[EM] MaxMinPA

[Michael Ossipoff]

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> 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> 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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