Book-Basic Geometry of Voting

[Mike Ossipoff]

Demorep, this list isn't here for posting book reviews. If the author
referred to has actual reasons for saying that Pairwise-Count methods
can't be as good as Borda's point system (which is widely agreed
to have major strategy problems and which is well-known to be
(so far as I've heard) the only rank balloting method tha can
fail to elect someone who's the 1st choice of a majority), then you
don't you find out what they are. And then, if you agree with them,
then write them to this list in fairly concise form, as opposed to
posting articles, chapters or books.

Straffin, the author of _Selected Topic in the Theory of Voting_,
said that if majority rule is considered important, then Borda's
method would seem not desirable. For Straffin's exact words, I
refer you to his book. The word "Selected" may not be in the 
title of his book--I'm not sure--and I'm not certain that
the author's name has 2 "f"s. It could just be Strafin. Straffin
is more likely though.

***

Actually, there's much truth in what many anti-Pairwise authors
say, when they say that Pairwise-Count methods are subject to
strategy. All 1-balloting methods can sometimes, at least in
principle, require defensive strategy. That's very true of most
Pairwise methods too. In fact I don't consider most of them, including
Copeland, in its various versions, to be as good as Approval.

I believe it was Samuel Merrill who advocated Approval and said
that Pairwise methods were subject to offensive strategy. I don't
blame him for saying that, because the popular Pairwise method among
academics is Copeland, and what he says is quite true of that 
method.

But a blanket indictment of all Pairwise methods is premature. Authors
who do that haven't really investigated the methods with respect
to strategy problems. Pairwise methods aren't all the same. 

Condorcet's method, as I've been proposing it, doesn't have the
problems that those authors talk about. It can be shown to have
less of a strategy problem than other 1-balloting methods, including
the point systems.

Borda is an especially undesirable point system, due to its 
inflexibility. Say there are 10 candidates. Your 1st choice gets
9 points, your 2nd choice gets 8 points, etc. But maybe you wouldn't
give your 2nd choice 8/9 as much as your 1st choice. Tough. That's
what Borda does. You're giving that 2nd choice almost as much as
your favorite, enough probably to help him beat your favorite.
If you're sucker enough to do that, then you'd better hope that his
voters are as honest as you are, or else you've just given away
the election. What's a defensive strategy for Borda? Don't vote
for anyone unless you believe you need them. And, in that case,
vote them all in 1st place, if the rules allow that. Of course,
even if the rules allow that, they still might not allow you
to give maximum points to all of them. Probably not. Not only
that but one author (was it Saari?) who advocated Borda said
that voters should be _required_ to rank all of the candidates.
So much for choice. Not much voter freedom.

The other kind of point system, where we can give _any_ candidate
_any_ point rating we want to, within a specified range, that type
of system is much better than Borda. Such a method is as good as
Approval, since it can be voted as Approval (by giving maximum points
to the candidate you're likely to need as lesser-evil compromise,
and also to everyone you like better). In fact that's the strategy
I'd recommend for flexible point systems, which I call
"Point Assignment" methods, but which are sometimes called
"Weighted Balloting", or WB.

I mean that's the strategy I'd recommend when strategy is
appropriate, as it would always be, with WB, in a public political
election, or almost any other election, except for an election
in a close-knit group with common interest & complete trust
of eachother and completely good intentions toward eachother
and confidence in those good intentions. Public elections? Forget
it. But in the rare kind of honest elections I named in thiss
paragaph, one should probably vote sincerely in WB, with trust
that everyone else will. Not relevant to our search for the
best method to propose to the public for public political elections.

And when strategy is called for in WB, which is always in public
elections, it's like Approval. A direct comparison shows that
under the worst conditions of likely order-reversal, in the most
devious electorates, order-reversal can succeed in Condorcet's
method only if enough of its intended victims vote for the perpetrators'
candidate(s) so that an equal number would have given the election
away to those candidates in Approval, had they voted for them
in an Approval election. In other words, only under its worst conditions
can Condorcet have a strategy situation anything like Approval.
Even then it isn't really like Approval, since the order-reversal
is so well deterred that it wouldn't happen anyway, on a scale
sufficient to do anything, especially in a public election.

***

Sorry about the length of this letter, but I just wanted to tell
why no points system is as good as Condorcet. I'm saying that
in reply to the posting of a book review (?) of a book by someone
who likes Borda. Borda, in fact, has got to be the worst point
system, due to its denial of voter freedom, compared to other
point systems. Especially the version proposed by the author
who would require all ballots to rank all of the candidates.

***

As always, I'm willing to verify anything I say, upon request.
I ask only that, if you ask for verification, you are really going
to read it, even if it's long.

***

Mike



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