[EM] SODA criteria

[Jameson Quinn]

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?

Jameson

>
> Kevin
>
>
>
>   *De :* Jameson Quinn <jameson.quinn at gmail.com>
> *À :* EM <election-methods at lists.electorama.com>
> *Envoyé le :* Mardi 31 janvier 2012 20h50
> *Objet :* [EM] SODA criteria
>
> SODA passes:
>
> Majority
> MMC (as voted)
> Condorcet (as voted, and in a strong Nash equilibrium as honest)
> Condorcet loser (ditto)
> Monotone
> Participation (with the fix that delegation can be any fraction)
> IIA (delegated version - that is, if a new candidate is added, the winner
> is either the same, or someone higher on the new candidate's delegation
> order.)
> Cloneproof
> Polytime (there is no guarantee that optimal delegated assignment strategy
> is polytime calculable, but it will be in any real case, and anyway,
> candidates can just choose some near-optimal strategy.)
> Resolvable
> Summable
> Allows equal rankings
> FBC
>
> So, of the criteria in the wikipedia voting systems table<http://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29>,
> the only ones it out-and-out fails are:
> Consistency (though it comes damn close)
> Later-no-harm and later-no-help (though it does satisfy LNHarm for the one
> (two????) candidate(s?) with the most voted approvals, and for other
> candidates, adding later preferences is probably strategically forced; so
> I'd say it fulfills the spirit of both of these. Similarly, it satisfies
> LNHelp for the last-to-delegate candidate, and nearly so for other
> late-delegating candidates, and the point of LNHelp is to prevent a weak
> candidate from winning through clever bottom filling, so again it satisfies
> the spirit.)
> Allows later preferences (though delegation substitutes for this
> affordance in some cases.)
>
> If we could just get some wikipedia-notable mention of SODA, we could put
> it in the table, and I think it would graphically stand out as the most
> criteria-compliant method there.
>
> I'm working on an academic article on SODA, which would not be focused on
> these criteria or even on SODA, but would quickly state the above. But if
> anyone can make an article happen in a wikipedia "reliable source", that
> would be great.
>
> Jameson
>
>
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