# The EM vote on single-winner methods

Mike Ossipoff dfb at bbs.cruzio.com
Fri Jul 5 18:15:06 PDT 1996

Good points & questions in the forwarded letter. Let me briefly
define some of the methods that have been proposed. After defining
them, in a subsequent message, I'll briefly comment on their merit.
That subsequent message will be entitled "What Condorcet offers".
Advocates of other methods may, of course, post similar statements

Well, before defining the methods, let me say that I agree with
what Steve said, that any member of EM may vote in this election.
The Single-Winner Committee simply consists of everyone on EM who
wishes to discuss or vote on single-winner methods.

I also agree with reporting to ER the results of counting the
ballots by each of the count methods that has been proposed during
these discussions--if they give different results.

Definitions of some methods for counting ranked ballots:

MPV (aka "Instant Runoff", "Hare's method", "the Alternative Vote"):

Repeatedly eliminate from the rankings the alternative occupying
highest position in fewest rankings.

(Though this doesn't affect the result, any alternative that comes
to occupy highest position in majority of the rankings is at that
time declared winner. Though this added rule doesn't change the
outcome, it shortens the count labor).

Condorcet's method:

A beats B if more voters have ranked A over B than vice-versa.
If 1 alternative beats each one of the others, then it wins.

If no 1 alternative beats each one of the others, 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:

If no 1 alternative beats each one of the others:

Determine, for each alternative, 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 which is least beaten
by that measure.

Smith//Condorcet:

Use the Condorcet choice rule, defined above, to choose from the
"Smith set", which I'll define here:

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

It's been suggested that people don't like the word "set" in
a definition, and, also, Smith//Condorcet can be defined in
terms of the Smith Criterion, rather than the Smith set:

The Smith Criterion says that if there's a group of alternatives
that all beat everything not in that group, then the winner should
come from that group.

Smith//Condorcet says to use the Condorcet choice rule, defined
above, to choose from among the alternatives which are permitted
to win by the Smith Criterion.

So I've defined Smith//Condorcet in terms of the Smith set, &
also in terms of the Smith Criterion. I don't know which definition
people will prefer.

The term "plain Condorcet" refers to the Condorcet's method that
I initially defined in this message.

Smith//Random:

As with Condorcet's method, A beats B if more voterss rank A
over B than vice-versa. And any alternative that beats each one
of the others wins. If no 1 alternative beats each one of the others,
then a winner is chosen randomly from the members of the Smith set.

As I understand Lucien's proposal, Smith//Random is what he proposes,
except that he proposes that the option of "disapproval votes" be
added, so that you can vote disapproval against any alternative(s)
that you want to, and anything disapproved by a majority is disqualified.

But, since the disapproval option could be added to any method,
I've suggested that it's a separate issue. I'd suggest adding
that issue to this election, but I'm convinced that to do so
would complicate it. I suggest that the issue of the disapproval
option (and the related NOTB--none of the below--option) be
something to deal with after a method has been voted on and
the report on that election has been sent to ER.

Regular Champion:

As "beat" is defined above, an alternative's "Copeland score"
is the number of alternatives that it beats minus the number of
alternatives that beat it. The winner is the alternative with
the hightest Copeland score. If 2 or more alternatives tie for
the highest Copeland score, then the one with the most 1st choice

[Excuse me if I depart from objectivity here: If the above definition
of Regular Champion seems reasonable & ok, then I want to repeat
that Regular Champion doesn't meet any of the lesser-of-2-evils
criteria that plain Condorcet & Smith//Condorcet meet. Regular
Champion doesn't get rid of the lesser-of-2-evils problem, and
Condorcet does. What are we doing single-winner reform for, if not
to get rid of the lesser-of-2-evils problem. EM's advocate of
Regular Champion has said that he doesn't consider the lesser-of-2-
evils problem to be important. Millions of voters would disagree
with him on that, since their voting is completely dominated by
that problem. This is well understood by electoral reformers, and
it's widely agreed that we want sw reform to get rid of the
lesser-of-2-evils problem].

Double-Complement (Modified Runoff):

Same as the Runoff system widely used in municipal elections,
except that victory in the primary, instead of requiring a
majority, only requires a vote total twice as close to a majority
as the runner up is.

In that sense, Double-Complement is inbetween Runoff & Plurality.

Approval:

A nonranked method. On a nonranked ballot, like the ones in
use now, a voter may vote for as many alternatives as he/she
wishes to, giving a whole vote to every alternative for which

It's very widely agreed among electoral reformers that the best
rank-balloting methods are better than Approval, and I agree with
this. I differ from many electoral reformers when I say that
Approval is better than all but the best rank-balloting methods.
In my vote, I ranked only plain Condorcet & Smith//Condorcet over
Approval.

***

I second Steve's suggestion to change the voting deadline to
7/10/95, which is 5 days from today. Does anyone oppose that
date? Does anyone prefer making it 7 days from today?

If the deadline is 7/10/96, I suggest that include the evening
of that day, so that the actual deadline would be 12:01 a.m.
7/11/96, which would be 12:01 right after the evening of 7/10/96.

***

over a long time. As I said, I'll soon post a message entitled
"What Condorcet Offers". I encourage advocates of other methods

***

Mike

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