[EM] Random Ballot fails IIAC
nkklrp at hotmail.com
Sat Jan 19 15:59:57 PST 2002
Say the voting system is Random Ballot.
Say there are just 2 candidates, and all the voters vote for their
favorite. Now we add a 3rd candidate.
Say, in this big national election with 100,000,000 voters, there's
one voter who doesn't watch the news or read newspapers or magazines,
and hasn't read the materials at the polling place. He's heard
something about a new voting system, but he doesn't know that it's
a completely new voting system as opposed to Plurality with a more
reliable count procedure. Or, if he does, he doesn't know that it's
so profoundly different that Plurality strategy no longer applies.
Say that new candidate is that voter's last choice. He feels strongly
that his 2nd choice has a much better chance of beating that new last
choice, and so, being a lesser-of-2-evils voter, he now votes for
his 2nd choice instead of his favorite. His 2nd choice, one of the
2 original candidates, now gets one more vote than he'd get if the
new candidate hadn't been added. The addition of the new candidate
has increased a previously-existing candidate's probability of winning.
This is why I asked Markus if anything was stipulated about how people
vote. He indicated that there's no such assumption. For that reason,
Random Ballot fails IIAC, as Markus defined it.
Now, someone might say that RB has a rule that one must vote for one's
favorite. But is it meaningful to talk about a rule whose violations
are undetectable in principle? "Vote for your favorite" can only
be a strategy suggestion--a good one of course.
Markus can't say that it's understood that voting is sincere, or
that people vote for his favorite, because I asked him about that
and he indicated in the negative.
Here are some ways that Markus's IIAC could be made complete, by
adding, at the beginning of the wording:
"If everyone votes their favorite over every other alternative..."
"If everyone votes sincerely..."
"If everyone votes in a way that maximizes his utility expectation..."
"If everyone votes in a way that isn't dominated by any other way
As I said, I've probably never heard a complete IIAC definition,
other than my actual-votes definition, and these repaired versions
of Markus's definition.
My actual-votes definition says:
Deleting a loser from the ballots and then recounting those ballots
should never change who wins.
[end of definition]
I don't know which, if any, of those was Arrow's IIAC, but my
actual-votes definition seems the most useful for practical purposes,
since it distinguishes between methods that are actually proposed
as main methods for elections (as opposed to tiebreakers).
And yes, Random Candidate still meets Markus's IIAC, but RC
isn't a voting system.
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