Optimal? not

[Saari at aol.com]

In a message dated 98-07-09 19:27:51 EDT, you write:

>In my most recent posting, I said that it's optimal, with 
>Saari's -100 to 100 system, to give -100 to everything that one
>wouldn't vote for in Plurality. I meant, -100 to everything worse
>than what one would vote for in Plurality. Obviously one would
>give 100 to what one would vote for in Plurality, and to everything
>one likes more.

I no longer advocate a fixed-scale point system.  However, I am addressing
this anyway because there is a more general point that needs to be made.

Consider a case with a very small number of voters and twenty or so
alternatives.  The "Mike O" voter casts only +100 and -100 votes.  (Say, eight
+100 votes and the rest -100 votes.)  The "Mike S" voter casts a mild spread:
seven votes as +100, +95, +90, +85, +80, +75, +70 and the remainder as all
-100 votes.

It turns out that there were only two voters.  Which strategy was more
optimal?

In the case where there were NO candidates "liked" by both voters, then there
will be a tie between the 8 candidates liked by Mike O and the one candidate
liked by Mike S.  Depending on the tie-break method used, there might be an
advantage to Mike O or there might not.

In the case where there was exactly ONE candidate "liked" by both voters, then
that candidate wins outright.  Neither strategy was better.

In the case where there are TWO or MORE candidates "liked" by both voters,
then the spread vote by Mike S will determine the winner between the high-
scoring choices.  There is a definite advantage to the "vote spread" method in
this instance.

Thus I see no compelling evidence that the "all or nothing" voting strategy
advocated by Mike O is necessarily optimal.  

And I do not see any compelling evidence that I should use a different
strategy when there are more voters rather than fewer voters.

Comments?
Mike Saari