Re: [EM] Smith//MMPO
Mike,
Your "MAM-like strategy" example:
30: A (sincere may be A>B)
20: B>A
25: C>B
And you are happy that WV and Smith//MMPO elects B (the supposed/maybe
"sincere CW").
But WV (including MAM) and Smith//MMPO both have a random-fill
incentive. From a recent email:
C: If the method has a random-fill incentive then it is more logical
to assume that truncators are more sincere than those
who rank more candidates.
M: True.
Therefore any assumption that B is the "sincere CW" has a very flimsy
basis. A, being positionally dominant (if these are 3-slot
ratings ballots then A is the most Top-Rated and the most Approved) and
uncovered is arguably the prettiest winner. Most likely
there is no "sincere CW" and A is the highest Social Utility candidate.
In any case under WV and Smith//MMPO the A supporters can make A the
winner by voting A>C. I don't think that "thwarting"
a bad "strategy" that is probably sincere or not very insincere at the
cost of allowing a more insincere strategy to work fine is
any achievement.
30: A>C
20: B>A
25: C>B
B>A 45-30, A>C 50-25, C>B 55-20. Max PO scores: A45 < C50 <B55.
A method that I like that does elect B in your example is Approval
Sorted Margins.
http://wiki.electorama.com/wiki/Approval_Sorted_Margins
It initially orders the candidates from most approved to least approved.
If any adjacent pair is out of order pairwise
it switches the order of the pair with the smallest difference in their
approval scores. If there is a tie for that it switches
the tied pair lowest in the order. At the end of the process it elects
the highest-ordered candidate.
The method meets Plurality and Minimal Defense and fails Weak CD. In the
second example (with 30 A>C) it narrowly elects C:
Approval scores: C55 > A50 > B45. Both C>A and A>B are pairwise out
of order and in both cases the difference in approval scores
is 5, so we switch the lower-ordered of the two pairs to give C>B>A. Now
no adjacent pair is pairwise out of order so that order is final
and C wins.
Chris Benham
I at first didn't realize that this message was sent to EM. So that's why
this reply is so late.
On Sep 27, 2016 7:21 AM, "C.Benham" cbenham@adam.com.au wrote:
Mike,
Your "MAM-like strategy" example:
30: A (sincere may be A>B)
20: B>A
25: C>B
And you are happy that WV and Smith//MMPO elects B (the supposed/maybe
"sincere CW").
(endquote)
Voters will do what it takes, to elect a candidate whom they perceive as
the CWs (sincere CW).
Making that as easy as possible has been the appeal of wv.
But WV (including MAM) and Smith//MMPO both have a random-fill
incentive. From a recent email:
C: If the method has a random-fill incentive then it is more logical to
assume that truncators are more sincere than those
who rank more candidates.
M: True.
But strategic truncation can take the win away from the CWs.
Therefore any assumption that B is the "sincere CW" has a very flimsy
basis.
(endquote)
As I said above, voters will do what it takes to elect a candidate whom
they perceive as a CWs.
Making that as easy as possible has been the appeal of wv.
The message continued:
A, being positionally dominant (if these are 3-slot
ratings ballots...
wv & MMPO are intended for unlimited rankings.
...then A is the most Top-Rated and the most Approved) and uncovered is
arguably the prettiest winner. Most likely
there is no "sincere CW" and A is the highest Social Utility candidate.
(endquote)
Natural, non-strategic, top-cycles are vanishingly rare in political polls.
At CIVS (Condorcet Internet Voting Service) I'm not aware of there ever
having been a top-cycle for top-finisher.
So. Most likely there is a CWs (sincere CW).
The message continued:
In any case under WV and Smith//MMPO the A supporters can make A the
winner by voting A>C.
(endquote)
Yes, that's why the B voters should plump if they feel that B is likely to
be a CWs.
If the CWs's voters plump, in WV or MMPO, that thwarts & penalizes burial.
The message continued:
I don't think that "thwarting"
a bad "strategy" that is probably sincere or not very insincere at the
cost of allowing a more insincere strategy to work fine is
any achievement.
(endquote)
The purpose is just to minimize the strategy needs of voters trying to
protect a perceived CWs.
I don't have a way to delete text. I reply farther down:
...as voters will do.
30: A>C
20: B>A
25: C>B
B>A 45-30, A>C 50-25, C>B 55-20. Max PO scores: A45 < C50 <B55.
A method that I like that does elect B in your example is Approval Sorted
Margins.
Interestingly, ASM seems (at 1st examination at least) to have wv-like
strategy, without wv's bottom-end burial-incentive.
If so, that means that, in a strategically-voted election, ASM retains wv's
advantages better than wv would.
Michael Ossipoff
http://wiki.electorama.com/wiki/Approval_Sorted_Margins
It initially orders the candidates from most approved to least approved.
If any adjacent pair is out of order pairwise
it switches the order of the pair with the smallest difference in their
approval scores. If there is a tie for that it switches
the tied pair lowest in the order. At the end of the process it elects
the highest-ordered candidate.
The method meets Plurality and Minimal Defense and fails Weak CD. In the
second example (with 30 A>C) it narrowly elects C:
Approval scores: C55 > A50 > B45. Both C>A and A>B are pairwise out
of order and in both cases the difference in approval scores
is 5, so we switch the lower-ordered of the two pairs to give C>B>A. Now
no adjacent pair is pairwise out of order so that order is final
and C wins.
Chris Benham
Mike,
The example we are discussing:
30: A (sincere may be A>B)
20: B>A
25: C>B
You like that Winning Votes and Smith//MMPO elects B.
On 9/29/2016 12:49 AM, Michael Ossipoff wrote:
Voters will do what it takes, to elect a candidate whom they perceive
as the CWs (sincere CW).
C: How do you know that? Won't they (at least also) try to elect
candidates they prefer to their perceived "sincere CW"?
If you are right, then presumably in our example the 3 factions of
voters all have different "perceived sincere CWs" because
they voted for different candidates.
Natural, non-strategic, top-cycles are vanishingly rare in political
polls. At CIVS (Condorcet Internet Voting Service) I'm not aware of
there ever having been a top-cycle for top-finisher.
So. Most likely there is a CWs (sincere CW).
C: That isn't rational. Presumably a ballot set like our example, with
30 A or 30 A>C is also vanishingly rare. The question isn't how rare
top-cycles in general are.
The question is how reasonable is to assume that the A truncators in
this particular example are insincere.
In essence an election method should aim to achieve just two things:
maximise probable Social Utility and minimise possible voter regret.
If fulfilling those aims
is done without electing some candidate that someone imagines is the
"sincere CW", then that isn't a problem.
In the example there is no compelling rational reason to assume that any
of the ballots are insincere. So there is no "sincere CW".
A, as an uncovered positionally dominant candidate is presumably the
highest SU candidate. (All the Condorcet methods I currently advocate
would elect A).
So say we elect A. In that case the 25 C>B voters might regret not
making their second-choice win (in any Condorcet method) by voting C=B
(or B>C or B).
But say instead Winning Votes or Smith//MMPO is used and we elect B.
In that case the 30 A voters would regret not causing their favourite to
win by
voting A>C.
And that clinches the case for any good method that elects A versus any
method that elects B with the 30 A voters truncating, and A when they
vote A>C.
Approval Sorted Margins isn't as bad because under it if the A
supporters vote A>C it results in C winning. Also it meets
mono-switch-plump and of course
(since above-bottom ranking is interpreted as approval) has some
truncation incentive.
Chris Benham
On Sep 29, 2016 11:48 AM, "C.Benham" cbenham@adam.com.au wrote:
Mike,
The example we are discussing:
30: A (sincere may be A>B)
20: B>A
25: C>B
You like that Winning Votes and Smith//MMPO elects B.
Yes.
On 9/29/2016 12:49 AM, Michael Ossipoff wrote:
Voters will do what it takes, to elect a candidate whom they perceive
as the CWs (sincere CW).
C: How do you know that?
That's typically the best they can get.
(You wrote) :
Won't they (at least also) try to elect candidates they prefer to their
perceived "sincere CW"?
(endquote)
Sure, it's a fair assumption that people who rank want to rank in sincere
order for that reason.
I won't approve the expected CWs (CWse) if s/he's bottom-set. (Maybe I'd
rank hir in MMPO). So if some others feel similarly, that's an exception to
helping the CWse. I don't know how many agree. It would complicate the
examples.
If you are right, then presumably in our example the 3 factions of voters
all have different "perceived sincere CWs" because
they voted for different candidates.
The assumption is that the A voters truncate because they want to make A
win instead of the CWse, or that it's lazy or principled truncation.
The C voters rank B over C, helping the CWse.
I think it's a good presumption that all perceive the same CWse, because
the same information is available to all.
(I'd said) :
Natural, non-strategic, top-cycles are vanishingly rare in political
polls. At CIVS (Condorcet Internet Voting Service) I'm not aware of there
ever having been a top-cycle for top-finisher.
So. Most likely there is a CWs (sincere CW).
C: That isn't rational.
How so?
(You wrote) :
Presumably a ballot set like our example, with 30 A or 30 A>C is also
vanishingly rare.
(endquote)
Yes, if it is a sincere cycle. But otherwise no.
(You wrote) :
The question isn't how rare top-cycles in general are.
The question is how reasonable is to assume that the A truncators in this
particular example are insincere.
(endquote)
The rarity of sincere top cycles is highly relevant to the matter of this
cycle's sincere-ness.
The A voters could prefer B to C, but do principled or strategic truncation.
B would then still be CWs.
(You wrote) :
In essence an election method should aim to achieve just two things:
maximise probable Social Utility and minimise possible voter regret. If
fulfilling those aims
is done without electing some candidate that someone imagines is the
"sincere CW", then that isn't a problem.
(endquote)
That's a matter of individual preference. I prefer making easy for those
wanting to protect a perceived CWs. You want to maximize SU. Neither goal
is wrong.
BTW, if distance in issue-space is measured by city-block distance, then
the CWs is the SU maximizer.
...& there's good justification for city block distance.
But SU is of doubtful importance. Greater disutilities are more important
to reduce than smaller ones. Is giving a dollar to a millionaire really as
good as giving it to a homeless person? (or giving the millionaire some
larger amount that has equal utility to him)
In the example there is no compelling rational reason to assume that any
of the ballots are insincere. So there is no "sincere CW".
1.Sincere top cycles are evidently vanishingly rare.
- It's good to minimize the strategic insincerity needed by someone who
wants to protect a perceived CWs.
(I'm not saying that other goals are wrong.)
A, as an uncovered positionally dominant candidate is presumably the
highest SU candidate.
A perfectly valid goal. But the CWs is a likely SU maximizer.
(Replying farther down)
(You wrote) :
(All the Condorcet methods I currently advocate would elect A).
So say we elect A. In that case the 25 C>B voters might regret not
making their second-choice win (in any Condorcet method) by voting C=B (or
B>C or B).
But say instead Winning Votes or Smith//MMPO is used and we elect B.
In that case the 30 A voters would regret not causing their favourite to
win by
voting A>C.
That wouldn't have worked, if the B voters defensively plumped. The A
voters would be taking a big risk.
And that clinches the case for any good method that elects A versus any
method that elects B with the 30 A voters truncating, and A when they vote
A>C.
Depends on one's goal.
Approval Sorted Margins isn't as bad because under it if the A supporters
vote A>C it results in C winning.
(endquote)
If B voters plump, wv does the same.
Also it meets mono-switch->plump and of course
(since above-bottom ranking is interpreted as approval) has some
truncation incentive.
ASM is worth checking out. A disadvantage is that principled truncation of
the CWs is more likely to defeat the CWs & elect someone whom the
truncators dislike more.
Michael Ossipoff
Chris Benham
I'd just like to add that minimizing the strategic insincerity needed by
people wanting to protect the CWs isn't the only voting standard or goal
that I value.
What I like about Approval (especially its CD version, 3-Slot ICT), and why
it's my favorite, is its natural perfect match to the two valued
top-set/bottom-set distinction.
...for directly, simply, fully supporting one's top-set-- voting to
maximize Pt (probability of electing from your top-set).
A social optimization is achieved: a winner who is in the top-set of the
most people.
Maximizing the number of people for whom the winner is in their top-set.
CWs-protection isn't unrelated to that goal.
In an MMC-complying rank method, like Bucklin or some pairwise methods, if
you're majority-favored (a majority prefer at least some of your top-set to
everyone else), then with you & the other MM members voting sincerely,
someone in your top-set will win.
The problem is when you aren't MF (majority favored).
It's no longer certain that a top-set candidate will win. But if the CWs is
in your top-set, then electing hir obviously keeps the winner in your
top-set.
If the CWs isn't in your top-set...well, the CWs is likely the best you can
get, & so your top-set then isn't very winnable.
Given that the CWs is probably the best you can get, it makes sense to
minimize the strategic insincerity needed to elect hir.
Insincerity, people voting contrary to their preferences, can't be good for
the social likedness of the result.
(Hint: Hillary)
Michael Ossipoff
On Sep 29, 2016 3:12 PM, "Michael Ossipoff" email9648742@gmail.com wrote:
On Sep 29, 2016 11:48 AM, "C.Benham" cbenham@adam.com.au wrote:
Mike,
The example we are discussing:
30: A (sincere may be A>B)
20: B>A
25: C>B
You like that Winning Votes and Smith//MMPO elects B.
Yes.
On 9/29/2016 12:49 AM, Michael Ossipoff wrote:
Voters will do what it takes, to elect a candidate whom they perceive
as the CWs (sincere CW).
C: How do you know that?
That's typically the best they can get.
(You wrote) :
Won't they (at least also) try to elect candidates they prefer to their
perceived "sincere CW"?
(endquote)
Sure, it's a fair assumption that people who rank want to rank in sincere
order for that reason.
I won't approve the expected CWs (CWse) if s/he's bottom-set. (Maybe I'd
rank hir in MMPO). So if some others feel similarly, that's an exception to
helping the CWse. I don't know how many agree. It would complicate the
examples.
If you are right, then presumably in our example the 3 factions of
voters all have different "perceived sincere CWs" because
they voted for different candidates.
The assumption is that the A voters truncate because they want to make A
win instead of the CWse, or that it's lazy or principled truncation.
The C voters rank B over C, helping the CWse.
I think it's a good presumption that all perceive the same CWse, because
the same information is available to all.
(I'd said) :
Natural, non-strategic, top-cycles are vanishingly rare in political
polls. At CIVS (Condorcet Internet Voting Service) I'm not aware of there
ever having been a top-cycle for top-finisher.
So. Most likely there is a CWs (sincere CW).
C: That isn't rational.
How so?
(You wrote) :
Presumably a ballot set like our example, with 30 A or 30 A>C is also
vanishingly rare.
(endquote)
Yes, if it is a sincere cycle. But otherwise no.
(You wrote) :
The question isn't how rare top-cycles in general are.
The question is how reasonable is to assume that the A truncators in
this particular example are insincere.
(endquote)
The rarity of sincere top cycles is highly relevant to the matter of this
cycle's sincere-ness.
The A voters could prefer B to C, but do principled or strategic
truncation.
B would then still be CWs.
(You wrote) :
In essence an election method should aim to achieve just two things:
maximise probable Social Utility and minimise possible voter regret. If
fulfilling those aims
is done without electing some candidate that someone imagines is the
"sincere CW", then that isn't a problem.
(endquote)
That's a matter of individual preference. I prefer making easy for those
wanting to protect a perceived CWs. You want to maximize SU. Neither goal
is wrong.
BTW, if distance in issue-space is measured by city-block distance, then
the CWs is the SU maximizer.
...& there's good justification for city block distance.
But SU is of doubtful importance. Greater disutilities are more important
to reduce than smaller ones. Is giving a dollar to a millionaire really as
good as giving it to a homeless person? (or giving the millionaire some
larger amount that has equal utility to him)
In the example there is no compelling rational reason to assume that
any of the ballots are insincere. So there is no "sincere CW".
1.Sincere top cycles are evidently vanishingly rare.
- It's good to minimize the strategic insincerity needed by someone who
wants to protect a perceived CWs.
(I'm not saying that other goals are wrong.)
A, as an uncovered positionally dominant candidate is presumably the
highest SU candidate.
A perfectly valid goal. But the CWs is a likely SU maximizer.
(Replying farther down)
(You wrote) :
(All the Condorcet methods I currently advocate would elect A).
So say we elect A. In that case the 25 C>B voters might regret not
making their second-choice win (in any Condorcet method) by voting C=B (or
B>C or B).
But say instead Winning Votes or Smith//MMPO is used and we elect B.
In that case the 30 A voters would regret not causing their favourite to
win by
voting A>C.
That wouldn't have worked, if the B voters defensively plumped. The A
voters would be taking a big risk.
And that clinches the case for any good method that elects A versus any
method that elects B with the 30 A voters truncating, and A when they vote
A>C.
Depends on one's goal.
Approval Sorted Margins isn't as bad because under it if the A
supporters vote A>C it results in C winning.
(endquote)
If B voters plump, wv does the same.
Also it meets mono-switch->plump and of course
(since above-bottom ranking is interpreted as approval) has some
truncation incentive.
ASM is worth checking out. A disadvantage is that principled truncation
of the CWs is more likely to defeat the CWs & elect someone whom the
truncators dislike more.
Michael Ossipoff
Chris Benham