 A=B>D(90%)
35 B=C>D(90%)
25 A=C>D(90%)
then D is the sincere Range winner, as well as the Sincere Approval
winner, but is the Condorcet Loser.
I have constructed an example that yields this profile based on three
neighborhoods whose centers form an equilateral triangle, and four proposed
sites for a deep well (into a pure aquifer far below the contaminated
surface water)
Site D is the center of the triangle. The other three sites (A, B, and C)
are exterior to the triangle on the perpendicular bisectors of the segments
connecting the neighborhood centers, but not quite as far from the
midpoints of those segments as the center of the triangle.
As for "sincere approval, " I have described it elsewhere. Basically, for
a score ballot divide the total score of the candidates on that ballot by
the max possible score. Take the integer part and approve that many
candidates. The fractional part left over determines the probability of
approving the next candidate in line. A spin of a spinner can make that
decision.
Or in the above case, community spirit can make the difference..
In this case Sincere Approval and Range give the same expected results:
D(90), A(65), B(75), and C(60)
In conclusion, I don't think we need to be embarrassed if Simmons doesn't
choose the CWs revealed by the second (sincere) set of ballots, especially
if the ballots in the second set are merely ranked preference ballots,
which are perfectly adequate for their purpose.
Thanks,
Forest
On Wed, Oct 19, 2016 at 2:24 PM, Michael Ossipoff email9648742@gmail.com
wrote:
Yes, saying that everyone ranked is approved would unnecessarily inhibit
people's MMPO rankings, as would a Score-count.
So an approval-cutoff inferred at the candidates rating-midrange would be
better. ...in the ratings from whose order the MMPO rankings are Inferred.
...or an explicitly-voted approval-cutoff in a ranked MMPO ballot. If
course it comes to the same thing, just different ballot-implementation.
If I'd introduced this best-appearing method, I'd want it named after me.
Beatpath is named after Markus. So: Simmons' method, in its various
variations.
...which, anyway, is lot less cumbersome than something like
MMPO/Approval-like Fnalist-Choice.
That is relevant because, when discussing something, it helps to have a
name by which to refer to it.
It avoids chicken dilemma, because, even if the A voters give an approval
to B, and B wins the Approval count, A (the MMPO winner) pairwise-beats B,
and so A wins & the defection fails.
Truncation of the CWs doesn't take away hir win in MMPO. Even if the
truncators' candidate wins the approval count, the CWs pairwise-beats hir,
& wins the runoff.
Burial of the CWs?:
Here, MMPO & wv need the CWs's voters to plump, or at least not rank the
buriers' candidate over the candidate insincerely ranked over hir.
So, too, Approval, Score & Bucklin need that plumping. It seems a
universal requirement.
So Simmons doesn't escape that requirement.
But, when done, that defensive plumping protects the CWs's win, in both
finalist-choosing counts.
...And, if the burial is deterred, as it often or usually will be in
MMPO, but the plumping isn't actually done, then the CWs still wins in
MMPO.
Even if the truncators' candidates wins in the Approval-like method, the
CWs pairbeats hir, & wins the runoff.
So Simmons has wv strategy.
But that means it also has the possibility of the perpetual burial
fiasco, which goes with it.
But that possibility doesn't keep wv from being one of the most popular
classes of methods.
Simmons, though using MMPO, doesn't have Kevin's MMPO bad-example:
C doesn't win in any Approval-like method. They give an A & B tie. A & B
pairbeat C, and would therefore win the runoff.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my
forwarding an email with his private earlier input included. It was too
late when I realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest
potential problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the
two base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote
at the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can
externalize the paradoxes of voting. To a certain extent Approval avoids
bad properties by externalizing them. The cost is the "burden" of the
voter deciding whom to approve. As Ron LeGrand has so amply demonstrated,
any time you try to automate approval strategy in a semi-optimal way, you
end up with a non-monotone method. By the same token IRV can be thought of
as a rudimentary DSV approach to plurality voting, so it should be no
surprise that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <
email9648742@gmail.com> wrote:
If course the balloting for choosing between the 2 finalists need only
be rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would
be better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison
to the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in
addition to the MMPO count.
One argument against that variation is that a voter's inferred
approvals are likely to be more optimal for hir than the Score ratings on
which they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The
first set of ballots is used to narrow down to two alternatives. It is
expected that these ballots will be voted with all possible manipulative
strategy ... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives
served up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from
blank (=0) to 10, there would be enough resolution for all practical
purposes. Approval voters could simply specify their approvals with 10 and
leave the other candidates' scores blank.
There should be no consistency requirement between the two ballots.
They should be put in separate boxes and counted separately. Only that
policy can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit
Approval, respectively, applied to the first set of ballots. People's eyes
would be opened when they saw how often the Approval Winner was sincerely
preferred over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would
be B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would
be A, the CWs. The chicken defection was to no avail. Note that even
though this violates Plurality on the first set of ballots, it does not on
the sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt
to win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that
are immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only
top
and bottom votes are used, in particular when Condorcet methods
allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval
style
ballots.
Everything else (besides approval strategy) that we do seems to be
an
effort to lift the strategical burden from the voter. We would
like to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should
do so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent
that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most
voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only
votes
Approval style if he can coordinate with enough other voters to pass
the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties
(like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.
Typo:
I meant to say:
Improvements over Approval are largely, if not entirely, illusory.
Michael Ossipoff
On Oct 20, 2016 12:52 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Very kind of you to suggest "Simmons" for this method, and I certainly
don't mind associating my name with it, although every idea in it owes much
to input from you all, especially Chris Benham, Michael Ossipoff, Kevin
Venzke, Kristofer M, Jameson Q, Andy Jennings, Jobst Heitzig, Joe
Weinstein, Craig Layton,Warren Smith, Toby Pereira, Rob LeGrand, Rob
Lanphier, Richard Moore, Bart Ingles, Rick Denman. Steven J Brams, Steve
Eppley, Francis Edward Su, Sylvia Owl, Adam Tarr, Alex Small, Stephane
Rouillon, Craig Carey, Dave Ketchum, Douglas Greene, Blake Cretney, James
Gilmour, Jan Kok, Josh Narins, Steve Barney, Joseph Malkevitch, Olli Salmi,
Gervase Lam, Elisabeth Varin, Mike Rouse, Donald E Davison, Markus Schulze,
Martin Harper, DEMOREP1, Buddha Buck, David Catchpole, Anthony Simmons, James
Green-Armytage, Kathy Dopp, Juho Laatu, and too many more to mention.
If it turns out to have a serious Achilles heel, I will disavow the whole
thing!
When Approval doesn't elect the CWs, there are several possible excuses,
among them ...
(1) lack of information
(2) too much disinformation
(3) poor approval strategy by the CW supporters
(4) sincere reflection of the intensity of support
To elaborate on (4), if the preference profile is
40 A=B>D(90%)
35 B=C>D(90%)
25 A=C>D(90%)
then D is the sincere Range winner, as well as the Sincere Approval
winner, but is the Condorcet Loser.
I have constructed an example that yields this profile based on three
neighborhoods whose centers form an equilateral triangle, and four proposed
sites for a deep well (into a pure aquifer far below the contaminated
surface water)
Site D is the center of the triangle. The other three sites (A, B, and C)
are exterior to the triangle on the perpendicular bisectors of the segments
connecting the neighborhood centers, but not quite as far from the
midpoints of those segments as the center of the triangle.
As for "sincere approval, " I have described it elsewhere. Basically, for
a score ballot divide the total score of the candidates on that ballot by
the max possible score. Take the integer part and approve that many
candidates. The fractional part left over determines the probability of
approving the next candidate in line. A spin of a spinner can make that
decision.
Or in the above case, community spirit can make the difference..
In this case Sincere Approval and Range give the same expected results:
D(90), A(65), B(75), and C(60)
In conclusion, I don't think we need to be embarrassed if Simmons doesn't
choose the CWs revealed by the second (sincere) set of ballots, especially
if the ballots in the second set are merely ranked preference ballots,
which are perfectly adequate for their purpose.
Thanks,
Forest
On Wed, Oct 19, 2016 at 2:24 PM, Michael Ossipoff email9648742@gmail.com
wrote:
Yes, saying that everyone ranked is approved would unnecessarily inhibit
people's MMPO rankings, as would a Score-count.
So an approval-cutoff inferred at the candidates rating-midrange would be
better. ...in the ratings from whose order the MMPO rankings are Inferred.
...or an explicitly-voted approval-cutoff in a ranked MMPO ballot. If
course it comes to the same thing, just different ballot-implementation.
If I'd introduced this best-appearing method, I'd want it named after me.
Beatpath is named after Markus. So: Simmons' method, in its various
variations.
...which, anyway, is lot less cumbersome than something like
MMPO/Approval-like Fnalist-Choice.
That is relevant because, when discussing something, it helps to have a
name by which to refer to it.
It avoids chicken dilemma, because, even if the A voters give an approval
to B, and B wins the Approval count, A (the MMPO winner) pairwise-beats B,
and so A wins & the defection fails.
Truncation of the CWs doesn't take away hir win in MMPO. Even if the
truncators' candidate wins the approval count, the CWs pairwise-beats hir,
& wins the runoff.
Burial of the CWs?:
Here, MMPO & wv need the CWs's voters to plump, or at least not rank the
buriers' candidate over the candidate insincerely ranked over hir.
So, too, Approval, Score & Bucklin need that plumping. It seems a
universal requirement.
So Simmons doesn't escape that requirement.
But, when done, that defensive plumping protects the CWs's win, in both
finalist-choosing counts.
...And, if the burial is deterred, as it often or usually will be in
MMPO, but the plumping isn't actually done, then the CWs still wins in
MMPO.
Even if the truncators' candidates wins in the Approval-like method, the
CWs pairbeats hir, & wins the runoff.
So Simmons has wv strategy.
But that means it also has the possibility of the perpetual burial
fiasco, which goes with it.
But that possibility doesn't keep wv from being one of the most popular
classes of methods.
Simmons, though using MMPO, doesn't have Kevin's MMPO bad-example:
C doesn't win in any Approval-like method. They give an A & B tie. A & B
pairbeat C, and would therefore win the runoff.
Michael Ossipoff
On Oct 18, 2016 1:42 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
I appreciate all of the great insights from Kristofer, Chris Benham, and
Michael Ossipoff.
Especially thanks to Kristofer for being a good sport about my
forwarding an email with his private earlier input included. It was too
late when I realized I hadn't deleted that part.
Intuitively, I think Chris is right that Pushover is the biggest
potential problem. But I don't see an obvious example.
Michael is right that we need to consider other possibilities for the
two base methods for picking the finalists.
I like MMPO or Smith//MMPO as one of them since MMPO is one method that
doesn't just reduce to Approval when all candidates are ranked or rated at
the extremes. I think that the other method should be one that does reduce
to Approval at the extremes, like River, MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a Bucklin variant like MJ, Andy
Jennings's Chiastic Approval, or Jameson's MAS.
Like Michael I think that Range itself gives too much incentive to vote
at the extremes on the strategic ballots. Better to use Approval or an
approval variant so that the strategic ratings are not unduly compressed
for the other base method.
I like Kristofer's insights about the subtle differences between the
proposed "manual" version in contradistinction to a DSV version that
automates strategy for the two methods based on the first set of (perhaps
somewhat pre-strategized) ratings.
In particular he pointed out how certain procedural rules can
externalize the paradoxes of voting. To a certain extent Approval avoids
bad properties by externalizing them. The cost is the "burden" of the
voter deciding whom to approve. As Ron LeGrand has so amply demonstrated,
any time you try to automate approval strategy in a semi-optimal way, you
end up with a non-monotone method. By the same token IRV can be thought of
as a rudimentary DSV approach to plurality voting, so it should be no
surprise that IRV/STV is non-monotone.
A better example, closer to the Kristofer's, idea is Asset Voting. It
externalizes everything, which makes it impossible to contradict any nice
ballot based property. Because of this there is an extreme resulting
strategic burden, but in this case that burden is placed squarely onto the
shoulders of the candidates, not the voters. Presumably the candidates are
up to that kind of burden since they are, after all, politicians (in our
contemplated public applications).
But this brings up another intriguing idea. Let one of the two base
methods be Asset Voting, so that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.
Thanks Again,
Forest
On Tue, Oct 18, 2016 at 12:32 PM, Michael Ossipoff <
email9648742@gmail.com> wrote:
If course the balloting for choosing between the 2 finalists need only
be rankings, to show preferences between the 2 finalists, whoever they turn
out to be.
Some variations occurred to me. I'm not saying that any of them would
be better. I just wanted to mention them, without any implication that they
haven't already occurred to everyone.
Both of the following possibilities have disadvantages, in comparison
to the initial proposal:
- What if, for the initial 2 counts, it were a Score-count, in
addition to the MMPO count.
One argument against that variation is that a voter's inferred
approvals are likely to be more optimal for hir than the Score ratings on
which they're based.
- For the 2 initial counts, what if the MMPO count used a separate
ranking, & the Approval count used a separate set of Approval-marks?
Would that make it easier for Chris's pushover strategist?
What other positive & negative results?
One possible disadvantage that occurs to me is that overcompromising
voters might approve lower than than necessary, if the approval were
explicitly voted. ...in comparison to their ratings-which tend to soften
voting errors.
So far, it appears that the initial proposal is probably the best one.
Michael Ossipoff
On Oct 17, 2016 1:49 PM, "Forest Simmons" fsimmons@pcc.edu wrote:
Kristofer,
Perhaps the way out is to invite two ballots from each voter. The
first set of ballots is used to narrow down to two alternatives. It is
expected that these ballots will be voted with all possible manipulative
strategy ... chicken defection, pushover, burial, etc.
The second set is used only to decide between the two alternatives
served up by the first set.
A voter who doesn't like strategic burden need not contribute to the
first set, or could submit the same ballot to both sets.
If both ballots were Olympic Score style, with scores ranging from
blank (=0) to 10, there would be enough resolution for all practical
purposes. Approval voters could simply specify their approvals with 10 and
leave the other candidates' scores blank.
There should be no consistency requirement between the two ballots.
They should be put in separate boxes and counted separately. Only that
policy can guarantee the sincerity of the ballots in the second set.
In this regard it is important to realize that optimal perfect
information approval strategy may require you to approve out of order, i.e.
approve X and not Y even if you sincerely rate Y higher than X. [We're
talking about optimal in the sense of maximizing your expectation, meaning
the expectation of your sincere ratings ballot, (your contribution to the
second set).]
Nobody expects sincerity on the first set of ballots. If some of them
are sincere, no harm done, as long as the methods for choosing the two
finalists are reasonable.
On the other hand, no rational voter would vote insincerely on hir
contribution to the second set. The social scientist has a near perfect
window into the sincere preferences of the voters.
Suppose the respective finalists are chosen by IRV and Implicit
Approval, respectively, applied to the first set of ballots. People's eyes
would be opened when they saw how often the Approval Winner was sincerely
preferred over the IRV winner.
Currently my first choice of methods for choosing the respective
finalists would be MMPO for one of them and Approval for the other, with
the approval cutoff at midrange (so scores of six through ten represent
approval).
Consider the strategical ballot set profile conforming to
40 C
32 A>B
28 B
The MMPO finalist would be A, and the likely Approval finalist would
be B, unless too many B ratings were below midrange.
If the sincere ballots were
40 C
32 A>B
28 B>A
then the runoff winner determined by the second set of ballots would
be A, the CWs. The chicken defection was to no avail. Note that even
though this violates Plurality on the first set of ballots, it does not on
the sincere set.
On the other hand, if the sincere set conformed to
40 C>B
32 A>B
28 B>C
then the runoff winner would be B, the CWs, and the C faction attempt
to win by truncation of B would have no effect. A burial of B by the C
faction would be no more rewarding than their truncation of B.
So this idea seems to take care of the tension between methods that
are immune to burial and methods that are immune to chicken defection.
Furthermore, the plurality problem of MMPO evaporates. Even if all of
the voters vote approval style in either or both sets of ballots, the
Plurality problem will automatically evaporate; on approval style ballots
the Approval winner pairwise beats all other candidates, including the MMPO
candidate (if different from the approval winner).
What do you think?
Forest
On Sun, Oct 16, 2016 at 1:30 AM, Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 10/15/2016 11:56 PM, Forest Simmons wrote:
Thanks, Kristofer; it seems to be a folk theorem waiting for
formalization.
That reminds me that someone once pointed out that almost all of the
methods favored by EM list enthusiasts reduce to Approval when only
top
and bottom votes are used, in particular when Condorcet methods
allow
equal top and multiple truncation votes they fall into this category
because the Approval Winner is the pairwise winner for approval
style
ballots.
Everything else (besides approval strategy) that we do seems to be
an
effort to lift the strategical burden from the voter. We would
like to
remove that burden in all cases, but at least in the zero info case.
Yet that simple goal is somewhat elusive as well.
Suppose we have a proof for such a theorem. Then you could have a
gradient argument going like this:
- If you're never harmed by ranking Approval style, then you should
do so. - But figuring out the correct threshold to use is tough (strategic
burden) - So you may err, which leads to a problem. And even if you don't, if
the voters feel they have to burden their minds, that's a bad thing.
Here, traditional game theory would probably pick some kind of mixed
strategy, where you "exaggerate" (Approval-ize) only to the extent
that
you benefit even when taking your errors into account. But such an
equilibrium is unrealistic (we'd have to find out why, but probably
because it would in the worst case require everybody to know about
everybody else's level of bounded rationality).
And if the erring causes sufficiently bad results, we're left with two
possibilities:
-
Either suppose that the method is sufficiently robust that most
voters
won't use Approval strategy (e.g. the pro-MJ argument that Approval
strategy only is a benefit if enough people use it, so most people
won't, so we'll have a correlated equilibrium of sorts) -
That any admissible method must have a "bump in the road" on the way
from a honest vote to an Approval vote, where moving closer to
Approval-style harms the voter. Then a game-theoretical voter only
votes
Approval style if he can coordinate with enough other voters to pass
the
bump, which again is unrealistic.
But solution #2 will probably destroy quite a few nice properties
(like
monotonicity + FBC; if the proof is by contradiction, then we'd know
some property combinations we'd have to violate). So we can't have it
all.