[EM] SODA criteria
Kevin Venzke
stepjak at yahoo.fr
Wed Feb 1 14:59:28 PST 2012
Hi Jameson,
De : Jameson Quinn <jameson.quinn at gmail.com>
À : Kevin Venzke <stepjak at yahoo.fr>
Cc : em <election-methods at electorama.com>
Envoyé le : Mercredi 1 février 2012 11h12
Objet : Re: [EM] SODA criteria
2012/2/1 Kevin Venzke <stepjak at yahoo.fr>
>>
>>Hi Jameson,
>>>
>>>I expect that unpredictability (whatever there may be) of candidates' decisions can only hurt criteria compliance.
>>>At least with criteria that are generally defined on votes, because with such criteria you usually have to assume
>>>the worst about any other influences incorporated into the method.
>>
>>
>>This is true. For most of the criteria, I was implicitly talking about a version of SODA where all candidates use optimum strategy according to their predeclared preferences. This is well-defined and unique, but is not necessarily polytime-calculable. Still, even without being able to calculate results, you can prove criteria compliances for this version by contradiction.
>>
>>
>>For a polytime-calculable version which satisfies most of the same criteria, assume that each candidate, when it is their turn to assign delegated votes, looks at the two "distinct frontrunners"; that is:
>>Candidate X, their most-preferred member of the current Smith set
>>and candidate Y, the candidate, of those whom they prefer differently from X, who does best pairwise (again, using current assignments and unassigned preferences) against X
>>They approve as many candidates as possible without approving both X and Y.
>>
>>
>>This version does not satisfy participation (though again, it's damn close) or IIA, and I'm not 100% sure about its cloneproofness (though I think it is). Otherwise, it satisfies the criteria I said.
>>
>>>So I wonder, can you suggest a deterministic version of SODA, where the "negotiations" of SODA are instead
>>>calculated directly from the pre-announced preferences of the candidates? And if so, does it satisfy the same
>>>criteria in your view?
>>>
>>>I can say I would be skeptical of how a criterion is being applied, or how clearly it is being defined, if the
>>>satisfaction of it *depends* on the fact that candidates have post-voting decisions to make.
>>
>>
>>Are you still suspicious of participation and [delegated] IIA, given that satisfying them depends on assuming optimal strategy?
Hmm, I think so, just because "optimal strategy" is hard to define in general. Do you think that it will be possible to produce
convincing proofs when somebody asks for one? Pretty daunting task I would think.
I find myself trying to suggest that it may never be necessary to delegate any power to the candidates. That would make it
easier to analyze. But in that case the method is basically Approval and doesn't even satisfy Majority Favorite. Right? In
your criteria list you had "Majority" but for that you must actually be assuming the opposite of what I am trying, namely that
*everyone* is delegating, is that right?
Kevin
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