[EM] Your opinion on being able to vote no preference?

Alex Small asmall at physics.ucsb.edu
Mon Feb 24 11:21:32 PST 2003

Tom McIntyre said:
> The alternatives are to enforce
> strict ranking of the candidates the voter chooses to list, or to
> enforce strict ranking of all candidates on the ballot.
> but I'd like to know if there's consensus here on which of
> these alternatives would be better in actual practice.

Well, the consequences of allowing equal rankings and how to deal with
them have been discussed ad nauseum, particularly in the context of
Condorcet methods (more on that later).  In general, the opinion seems to
be that if a voter feels that the best way to protect his interests is by
voting two candidates equal then more power to him.

Indeed, many people on this list like Approval Voting, in which you sort
the candidates into two categories:  approved and not approved.  Some also
like Cardinal Ratings:  Give each candidate however many points you like
on a scale of 0 to 4 or 0 to 10 or -1 to +1 or whatever other scale is
decided upon.  It's often argued that such methods are equivalent to
Approval Voting, in that your best strategy is to give each candidate
either the top rating or the bottom rating.  In any case, even though most
people here hold that Cardinal Ratings and Approval are strategically
equivalent, if the public really preferred Cardinal Ratings and the
_option_ of giving intermediate scores I don't think many of us would

In Condorcet methods, the handling of equal rankings becomes tricky.  If
somebody considers two candidates equal then in pairwise contests that
person obviously has no say.  If there's a candidate who wins all of his
pairwise contests then there's no problem.  But, if nobody wins all
pairwise contests then there's a subtle but important question to resolve.

Say we use a method where we drop the weakest pairwise defeats until
somebody is "undefeated", and we have a situation where A>B>C>A.  Say also
that there are 100 voters.

If A beats B 51-49, B beats C 45-40, and C beats A 55-45, A clearly
suffers the most decisive defeat.  But, who suffers the weakest defeat?

Some would say B suffers the weakest the weakest defeat.  He was beaten by
a margin of 2 points.  Others say "That's true, but an absolute majority
came out against B.  An absolute majority did NOT come out against C. 
Sure, B won a significant victory among those who expressed a preference
between B and C.  Still, because a lot of people sat out that contest, it
doesn't carry the same weight as the ABSOLUTE MAJORITY who came out
against B in the A-B contest."

Those who express the above sentiment then say that instead of looking at
margins of defeat, we should look at the absolute number of people who
came out against a candidate.  In that case, the 45 who came out against C
constitute a weaker defeat for C than the 51 who came out against B. 
Looking at the absolute number of people who voted against a candidate is
known as the "Winning Votes" method measuring the strength of a pairwise
defeat.  Looking at the margin is known as the margins method.

The above discussion of absolute majorities is the normative, or political
argument in favor of the "winning votes" (wv) method.  The political
argument in favor of margins is essentially that winning by a wide margin
is a mark of excellence.  I'm probably not making the case for margins
very well, mostly because I'm not familiar with the intricacies of the

There are also technical arguments concerning which method gives more
incentives to vote insincerely.  I'll stay on the sidelines of that

Anyway, you won't find much in the archives on equal rankings per se, but
you'll find a lot of discussion of matters related to equal rankings.


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