No Subject

[Mike Ossipoff]

Though I can't comment on the PR issues, because now the only
electoral reform I deal with is single-winner reform (because
I feel that PR is being competently handled, and because I've
already said everything I can about it), I'd like to comment on
the single-winner aspect of that message to which this message
is a reply:

Tom named 2 solutions for use when no 1 alternative beats
each one of the others in pairwise comparisons. But there are
more proposed solutions than just those.

The 2 solutions that Tom mentioned were a) Copland's method,
which scores an alternative according to how many alternatives
that it beats (& how many it's beaten by); & b) An elimination
system based on pairwise comparisons.

Copland's method turns out to be pretty terrible, because, with
Copeland, in a multi-party single-winner election, the winning
party (the party of the winning candidate) depends on how many
candidates the various parties are running. No good. Should a
party that can't afford to run as many candidates lose for that
reason?

***

The choice of single-winner method should be based on what we
want from such a method. What properties we, in advance, specify
that we want. What criteria we want a method to meet.

***

I suggest that 2 important standards are:

1. Getting rid of the lesser-of-2-evils problem. This problem
is very important in U.S. voting, since a large percentage of voters
here are thoroughly dominated & cowed by that problem, which
makes them afraid to vote for someone they actually like, believing
that they must, instead, vote "pragmatically" for a "lesser-evil"
who is perceived as more winnable, as despicable as he/she might
be.

I don't know if the lesser-of-2-evils problem is considered a
problem in other countries where important single-winner elections
are held.

2. Majority Rule. I believe we all agree that majority rule is
important.

***

Condorcet did more than suggest that someone who pairwise beats
everyone else should win. He also suggested a solution for when
no such candidate exists. The overall method incorporating
Condorcet's circular tie solution is called "Condorcet's
method".

Unfortunately, Condorcet didn't precisely specify the details
of his proposal, and so there are a number of versions of it
that could correctly be called "Condorcet's method". One reason,
most likely, for this lack of specific-ness is that Condorcet,
like many theorists, might have assumed that every voter will
rank all of the alternatives, which would avoid the differences
between some of the versions.

 A number of us have been discussing what single-winner method
would be best for a public proposal, and we've taken a vote,
and chosen a method called "Smith//Condorcet". It's a version
of Condorcet's method, used to choose from the "Smith set", which
I'll define in this letter.

But the point that I'm getting to is that Smith//Condorcet,
or even our version of Condorcet's method when used without the
Smith set, does better than an other proposed method, as regards
the lesser-of-2-evils problem, and the majority rule standard.

***

So first let me define our version of Condorcet's method, and
then the Smith set, and Smith//Condorcet:

Condorcet's method:

If no 1 alternative beats each one of the others (where A
beats B iff more voters rank A over B--even if by ranking
A & not B--than vice-versa), then  the winner is the alternative
over which fewest voters have ranked the alternative which,
among those that beat it, is ranked over it by the most voters.

In other words:

For each alternative, determine which alternative that beats it
is ranked over it by the most voters. The number of voters ranking
that other alternative over it is the measure of how beaten it
is. The winner is the alternative least beaten by that measure.

***

Smith//Condorcet:

Use Condorcet's method, defined above, to choose from the Smith
set.

The Smith set is the smallest set of alternatives such that every
alternative in the set beats every alternative outside the set.

***

Alternative definition of Smith//Condorcet:

The "Smith Criterion" says: If there's a set, S, such that every
alternative in S beats every alternative outside S, then the
winner should be from S.

Smith//Condorcet: Use Condorcet's method to choose from among
the alternatives whose victory wouldn't violate the Smith Criterion.

***

Those are 2 equivalent wordings for the same method.

With the Condorcet's method version that I've defined, it's 
transparent that an alternative with a majority against
it (where an alternative has a majority against it if
there's some other alternative ranked over it by a full
majority of all the voters) can't possibly win unless
every alternative has a majority against it. This is an
obvious & natural majority rule criterion, an extension
of the familiar Majority Criterion:


The Generalized Majority Criterion:

An alternative with a majority against it (as defined above)
shouldn't ever win unless every alternative has a majority
against it.

This criterion, which I'll abbreviate "GMC" is the result of
avoiding unnecessary violation of the following basic democratic
principle:

If a majority indicate that they'd rather have A than B, then,
if we choose A or B, it should be A.

***

That's obvious. As I said, avoiding unnecessary violation of
that basic democratic principle leads to GMC, a criterion
met by Condorcet's method, as I've defined it, but not by
any other proposed method.

***

GMC is one of 3 basic democratic principles that I'll list
here:

1. If a majority (by which I mean a full majority of all the
voters, indicate that A is their favorite, then A should win.

2. If the number of voters indicating that they'd rather have
A than B is greater than the number indicating that they'd rather
have B than A, then, if we choose A or B, it should be A.

3. If a majority of all the voters indicate that they'd rather
have A than B, then, if we choose A or B, it should be A.

***

#1 is, of course, the familiar Majority Criterion, which could
also be called the "Majority Favorite Criterion".

A requirement to not unnecessarily violate #2 leads to the
Condorcet Criterion: If an alternative pairwise beats each
of the others, then it should win.

A requirement to not unnecessarily violate #3 leads to GMC,
which I've defined above.

Basic democratic principle #3, and GMC, are what's missing
from all of the proposed methods except for the Condorcet's
method version that I've defined. Lots of methods meet the
Majority Criterion. Lots of methods meet the Condorcet
Criterion. How to choose from among the methods that meet
the Condorcet Criterion & the Majority Criterion? Democratic
principle #3, and GMC, weed out everything but Condorcet's
method, requiring majority rule in a more demanding sense.

***

It can also be shown that Condorcet's method is the one that
gets rid of the lesser-of-2-evils problem. Plainly, if you're
part of a majority who have ranked Clinton over Dole, but you
haven't ranked Clinton in 1st place, you've still been counted
as helping make Dole beaten with a majority against him, making
it quite difficult for him to win.

To put it more generally, for the lesser-of-2-evils problem:

Voters dominated by that problem are voters who insist on
negative voting, casting a vote _against_ the worst candidate,
instead of for the best one. By counting "votes-against", as
Condorcet does, that voter's need to vote against someone is
satisfied without requiring that voter to do other than rank
his favorite in 1st place. Isn't that what it means to get
rid of the lesser-of-2-evils problem?

***

Summary: Whether our goal is majority rule, or getting rid
of the lesser-of-2-evils problem, Condorcet's method is the
one that delivers--the only method that does.

Smith//Condorcet retains these valuable properties of Condorcet's
method, while adding compliance with other criteria that are
important to academic authors, including the Smith Criterion,
and a number of other criteria that are complied with by any
method complying witht he Smith Criterion.

***

Questions, disagreements, &/or comments can be addressed to:

dfb at bbs.cruzio.com

***

Mike Ossipoff







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