[EM] Rob: Condorcet's strategy problem

[Abd ulRahman Lomax]

At 01:34 AM 9/15/2005, Rob Lanphier wrote:
>My main goal is to correctly find the candidate who would beat every
>other candidate in a head-to-head election, because I believe that
>candidate is likely the best candidate for the position.

As I have written, there seems to be two distinct philosophies 
governing the choice of election method. Mr. Lanphier has stated one. 
The other position is that the candidate with widest approval is the 
best candidate, the argument being that society should ideally be 
united behind elected leaders and representatives. (Single-winner 
elections for representatives, however, are inherently 
disenfranchising; this problem won't be solved until we have PR, on 
which CVD and many of us converge, though not necessarily on PR 
election method.)

Given that Mr. Lanphier has clearly stated the philosophical 
underpinning of his analysis of election methods, we should not be 
surprised at all that he would prefer Condorcet methods over Approval methods.

Let's agree on one thing: Condorcet is designed specifically to 
produce exactly the Condorcet winner, who is as described by Mr. 
Lanphier. In large elections, it is unlikely that there would be a 
true tie for top position, but cycles are more possible. Still, of 
those in a cycle, the cycle is artificial in that the pairwise 
election is simulated, not real. One solution would be to hold a 
runoff election among the members of the Smith set (those in the 
cycle of mutual victory and defeat). Trying to resolve the cycle with 
the original election data is probably a doomed effort. By doing 
this, strategies that aim to create a cycle and then win the cycle by 
some additional criterion are frustrated, insofar as they are 
attempts to assert a false winner. All they could do is to push their 
candidate into a runoff. Which might well be wasted effort.

How would the runoff be run? It would be Approval, I'd suggest. 
Simple. Would probably resolve the Condorcet cycle, even if it were genuine.

I favor the introduction of approval cutoff into Condorcet methods, 
not for the purpose of resolving cycles, but for general information. 
We should know if an election result is apparently unsatisfactory to 
a majority of voters!

But using Approval in the election calculations creates, I suspect, 
strategic motivations to Approve insincerely. Splitting up the 
election into two phases, with the second phase being extremely rare, would

(1) Almost always choose the Condorcet winner.
(2) Resolve the rare cycles with the election of the truly most 
broadly approved candidate.

(When there are only three candidates in an election, which would be 
by far the most common cycle result, voters would know that the 
election is very close, that any of the candidates could win. It 
would be their choice whether to vote for only their favorite, or to 
vote for two. But plurality would also be acceptable under the 
circumstances, I suspect.)