# Ideal voting method

Mike Ossipoff dfb at bbs.cruzio.com
Wed Oct 16 22:38:59 PDT 1996

```I'd like to reply to some of the topics in the latest letters with
this subject line.

Topics replied to in this letter:

1. Meaning of "Condorcet's method"
2. Bad Examples for margin count (Young's or Dodgson's method)
3. Truncation resistance--one of Condorcet's advantages
4. Equal ranking of candidates in a ballot
5. Open meetings
6. Smith set stops short of Copeland's problems
7. Iterated Condorcet & Stepwise Condorcet

1. Definitions of Condorcet's method:

The term "Condorcet's method" is often used in a very general
sense, to mean a pairwise count used to search for a candidate
who beats each one of the others pairwise. Condorcet, however,
proposed a solution for when there's no such candidate. Condorcet
wasn't completely specific about how truncations would be
interpreted, however, probably because theoristss have tended
to assume that everyone ranks every alternative. Condorcet suggested
that the candidate whose greatest deafeat was the least should be
the winner, but he didn't say exactly how that defeat should
be measured. It could be by margin of defeat, votes-against, or
votes-for, in the candidate's pairwise comparisons.

We on EM have chosen votes-against, because of the important
& valuable propoerties that it confers, with regard to majority
rule, & the goal of getting rid of the lesser-of-2-evils problem.

Actually, then, when people call Dodgson's method or Young's
method, which measure defeats by margin of defeat, "Condorcet's
method", I can't say that they're using the term wrong. If
other versions are eventually competing with the version we
advocate, then we could start calling it "Condorcet(EM)".

2. Bad Examples for margin methods (Dodgson & Young):

Sincere rankings:

Say the Dole voters truncate:

Actual rankings:

41: Dole
20: Clinton, Dole

I won't use up space & lengthen this message by working the
results out there, but Young's method, which scores defeats
by margin-of-defeat, would elect Dole here. The Dole voters'
truncation would result in Dole beating Clinton. In spite of the
fact that Dole is the only candidate over whom a full majorilty
havae expressed preference for someone else. I consider this
a gross violation of majority rule.

Say the Clinton voters truncate too, or don't ahve a 2nd choice.
Here's an example with that modification. These numbers don't
add up to 100, and so they can't be called percentages, but are
just numbers of ballots:

Actual rankings:

41: Dole
20: Clinton

Again, Young's method elects Clinton, allowing truncation by
Dole voters to make Dole win instead of the candidae who'd beat
each one of the others in 2-way races, and electing the only
candidate with a full majority against him.

***

In both of those 2 examples, Condorcet's method, as defined on
EM, would elect Clinton.

***

3. Truncation Resistance a Condorcet advantage:

The previous topic brings me to the question abaout whether
thwarting truncation is a reason for choosing Condorcet's method.
Yes, it's one of the reasons, but not the only one.

A method is "truncation resistant" if truncation can never gain
the election of an alternative over which a full majority of the
voters have ranked the Condorcet winner (the alternative which,
when compared separately to each one of the others, is ranked over
it by more voters than vice-versa).

Condorcet(EM) is truncation resistant. Young's method isn't.
Copeland's method isn't. No proposed pairwise-count method other
than Condorcet(EM) is truncation-resistant. Truncation resistance
is a criterion for comparing pairwise-count methods. Only 2 things
can defeat a Condorcet winner in a pairwise-count method:
truncation & order-reversal. Truncation will happen on a large scale
in any election, especially when there are many alternatives. It
needn't be strategically-motivated. It's good for a method
to be invulnerable to having its results screwed up by truncation.

***

But truncation-resistance isn't the only reason for choosing
Condorcet's method. As I said, majority rule & the goal of
getting rid of the lesser-of-2-evils problems are also good
reasons.

Here's a basic democratic principle:

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

This may seem obvious, but Condorcet(EM) is the only method
that will never unnecessarily violate that basic democratic
principle.

***

As for lesser-of-2-evils (LO2E), some very specific LO2E
criteria have been written, as a benchmark for measuring
compliance with that standard. They're available upon request,
but I shouldn't lengthen this letter with them.

But Condorcet's "votes-against" very transparently gets rid
of the LO2E problem better than other methods: LO2E voters are
voters who want to vote _against_ Dole so badly that they're
willing to abandon their desire to vote _for_ their real favorite,
Nader. So it's obvious that these negative voters will be satisfied
by a method, which, by counting votes-against, fully counts them
against Dole, due to ranking Clinton over him, even though they
didn't ran Clinton 1st. This isn't true of other rank-balloting
methods, or even of other pairwise methods. So "votes-against"
is simply exactly what the negative voter, the LO2E voter, insists
on having counted. Condorcet counts it.

In particular, if a majority rank Clinton over Dole has a
majority against him, then he obviously can't win unless every
candidate similarly has a majority against him.

Generalized Majority Criterion (GMC):

Definition: An alternative has a majority against it if there's
another alternative ranked over it by a full majority of all the
voters.

A method meets GMC if & only if an alternative with a majority
against it can't win unless every alternative has a majority
against it.

The requirement not to violate that basic democratic principle that
I stated earlier results in a requirement to meet GMC.

Of the methods proposed, only Condorcet(EM) meets those
requirements.

***

so I've listed some in this section.

***

I should post this now, and then continue the reply in an
immediately subsequent message.

***

Mike Ossipoff

--

```