[EM] Alternatives to Borda Count

[Bart Ingles]

I can't speak for Mike, but my own view is that there really is no good
way to convert rankings to ratings.  There might be a way to argue that
some of the ranked choices have more relevance, and thus deserve more
weight than a strict Borda weighting, but I don't see how this could be
a major improvement.

Borda sort of catches the average case, but to say it's a good
representation simply because it represents a good average is kind of
like saying that a clock stopped precisely at 6:00 is accurate on
average.

Of course the more insane leap is to claim that the stopped clock is
better than one which runs consistently 10 minutes fast, or which only
gives a rough approximation of day and night, simply because the stopped
clock has a better average.

Bart



Forest Simmons wrote:
> 
> 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