[EM] Alternatives to Borda Count
Forest Simmons
fsimmons at pcc.edu
Thu Jan 25 16:09:21 PST 2001
In a recent posting Mike Ossipoff mentioned that there are better
alternatives than the Borda Count for converting ranked ballots to
ratings.
I'm not sure what he had in mind, but here's one thought along those
lines.
Suppose that someone came running after a two winner election and told me
that my two middle preferences had won. If the two middle preferences
were near the average of my personal ratings, i.e. if the median and the
mean of my ratings were close, I probably wouldn't get too excited. If
the median was well below the mean, I would be downright disappointed. If
the median was well above the mean, I would be happy.
Now suppose that someone told me that there had been a recount, and that
the winners were precisely my first and last place preferences. I would
definitely be excited. However, if the last place winner was David Duke
or someone like that, my enthusiam would be dampened.
The question is which would I prefer in general, the first/last
combination, or the two middle guys?
If you have a definite preference here, then the Borda Count doesn't
represent you additively, as in the common assumption of aggregation of
partial individual utilities. As Joe Weinstein pointed out, this problem
is related to the additive assumption of aggregation of individual
utilities to get group utility.
I have some opinions and other ideas along these lines, but I would like
to hear others on the topic before proceeding.
Forest
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