On 10/15/2016 11:56 PM, Forest Simmons wrote:

formalization.

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.

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:

 I think it sounds super. The best yet, with the best properties
 of the best methods, avoiding eachother's faults & vulnerabilities.

 More later.

 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:

         waiting for formalization.

         almost all of the

         Approval when only top

         methods allow

         this category

         approval style

         seems to be an

         We would like to

         zero info case.

         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.




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