[EM] Tiebreaker graphs for Condorcet

[Michael Ossipoff]

Kevin wrote:

Since the preferences in these simulations are based on distance, in
my experience it is so rare as to be unnoticeable that there are either
Condorcet cycles, or disagreements between Condorcet and the social
utility winner.

mrouse had written:

--- mrouse1 at mrouse.com a écrit :
>In addition, if the graph of minimum Bayesian regret were plotted, would
>it simply be a Voronoi diagram, and would it be possible to plot this on
>the Yee diagrams to see where voting methods diverge from it?

Assuming minimum Bayesian regret is the same as minimum average distance
(and highest utility), yes, it's a Voronoi diagram.

I comment:

It can be shown that, if voting is based on issue-distance, and if there is 
no non-spatial disutility (such as infidelilty scandals, etc.), and if 
distance in issue-space is measured by city-block distance, the Condorcet 
winner is always the social-utility maximizer.

If distance is measured by Pythagorean distance (also called Euclidean 
distance), then the Condorcet winner is the social-utility maximizer under 
the condtions always assumed in spatial studies.

It seems to me that, for Pythagorean distance, the condition is this:

There's a point, which could be called the central point, such that, if a 
straight line is drawn through that joint, the voter-population-density 
distribution is symmetrical along the line, with respect to that point.

That condition is met, for instance, by the multidilmensional normal 
distributions or uniform dilstributions used in spatial simulations.

That's not the same as saying that RV will give the same results as 
BeatpathWinner or Schwartz Sequential Dropping (SSD), because one can't 
assume that everyone will vote sincerely in RV.

Mike Ossipoff