[EM] full-ranking SODA: FBC compliant

[Jameson Quinn]

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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