Smith, MM, & Condorcet
dfb at bbs.cruzio.com
Mon Apr 15 05:43:11 PDT 1996
I included Smith & MM together here, because there's really nothing left
to say about Smith. Everything I said about CL is true of Smith, the only
difference being that violation of Smith is less dramatic (& therefore,
of course, less easy to stir up the public about).
I should state the criterion here though, as a formality. Smith Criterion:
"If every alternative in set S beats everything outside S, then the winner
should be chosen from S."
Sure, there's a case for doing that, but, again, it just isn't important.
Sure, the only reason why there's a circular tie is because every member
of the Smith set is beaten or tied, _by another member of the Smith set_.
But they're still beaten (no pairwise ties in a public election), aren't
they, and there's still a case for picking the least beaten alternative,
out of all the alternatives. The Smith Criterion has a case, but not
a compelling one, and anyway, it isn't important compared to the widely-
held standards met by Condorcet's method, the standards that originally
led us to want better single-winner methods.
As I said, everything I said in the previous letter, about the
CL Criterion, applies to the Smith Criterion too, though we're of
course talking about a less dramatic violation when we violate
The Mutual Majority Criterion:
"If a group of voters consisting of a majority of all the voters
prefer the alternative(s) in set S to the alternatives outside S,
then the winner should come from S."
Not much to add here, since I've already discussed why I don't
believe that MM qualifies for the "Generalized Majority Criterion"
name that has been given to it. It talks only about a specific, special,
particular kind of majority, not a general one.
Those voters of that majority, each of their favorites must be in S.
That means that they all prefer eachother's favorites, and perhaps some
other alternatives, to all the others. That's why I call it the
Mutual Majority Criterion, instead of the "Generalized Majority Criterion".
I've, in a previous message, entitled "Generalized Majority Criterion",
defined another criterion more general in the situations it covers, and
therefore more deserving of that name.
For example, in the Dole, Clinton, Nader example that I've been using,
MM says nothing about who should win. And if the Clinton voters all ranked
Dole 2nd, then MM would say to pick Clinton or Dole, but would remain
silent about which one to pick. It ignores the majority preferring
Clinton to Dole, because it isn't a mutual majority in which the Clinton
voters prefer Nader to Dole.
And, just as Smith//Condorcet meets the other academic candidate-counting
criteria, it meets MM too. And, in order for plain Condorcet to fail MM,
there's have to be a circular tie in which the set S alternatives all
beat eachother, and in which each one of them has a full majority ranking
another alternative over it. As I've said, that's reaching pretty far
to find a situation where plain Condorcet fails MM. So, when you're told
that plain Condorcet fails MM, consider what kind of a situation that
takes--a situation where everything in the election has a majority
against it, including the alternatives in S.
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