[EM] Mixed Condorcet-Plurality

[Tom Ruen]

I must be bored since I keep thinking of probably dumb ideas that I like for
a day or two.

Here's one, actually pretty much my original intuitive approach to Condorcet
pair elections:

With ranked ballots:
1. Tally first rank votes in full election.
2. If a majority candidate exist, a winner is found. (Full majority)
3. Otherwise compute winners in all pair elections:
4. if one candidate beats all others pairwise, a winner is found. (Pair
majority)
5. Otherwise find top set of mutually defeatable candidates.
6. Tally first rank votes among this set, and take candidate with the most
votes. (Plurality)

I offer this method because each step can be defended independently and
cover all the cases in a systematic and clear way.

Without cycles, Condorcet most represents the will of the majority, assuming
people have ranked thoughtfully. (That's a tough assumption perhaps, but a
fair one - afterall, we can expect but can't force people to be thoughtful.)

When cycles exist, I believe it is possible to find a "best" winner by some
magical divinations, but it's not at all clear to me that there will be
agreement in all cases on which magic we should use. I'm tempted to avoid
these cases and compromise to a process that is merely acceptable, even if
flawed.

That's why I would consider a plurality winner as the "fair" choice among
the top set of mutually defeatable candidates. Among that set no elimination
(candidates or defeats) is clearly fair and so it makes some sense to
retreat to plurality as the best choice. Well, this is perhaps the only good
use for plurality that I know!

I suppose this will fail certain properties like Monotonicity under special
cases, but it is a system I would be willing to defend.

Tom Ruen