(Fwd) Condorcet counter-example (fwd)
dfb at bbs.cruzio.com
Thu Apr 4 16:09:11 PST 1996
Mike Ossipoff writes:
[I've gotten this letter returned several times, so excuse the fact
that this reply is late. Also, excuse the extra header below, since I
don't have a way to delete lines or blocs of text]
> From dfb Mon Apr 1 13:54:08 1996
> Subject: Re: (Fwd) Condorcet counter-example
> To: Steve Eppley <seppley at alumni.caltech.edu>
> Date: Mon, 1 Apr 96 13:54:02 PST
> From: Mike Ossipoff <dfb at bbs.cruzio.com>
> Cc: dfb at bbs.cruzio.com
> In-Reply-To: <199603311037.CAA25404 at alumni>; from "Steve Eppley" at Mar 31, 96 2:38 am
> X-Mailer: ELM [version 2.3 PL0]
> Message-ID: <9604011354.aa23854 at bbs.cruzio.com>
> As I undestand Saari's Twins Test, he'd like the outcome to not be
> affected by adding or subtracting nonwinning alternatives from
> the election. This is Arrow's "Independence from Irrelevant Alternatives"
> criterion. No method can meet IIAC and still meet other basic &
> desirable critria.
For instance, Weighted Voting, where voters assign point scores to
the alternatives, and the alternative getting the most points wins,
may meet IIAC, which Saari referred to as the Twins Test, but it
fails the Majority Winner Criterion: Only the points systems can
fail to elect an alternative that is the favorite of a majority
of the voters, and which those voters indicate on their ballots
as their favorite (as by giving the highest point score to, or
by ranking 1st).
In addition to failing that criterion, Weighted Voting's extreme
need for defensive strategy disqualifies it from consideration.
The price that Weighted Voting pays to meet IIAC is too high.
> In a barroom brawl, someone who's got no endurance, and perhaps not
> much strength or skill either, can catch an expert boxer with an
> unexpected punch, and prevent him from winning. A loser can prevent
> an otherwise-winner from winning. Single-winner methods, like barroom
> brawls, can't be everything that the idealist would like them to be.
> It isn't reasonable to criticize Corndorcet's method because it
> doesn't meet IIAC.
> Aside from that, I don't understand what Saari's criticism is, in
> this example. Condorcet picks Chocolate, which only has 55% against
> it. Weighted voting also picks chocolate, if people vote sincerely,
> since the Apple people have no problem with Chocolate, and the
> Chocolate people despise Apple.
So Condorcet picks the same alternative as Saari's proposal, Weighted
Voting, in that example.
> Sure, there's a case for picking Apple. By the Mutual Majority
> Criterion, & by the Smith Criterion. The Smith Criterion says
> that if everything in set S beats everything outside set S
> then the winner must come from set S.
> But, if Smith's Criterion, &/or MM is important to someone, then
> we need only add a rule that Condorcet choose from the Smith set:
> That if there's a group of alternatives that each beat everything
> outside that group, then the winner must come from that group.
> Any method that meets the Smith Criterion automatically meets MM.
> So then, if that's what Saari's criticism is, that Condorcet
> doesn't meet Smith or MM, that's easily remedied. And please
> remind him that Weighted voting violates Smith & MM in that
> example also.
> If I were in that group, making that group choice of a flavor, I'd
> consider Chocolate the right choice, even though the Smith
> & MM criteria sound compelling.
In a choice involving a group of friends, one naturally wants to
avoid picking something that is intensely disliked by some members
of the group. Unfortunately that goal doesn't work out in larger
elections, and, in fact, can cause trouble even in small elections.
If you were one of the apple voters, you could say: "I voted your
chocolate almost equal to my favorite, & you gave my apple a
negative point score, and so chocolate won. Did you betray the
sincerely voting apple voters intentionally, in order to win?"
Even if you didn't say it, you might be thinking it, and the
possibility or appearance of that would make people uncomfortable.
On a committee that I was on, the chair of the organization of which
the committee was part rejected Weighted Voting because he didn't
have any confidence that the voters wouldn't strategize. I agreed
with him on that. Weighted Voting is a strategic mess.
> But I personally don't consider Smith or MM to be especially
> compelling. Sure it would be desirable to meet them, but the
> fact that Chocolate has fewest people saying something is better
> seems to mean something too.
> It's interesting that Saari has independently come up with Smith
> &/or MM, and invoked it even though his Weighted-Voting proposal
> also goes against those criteria.
> If failing IIAC is the problem, then Condorcet is in good company,
> since no method can meet IIAC, and a few other more desirable
> crieria simultaneously. (e.g. Weighted Voting meets IIAC but
can fail to elect the favorite of a full majority of the voters).
> If Smith &/or MM is the problem, then we simply have Condorcet
> choose from the Smith set, and then Condorcet will meet those
> 2 criteria, and all of the other academic criteria.
> I suggest that you forward my letters about this (this letter
> & the previous ones replyng to Saari) to Saari & the rest of the
> evote group.
> Or would you like me to forward copies to them? Of course it's
> your group, & I wouldn't write to them or forward anything to them
> without your ok.
> But I recommend forwarding to them everything that I've written
> to you about that, including this letter.
> But, with or without the Smith set, Condorcet lets a set of voters
> consisting of a majority of all the voters to get a result that
> they all agree on (that a certain candidate win, or that 1 or more
> candidates not win) without using any defensive strategy unless
> every candidate has someone ranked over him by a majority. And,
> under any conditions at all, a group of voters consisting of a
> majority never has to rank a less-liked alternative equal to or
> over a more-liked one in order to get a result that they all want.
> That can't be said for any other method (except Simpson-Kramer).
> As soon as we look at better voting systems, there are innumerable
> standards that we can come up with, and our choice of methods could
> depend on which standard we pick. I like the standard, in the paragraph
> before last, that Condorcet meets, because it means getting rid of
> the lesser-of-2-evils problem, and minimizing or eliminating the need
> for defensive strategy. Actually eliminating the need for defensive
> strategy under all conditions that are plausible & in which the
> result really matters anyway. That means a lot, I believe.
> I recommend forwarding this letter to Saari, & preferably to the
> whole evote group. And my previous letters that I wrote about
> the evote decision.
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