[Election-Methods] Smith exposes our false statements

[Abd ul-Rahman Lomax]

At 04:36 AM 7/26/2007, Michael Ossipoff wrote:
>I'm not replying to Lomax's rebuttals because that would be sending 
>some unnecessarily long postings to you, and because I'm firmly 
>convinced that everything he says is answered in my recent postings. 
>I won't read any posting that I don't intend to reply to. Why 
>subject myself to it if I'm not going to subject you to it?  :-)

Excellent advice, he's giving himself. Helps us, too.

However, one point. I'm offering a counterexample to what he's been 
claiming, over and over, without proof other than abstract theorizing 
that bristles with assumptions that may not be true. I would suggest 
one thing to Mr. Ossipoff if he is truly interested in the matter.

I have proposed a method for easily determining the exact expected 
utility for various vote patterns for a voter, voting in a many-voter 
environment with zero knowledge, Range 2, and the results show higher 
utility for sincere range strategy than for approval strategy. I've 
given the exact numbers, and have described the method in detail. 
Anyone could do it with a sheet of paper and a pencil. I also offered 
the spreadsheet, just to make it simple for those with access to a 
spreadsheet program. (There is also googledocs for people without 
their own computer, even, writing at a library, as Ossipoff used to 
do sometimes.)

Ossipoff has not responded *at all* to the many-voter claim. Perhaps 
he was misled by the fact that I first described the 2-voter 
situation, and made an error in it, an error, interestingly, that I 
was led into by assuming that something Ossipoff had written was 
correct, that the vote 220 was of the same utility as 200, if the 
voter had sincere utilities of 210. Seems obvious. Isn't true, 
*unless* the number of voters is large. Put it another way. It isn't 
true, period. The optimal vote is 200, if we are limited to approval 
style votes. The difference in utility disappears in large elections, 
gradually decreasing with size, because it depends on three-way ties, 
which cause a loss of utility for the Approval vote. Three-way ties 
become vanishingly rare. If a two way tie has probability of P, then 
three-way ties should have, roughly, zero-knowledge, a probability of P^2.

I neglect them in my many-voter analysis, which, not surprisingly, 
shows both Approval votes as having the same utility. But that 
utility difference remains, albeit increasingly small, so the 
statement that there is no difference was false, and blatantly false 
in the 2-voter case, which I was examining at the time.

I then moved on to the many-voter case, finding a way to generalize 
the approach. If there is something wrong with that, all that I've 
been asserting could be wrong. I really would appreciate it if 
anyone, including Ossipoff, irritating as it might be, would find any 
errors in it.

The approach is simple and has been described many times. I won't 
describe it again here, at least not now.