[EM] Proof Borda Count best in the case of fully ranked preference ballots

[Forest Simmons]

On Mon, 18 Feb 2002, Steve Barney wrote:

> 
> Just so you know, in the case of fully ranked ordinal preference ballots,
> Donald Saari has claimed to have proven, mathematically, that the Borda Count
> is the optimal procedure in the sense that it produces the smallest number, all
> together, of paradoxical outcomes. 

A paradox is a paradox only as long as our intuition remains uneducated.

What is counterintuitive to Saari may or may not be counterintuitive to
me or you.

The number of counterintuitive properties that a method resolves is in the
mind of the beholder.

Similarly, the number of objective criteria satisfied by a method is
a virtually useless measure of how good the measure is.  Random ballot
satisfies almost all objective criteria, and has no paradoxical outcomes
at all.

Some criteria are much more important than others. Only when the most
important criteria are satisfied does it make sense to bring the less
important one into consideration.

Voters want a method that doesn't penalize them for voting their
conscience.  Random Ballot satisfies this standard.  Single Elimination
seeded by random candidate satisfies this, while affording the voter a
greater chance of actually influencing the outcome. Approval satisfies
this and gives each voter even greater chance of being pivotal in the
outcome.  Demorep's ACMA seems to satisfies this.  Other more complicated
methods like some versions of Declared Strategy Voting (DSV) satisfy this
standard. Certain proxy methods satisfy this. The best Condorcet methods
come close enough to this standard for all practical purposes.

In my opinion Borda doesn't come close enough to this standard to warrant
routine use in public elections except as an adjunct method as in Black,
or for seeding an elimination method, or for what we used to call Nanson's
method but is now Borda runoff. 

In my opinion, it's no use talking about other criteria relative to public
proposals if those proposals don't measure up to this standard better than
Borda. 

The other problem that by itself is sufficient to eliminate Borda from
consideration is the extreme clone sensitivity that Rob LeGrand pointed
out.

It doesn't matter how many other "paradoxes" Borda avoids or how many
other criteria it passes, it doesn't measure up to the minimum
requirements of a public proposal. There are plenty of other applications
for Borda.  It seems to me that Saari should concentrate on promoting
those kinds of applications.

Forest