[EM] Saari's letter

[MIKE OSSIPOFF]

EM list:

A few comments on Saari's letter:

Saari says that Copeland with 3 candidates doesn't have
strategy problems as described by Gibbard & Satterthwaite.
Copeland with 3 candidates, when there isn't a candidate who
beats each one of the others, doesn't return a winner.

***

Saari says that he can say that any method is "best", by
a suitable choice of criteria. Then later he says that
a version of Borda is the theoretical best :-) Even theoretically,
there's no "best", except based on some particular standard(s).
Maybe by Saari's theory of symmetries Borda is the theoretical
best. Sorry, that doesn't make the unqualified theoretical best.

***

Saari says that the methods that always elect a majority winner
(candidate who beats all the others pairwise?) if there is one
must violate a certain kind of symmetry, and that a consequence
of that is that those methods have a high probability of electing
a Condorcet loser. Wrong. The better Condorcet versions never
elect a Condorcet loser. It's good to find out about methods before
telling about their properties.

***

Saari says that Borda can be modified to handle its difficulties.
How would he modify it so that a voter could have all of his
expressed preferences fully-counted? How would he modify it
to meet the defensive strategy criteria? Or to not violate
majority rule worse than Plurality does?

Speaking of the wish to have all of one's preferences fully
& reliably counted, a basic goal of rank-balloting, Borda
only lets you have _one_ pairwise preference fully-counted--
the preference for your voted 1st choice over your voted last
choice (unless you divide one of those rank positions between
more than 1 candidate, in which case none of your preferences
are fully-counted). By "fully-counted", I mean counted at full-
strength, maximum strength. Counted as strongly as any other
preference vote of anyone else.

That's a rhetorical question, because Saari doesn't participate
in this list. No problem. If his proposals ever become actual
public proposals, then we can deal with them at that time, and
they won't withstand public scrutiny.

***

Mike Ossipoff
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