Finding the probable best candidate?

[Forest Simmons]

On Mon, 18 Feb 2002, Steve Barney wrote:

> Yes, of course we have limited information by which to determine the group's
> best candidate, but what if we focus on nothing but the information which is
> contained in an ordinal preference ballot? 

Order of preference isn't sufficient to determine intensity of preference,
which also has a bearing on "best."

> In that case, the "best" candidate
> may be defined as the one who is most preferred according to the information
> contained in fully ranked ordinal preference ballots.

Most preferred according to which measure of preference?  The preferences
are given as vector valued functions.  For maximization, those vectors
have to be turned into scalars.  There are infinitely many different ways
of doing this, each yielding a different measure of preference.

> Once again, Donald Saari
> has claimed that he has proven the Borda Count to be the optimal method in such
> a case.

The Borda count is the best estimate of mean social utility based on
sincere preference ballots.  In public elections this estimate can be
manipulated by running clones and by leaking information (true or false) 
about other voter preferences.  So the result has little relevance to
public elections.

My earlier point is that maximizing mean social utility may be barking up
th wrong tree anyway. 

Which is better, the candidate that maximizes average voter satisfaction,
or the candidate that maximizes the number of voters that have above
average satisfaction?  They might sound the same, but they're not.  Borda
attempts the first and fails, Approval attempts the second and nearly
succeeds. 

Forest