[EM] full-ranking SODA: FBC compliant

[Jameson Quinn]

One more important criterion this system would meet (assuming honest
predeclarations and optimal candidate strategy; this optimal strategy is
unique and knowable, and although it's potentially NP-complete, that
wouldnt be a factor unless there were dozens of potential winners): the
voted Condorcet criterion for any number of candidates.

Also, like prior versions of SODA, this passes later-no-harm for the
candidate with the fewest direct votes (the one whose supporters'
second-choice votes are most important to elicit).

I think that a system which passes FBC and (arguably) Condorcet and a
weakened-but-significant form of LNH is a big deal! This LNH is enough to
ensure that "chicken dilemma" burial problems won't be significant; FBC is
enough to ensure that compromise won't be a problem; so votes will be
honest, and so the Condorcet compliance actually means something.

Note that this system is not of course Condorcet compliant over all voter
preferences, just over the ones they actually express through approval or
delegation. Full compliance would be impossible with this level of
strategic robustness. Still, if things are close to a 1D ideological
spectrum, almost all preferences will be expressible on the ballot. Even if
ideology is 2D or more, the worst case is that unexpressable preferences
are (100/((n-1)!))% rarer than approval (which in itself isn't so bad),
where n is the number of effective candidates (usually 3 or less).

Jameson

2012/5/23 Jameson Quinn <jameson.quinn at gmail.com>

> In SODA (Simple Optionally-Delegated Approval), candidates must
> pre-declare their preferences among the other candidates, and their
> post-election approvals using votes delegated to them[1] must be consistent
> with these pre-declared preferences. As defined until now, those
> pre-declared preferences were partial orderings; that is, tied preferences
> were allowed. I have recently realize that if you require full preference
> orderings, SODA's criteria compliances improve significantly. Specifically,
> I strongly suspect (though I have not yet fully proven) that it meets all
> of the following:
>
> 1. FBC
> 2. There is always some semi-honest vote which meets participation (this
> is closely related to FBC, but not quite exactly just a stronger version of
> it)
> 3. Participation for up to 4 (5?) candidates
> 4. Consistency for up to 4 candidates
> 5. Condorcet and ISDA for up to 4 candidates
> 6. Local IIA (ie, IIA for the weakest alternative) for up to 5 (or
> possibly any number of???) candidates
>
> Sadly, this system still doesn't meet plain IIA for even 3 candidates.
>
> Note of course that the "up to N candidates" mathematically, means "up to
> N serious candidates" in practical terms. Real-world elections with more
> than 4 serious candidates are quite rare; and those that do exist are
> typically non-partisan and non-ideological, and thus do not exhibit
> interesting enough inter-candidate dynamics to result in the
> tightly-constrained pathologies that are possible. So I'd bet that in
> practice, full-ranking SODA would pass all of the above criteria over 99%
> of the time.
>
> More to come on this, as I try to work through the relevant proofs.
>
> Jameson
>
> [1] I really wish I had better terminology for this, "approvals using
> votes delegated to them" is a mouthful for what should ideally be a single
> word.
>
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