[EM] Weak Condorcet Winners

[Jameson Quinn]

I fully agree with those who say that a "weak" Condorcet winner is in most
cases the best winner. The concern with the weak CW problem is, at least for
me, based on two different factors:


   - 1. It may be that some of the voters who helped make that candidate a
   CW would honestly regret their vote afterwards. Take the situation:


40: A>C
45: B>C
15: C

Clearly, the 45 B voters might strategically regret their vote. If they
hadn't voted for C, there would have been an A>C>B>A cycle. Although it's
true that, under many cycle-breakers, A would have won this cycle, the B
voters might feel that it would have been worth it to "roll the dice" and
vote strategically.

But, although that strategic regret does represent a problem (that's a
strong plurality of voters who are probably dissatisfied with the system),
it is not the issue I'm talking about. I'm talking about honest regret; A
and B voters who say, "wait a minute, if I'd know C was actually going to
win this, I would have thought harder about ranking them second, and
actually now that I face the reality, I think that I would have chosen not
to rank them second." This is most pertinent for A voters. If there are even
6 A voters who decide, "You know, B wouldn't have been so bad after all",
that makes a majority of voters who believe the system gave the wrong
result.

It's true that in a world of rational agents and perfect information, you'd
never have honest regret like this. But I don't think that that means that
you can just dismiss the problem by blaming the media or anything like that.
People are not 100% rational and knowledgeable, and all other things being
equal, a voting system should try to give good results in spite of that.


   - 2. Insofar as voters and, especially, politicians are afraid of result
   1, they will reject the voting system. This fear could be irrationally
   exaggerated, and that would not mean that it wouldn't be a problem for a
   voting system.

I believe that problem 2 is actually more serious than problem 1.

How do you deal with these problems? For problem 1, the obvious first step
is to try to ensure that voters are not surprised by results. If
pre-election polls use the same voting system as the election, that would
help avoid surprises.

For problem 2, there are essentially two ways to deal with it. You can try
to respond to concerned voters, and show them that their concerns are
irrational. Good luck with that. (I mean that sincerely; I'd be happy to
help craft simple arguments that would help reduce problem 2 for any good
voting system.) Or, you can propose a system which reduces such concerns in
the first place. This is the path that IRV advocates have chosen. It's also
the path that I would favor, though I think that my chosen systems (SODA or
MJ) are far superior to IRV.

One thing which won't work is "Condorcet fundamentalism". If voters dislike
an actual result, or are afraid of a result, it doesn't help to preach to
them about how actually the result was or would be correct. Yes, we on this
list can understand that in perhaps the most important ways, a "weak CW" is
*not actually weak*. But that's a losing argument on a public stage. And
even here among "experts", others could respond with "range fundamentalism"
(the utility winner is the best, and Range is the best system for finding
that) or "MJ fundamentalism" (the highest-rated candidate is the best, and
MJ elicits the most-honest ratings). Of course, you may find that the
Condorcet criterion is more convincing than these alternates, but you're not
going to convince anyone of that by just restating the criterion.

Jameson
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