[EM] Voting by selecting a published ordering

[Abd ul-Rahman Lomax]

At 11:13 PM 5/15/2006, David Cary wrote:
>Does geometric consistency mean here that the candidates and voters
>can be represented by points in some space so that a voter prefers
>candidate A over Candidate B iff the voter is "closer" to A than to
>B?

The idea of a selection space is appealing. If we consider a space 
consisting of dimensions corresponding to "issues," which must be 
defined quite generally, and which would include every possible 
characteristic of a candidate which would influence the choice of the 
voter, with the scale of each dimension corresponding to the 
importance of the characteristic, and we further define 
"characteristic" as being as perceived by the voter, I'd think a 
properly-designed selection space would be pretty accurate in predicting votes.

The problem is that it would predict the choices of that voter, not 
of all voters in general. The problem is this "as perceived by the 
voter," which is individual to each voter. Many politicians, in 
particular, try to distort these perceptions, to cause voters to 
misplace them and their opponents, and these distortions affect 
different voters to different degrees, not only because of differing 
characteristicts of the voters, but also of the accidents of 
exposure: not all voters see all campaign materials.

*However,* if we imagine a perfect election, with every voter equally 
informed and with equal time to consider the issues, and we create a 
composite selection space which averages the dimensions and scales 
across the voters, selection space would not be perfect, but would be 
a first approach to analyzing ideal voter behavior, and therefore 
could be useful in analyzing the behavior of different election methods.

Range Voting allows the expression of one dimension of analysis, 
considering distances. If one takes the selection space of an 
individual voter, and collapses it to a one-dimensional scale, being 
the absolute distance of the voter's ideal candidate from each of the 
actual candidates, Range Voting does represent more accurately the 
preferences of voters, and functions to sum the distances over all 
the voters, in a way. If we assume that distances are proportional to 
perceived benefit, then, Range Voting does produce results from 
selection spaces. If voters vote sincerely, that is, they accurately 
weigh and measure the relative benefits of the election of each 
candidate, and do not distort these results by aiming toward a desired outcome.

I.e., if I think A is 10, B is 5, and C is 0, I don't decide "I want 
A," and therefore vote 0 for both B and C.

There seems to be some wide agreement that Range is a quite desirable 
method, disagreement being mostly on whether or not voters will 
distort their votes like this, or will, as Warren Smith claims, 
generally vote sincerely. While Smith has some evidence to support 
his position, the evidence is not strong, in my opinion, being 
gathered from polls rather than actual elections. Hopefully, in the 
future, we will have actual election results which can be analyzed. 
Nevertheless, before then, Range should certainly be considered in 
election circumstances were most voters can be expected to vote 
sincerely; there are many such contexts. It will be its behavior in 
"hot" contests that will be of broader interest.