On Thu, Dec 4, 2008 at 1:18 AM, <[EMAIL PROTECTED]> wrote: > Imagine starting with a non-normal distribution with a sharp, infinite > central peak at the origin of a coordinate > system, say with a probability density function given by rho = (1/r)/e^r, > where r is the distance from the > origin.
I wonder would using logarithmic values for sigma give the best 'full' coverage. Sigma lower than a critical value will just give condorcet (or nearest candidate). Sigma greater than a critical value will give the extremist that is closest to the centre. In effect all centerists will be centre squeezed out. For the pathology graph, it might be possible to only test a few points. For example, the star like test could be tested by drawing a few test lines through each candidate position and only computing elections on those lines. If enough test lines were used, it is likely that a pathology would be detected. All the other pathologies will result in a failure of the star-like test. The only exception is the non-convex one and I am not sure if that is actually a problem. Also, if a candidate has no win-region, then it would pass the non-star like test. This means that the using the star-like test would be a reasonable way to compute the pathology diagram. ---- Election-Methods mailing list - see http://electorama.com/em for list info
