Smith, MM, & Condorcet (fwd)

[Mike Ossipoff]

Mike Ossipoff writes:
> From mail.eskimo.com!eskimo.com!election-methods-list Mon Apr 15 05:44:44 1996
> Date: Mon, 15 Apr 1996 05:43:11 -0700 (PDT)
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> From: Mike Ossipoff <dfb at bbs.cruzio.com>
> To: Multiple recipients of list <election-methods-list at eskimo.com>
> Subject: Smith, MM, & Condorcet
> X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas
> 
> 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.
> Cosmetic.
> 
> 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
> Smith.
> 
> ***
> 
> 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.
> 
> ***
> 
> Mike
> 
> 
> 
> -- 
> .-
> 


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