[EM] utility functions for Yee diagrams

[Forest W Simmons]

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