[EM] MaxMinPA
C.Benham
cbenham at adam.com.au
Tue Oct 18 20:22:58 PDT 2016
On 10/19/2016 5:17 AM, Michael Ossipoff wrote:
> Specifically, how would that pushover strategy work? Make a sure-loser
> win one of the finalist-choosing counts, while making your candidate
> win the other?
>
> Can you give an example?
>
Yes, and I'll think about it.
> Suppose the respective finalists are chosen by IRV and Implicit
> Approval, respectively, applied to the first set of ballots.
Very easy for this version. If you are happy to see the likely IRV
winner X win, then simply vote X top and then only rank candidates that you
think X can pairwise beat (taking advantage of IRV's compliance with
Later-no-Harm).
If things go well for you then if X doesn't win both counts then X will
be the IRV winner and one of the "turkeys" you also approved will be the
Implicit Approval winner and lose in the run-off to X.
(And of course if X doesn't make the final you have the happy fall-back
of voting sincerely in the run-off).
Chris Benham
> Specifically, how would that pushover strategy work? Make a sure-loser
> win one of the finalist-choosing counts, while making your candidate
> win the other?
>
> Can you give an example?
>
> Surely, strategically putting the right winner in both initial
> counts--especially if both counts operate on the same set of
> ratings--sounds like a daunting task, doesn't it?
>
> Michael Ossipoff
>
> On Oct 17, 2016 8:36 PM, "C.Benham" <cbenham at adam.com.au
> <mailto:cbenham at adam.com.au>> wrote:
>
> This "each voter has two ballots" idea certainly (strategically)
> allows the voter to be completely sincere on one of them,
> but the cost is that the overall method becomes a festival of
> fairly easy and obvious Push-over strategising.
>
> Of course one way to monitor this would be to look at the
> (strategically and so presumably) sincere ballots and discover
> who would have won according to various methods on those ballots.
>
> (But if that was done openly it might introduce some incentives
> based on fear of embarrassment and/or fear that the
> method will be abolished.)
>
> Chris Benham
>
>
> On 10/18/2016 11:13 AM, Michael Ossipoff 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 at pcc.edu
>> <mailto:fsimmons at 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 at t-online.de <mailto:km_elmet at 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.
>>
>>
>>
>>
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