[EM] MaxMinPA

[Michael Ossipoff]

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> 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> 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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