Majority Loser Criterion & Condorcet
dfb at bbs.cruzio.com
Mon Apr 15 05:44:53 PDT 1996
Again, as with the other academic candidate-counting criteria,
Smith//Condorcet meets Majority Loser, though plain Condorcet can
conceivably fail it.
Majority Loser Criterion:
"Never pick an alternative that is the last choice of a majority
of the voters."
As I said in my initial reply to Bruce's bad-example message, sent to
a few EM members, this criterion is overkill. It's undesirable to pick
an alternative with a majority against it at all, whether or not that
majority have ranked _everything_ else over it.
And if plain Condorcet picks a Majority Loser (ML), that means that
_every_ alternative in the election has a majority against it too.
In fact, it means that every alternative other than the one chosen
by plain Condorcet has a bigger majority against it that the winner
by plain Condorcet does. I bet Bruce didn't mention that in the
explanation accompanying his bad-examples.
Another thing he doesn't mention, and which those contrived bad-examples
don't show, is that Copeland can pick an alterntive with a majority
against it even if no other alternative has a majority against it.
ML is a candidate-counting criterion because it combines a majority
against an alternative with _how many_ alternatives that majority
have ranked over it (all the other alternatives).
So, in his bad-examples, in order to make the winner by plain
Condorcet a ML, Bruce had to make every alternative in the election
be beaten with a full majority against it.
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