The first case is pretty uncontroversial. What makes the second case interesting is that there's this psychological impact to it.
One good idea to explore is if each individual voter *knows* how the rest of the population voted. If each voter only knew that the majority preferred C to B and A, then the population would be pretty satisfied with C being the winner.
But if they know the full results as stated below; that C had almost no first-place votes, it's only then that the results become controversial - even though that fact is irrelevant to Condorcet scoring. The only reason the result is controversial to the population is because the population knows how everyone else voted.
I'm not a big math-head and don't know much about Nash, but this does remind me a bit of how Nash was explained in that movie. That it's not so much about what is good for the individual alone or the group alone, as it is about what's good for the combination. Similarly, the social comfort with a result isn't just feeling like one's individual vote is counted - it's about feeling comfortable that everyone's vote is counted. The reason that the second example doesn't feel good to many is not because someone feels like their own vote wasn't counted; it's because it's easy to feel that the population got collectively screwed.
I know Condorcet pretty well by now, so in the second example I very much would accept C as the winner. But it's still clearly an example where Condorcet doesn't shine, because what the population is really saying is just that they overwhelmingly want C to come in second, and can't really decide anything else decisively.
by the way -
IRV winner = B; CW wiener = C
freudian slip? :-)
On May 15, 2004, at 3:45 PM, James Gilmour wrote:
I wonder. Consider: 35 A<C<B 33 B<C<A 32 C<B<A
IRV winner = B; CW wiener = C
I suspect most electors would be happy to accept C as the "winner" of this election.
Now consider:
49 A<C<B
48 B<C<A
3 C<B<A
IRV winner = B; CW winner = C.
I doubt very much whether most electors would accept C as the "winner" if this were an election for
Sate Governor, much less for a directly elected President of the USA. If anyone has evidence to the
contrary I'd like very much to see it.
James Gilmour
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