[EM] "Compliant SODA?": seeking a SODA version which may meet more criteria

[Jameson Quinn]

In exploring SODA's criteria compliance, I've realized that 4 candidates is
a bit of a magic number for SODA. For many criteria, the non-compliant
scenarios for SODA require at least 5 candidates: one "threat candidate"
who will win unless three of the other four can pool their votes; 2
"delegator candidates" for whom the delegation order matters; and 2 "target
candidates" who can win if they get the votes from both delegator
candidates. The delegators both prefer either target over the threat, but
each delegator prefers the two targets in a different order.

Of course, in most real-world elections I've ever heard of, 4 candidates
are plenty. So is there a way to fix SODA to make those pesky 5-candidate
scenarios go away? Analogously, Condorcet's paradox arises for 3 or more
candidates, but you can make 3 candidates paradox-free if you require a 2/3
supermajority, and continue to etcetera with an arbitrarily high
supermajority.

One possibility would be for predeclared candidate preferences to be a
single approval ballot, rather than a preference ordering. That way, in the
scenario described above the delegator candidates could not disagree on the
order of preference of the target candidates. This would actually simplify
SODA rather than complicating it.

I've explored some other ideas, and the above is the only one I've found so
far which works, but from my exploration it seems possible that there are
others.

I'd like to further explore this "compliant SODA", and hear other
suggestions of how to sweep the annoying 5-candidate scenarios under the
rug. However, this is just exploration for now; as a serious proposal, I'm
leaving SODA as it is.

Jameson
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