[EM] About random election methods

[Forest Simmons]

Date: Mon, 14 Mar 2005 22:03:25 -0800
From: Russ Paielli <6049awj02 at sneakemail.com>
Subject: Re: [EM] About random election methods

Russ wrote to Andrew:

Andrew,

I think voters will reject any method that isn't deterministic. Barring
actual numerical ties, why should the selection of the winner depend in
any way on some random event? Yes, randomness may help thwart strategy,
but so what? Of course strategy is useless if we toss dice to determine
the winner. That's just my opinion, of course.

Regards,
Russ


Forest replies:

I think that you are right that the general public will reject randomness 
not needed for tie breaking.

But what constitutes a tie?

Suppose that (pairwise) candidate A beats B who beats C who beats A, and 
that Condorcet gives the win to A because the weakest defeat (by some 
measure) is the C beats A defeat.

Then C can say, "Sure my victory over A wasn't as strong as A's victory 
over B, but my victory was over a strong candidate (the putative winner) 
whereas A's victory was only over a loser."

Who is the real winner in rock, paper, scissors?

Right or wrong, many people consider majority beat cycles as "Condorcet 
ties."

Personally, I believe that approval information can resolve these "ties" 
most of the time.

But there are cases where there is still enough ambiguity to consider the 
result a "tie" even when there is a CW.

Consider (sincere utilities in parenthesis):

55 A(100), B(99), C(0)
45 B(100), C(50), A(0)

Candidate A wins in any Condorcet election.  But in a zero information 
approval election B wins, and the A supporters will not have much to 
complain about.

Examples like these lead me to believe that when the Approval Winner is 
not the Condorcet Winner, both should have a claim to some of the 
probability.

The approval winner can say, "My win was based on stronger, higher 
priority preferences."

The Condorcet winner can say, "But my win was based on more complete 
information."

The AW replies, "But that information was probably contaminated by 
insincere order reversals."

And so there is an impasse, a sort of tie.

Random ballot to pick between the CW and the AW is a far cry from the 
random candidate image conjured up by "tossing dice to determine the 
winner."

You said, "Randomness may help thwart strategy, but so what?"

If strategy is not thwarted, then the result of the deterministic method 
is garbage, no matter how nice it might work in a zero info environment.

Ironically, in many cases a good random method has a much greater 
probability of electing the sincere CW than any deterministic Condorcet 
efficient method.

Forest