[EM] Re: Blake's margins arguments

Alex Small asmall at physics.ucsb.edu
Mon Feb 24 19:50:29 PST 2003

On the subject of majorities and Margins vs. Winning Votes, my
understanding of the matter (which I will deliver without prejudice, since
I have no strong opinion on the matter) is this:

Say that two of our pairwise contests in an election are:

A>B  51-49
B>C  45-40

(Assume there are 100 people casting ballots, at least 3 candidates, and a
cyclic ambiguity to resolve.)

A majority of the people casting ballots have said "We prefer A to B."  A
plurality of the people casting ballots have said "We prefer B to C", with
15 voters abstaining.

A winning votes advocate can say "A has majority support relative to B. 
That's a stronger defeat for B than C's defeat, since B only beat C with a
minority (plurality) of the people casting ballots."

A margins advocate can say "Yes, A beats B with a majority of the people
casting ballots.  But, B beats C with a _majority of the people
participating in the B vs. C contest_.  Since the other people voluntarily
abstained from that contest, we shouldn't consider them, we should only
consider who got a larger percentage of the people participating in each

I hope that clears some air on the debate over the word "majority."  It
all comes down to "majority of whom?  People casting ballots or people
expressing preferences with respect to a particular pairwise contest?"

I don't claim to resolve any normative issues of which provides a more
socially desirable criteria, or technical issues of which method provides
more perverse strategic incentives.


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