[EM] simpler proof of "no conflict theorem" now trivial

[Jonathan Lundell]

At 10:07 PM -0400 8/20/06, Dave Ketchum wrote:
>Maybe time to start over, unless someone can find something decent 
>written down!
>
>We are talking of ranked choice, such as IRV does.

Right, or any other ranked method.

>Normally possible to rank every candidate.  Restrictions tolerable, 
>but MUST be able to rank at least best and second.
>
>Equal ranks permitted, when the voter sees a tie in value.

Well, most implementations in actual use don't allow equal ranks, but 
I see no objection in principle, though in practice the 
interpretation of equal rankings in STV systems may not be obvious.

>Cycles must be expected and attended to.  Here there are various 
>ways of attending to choose from.

With Condorcet methods, yes; with STV methods, no.

>BTW - I choke on the word "sincere" - I keep my work tolerable by 
>accepting a ballot as being what the voter meant!  Anyway, rare for 
>a voter to know enough about what other voters - guessing what this 
>voter might do - do in response.

I disagree. (Not, of course, with your assertion that you choke, or 
how you keep your work tolerable.)

I take "sincere" to be meant somewhat metaphorically in this context, 
using the definition I proposed earlier: a voter's rank of A over B 
is sincere if and only if the voter would break a tie between A & B 
in favor of A. (If the voter would flip a coin, or doesn't care, then 
we can take that as equal ranking.)

Given that definition, do voters vote insincerely? Of course they do. 
If a voter perceives that voting insincerely is likely to improve his 
overall outcome, he is very likely to vote insincerely. How many 
Nader supporters voted for Gore in 2000? Quite a few, I'd assert, and 
it didn't take rocket science to figure out that particular strategy. 
Not every voter did that, of course, but a significant number did, 
probably enough to turn the election in Gore's favor, absent the 
intervention of the Supremes.

When an election is perceived as critically important, voters will 
strategize, perhaps badly, perhaps well, perhaps with advice from 
their party. And if you believe that a voter will strategize only 
when she has high-quality information about the behavior of other 
voters, you've never sat at a blackjack table and watched the other 
players.
-- 
/Jonathan Lundell.