Warren, I think I understand the source of our difference in thinking. I haven't been taking "issue space" literally enough.
Or from another point of view, I haven't been thinking of the voters' ratings as a function of position in issue space, but only as a function of their distances from the candidates in any kind of space approximated by a rectangle. For example, the space could be a city with several large lights on high towers like the "moon light" towers they used to have in Zilker Park and other parts of Austin, Texas. Due to budget constraints, only one light can be kept. Assuming for the sake of argument, the more light the better, one's utility for a light will be inversely proportional to the square of its distance from one's residence. If the only issue is how much light, then the issue space is only one dimensional with all of the voters bunched up together at the extreme right. It's hard to see how one would fit the "candidates" into this strictly issue space picture. Another example: Propaganda Space. This is the most relevant space for our current public elections, since the issues are secondary to advertising budget. In propaganda space, proximity to a candidate reflects how much of his campaign propaganda is getting to you. As with my other example it might be impossible to convert a diagram based on this principle into an issue space diagram. However, I think that you are right in taking issue space literally for the purposes of these Yee diagrams, since one of the main purposes of these diagrams is to show what can go wrong with various methods even in the most idealized situations. So I've come around to your thinking for these explicitly issue space diagrams; the voter utility functions should be roughly bell shaped like the one you are using, or perhaps exp(-dist^2/k), where k is the same (at least in order of magnitude) as the variance of the voter distribution. Forest ---- election-methods mailing list - see http://electorama.com/em for list info
