[Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions

[Abd ul-Rahman Lomax]

At 07:31 PM 8/29/2007, Paul Kislanko wrote:
>I'd suggest that the zeroes in the last column are improbable if C is
>acceptable to both  A and B voters. That all A-first voters like C almost as
>much as A but don't like B (or all B voters like C almost as much as B but
>don't like A) is so improbable I can't believe it would happen.

On the contrary, I gave a travel example that explained the ratings 
as relative utilities. Then I showed how different absolute utilities 
underlying the relative utilities could lead to the conclusion that A 
was the best choice, B was the best choice, or C was the best choice.

It's not common that we can determine absolute utilities so easily, 
but it *is* possible in some cases. And it gives us, I think, 
valuable information about how election methods behave. For example, 
where absolute utilities can be known, the majority criterion is 
almost preposterous. It happens to *usually* indicate the best 
winner, if a majority winner exists, but it can fail spectacularly.

The most cogent objection to Range is not that it can fail MC. It is 
that it can fail to do what it is purported to do, which is to 
maximize social utility, and not only from "strategic voting," but 
merely from the normalization that we generally allow as still being 
sincere. Only if we have a way of encouraging voters to vote 
*absolute* utilities could we then be assured that Range would 
reliably elect the social utility winner.

However, the extremes I have described are not the usual case. This 
is where Warren's simulations come in. With reasonable assumptions 
about absolute utilities for candidates would be formed (I think he 
has used an issue space model, the point is not whether or not that 
model is accurate, but only whether or not the utility distributions 
it generates are reasonably similar to those present in real 
elections, and that seems likely), we can then use these absolute 
utilities to judge the performance of election methods. Contrary to 
what so many claim about Warren's simulations of Range, he does not 
simply assume sincere votes. Range still performs quite well with 
various mixes of "strategic voters," and, of course, in the extreme, 
the election has been reduced to Approval, which is not a bad 
outcome, Approval also performs well, though not as well as Range.

So, to me, the interesting question becomes whether or not we can 
detect what could be called S.U. failure in a Range election. I don't 
think there is any way to be sure of it, but there are, I strongly 
suspect, certain signs, and majority failure or the existence of a 
candidate who beats the Range winner pairwise, would be one. This is 
*not* a proof of SU failure, it is, however, something that can be 
associated with it. And so it becomes interesting, then, to test the 
preferences... by setting up a minor inconvenience in holding a 
runoff election. Voters with small preference strengths will be less 
likely to go to the trouble of voting, voters with strong preferences 
will be highly motivated, and there is more that I've described elsewhere.