[EM] Yee-Bolson Diagrams for Lotteries

[Brian Olson]

I actually already have a mode in my program to run multiple elections  
at each point and average the color of the winners over those rounds.

It doesn't hurt anything to have more than three candidates as long as  
each one gets a color reasonably distinctive from the others. As long  
as each choice has some region where they are dominant, there will be  
a pretty visible blending edge with neighboring choices.

If you want to add new election methods to test, my source is  
available via subversion respository at
http://voteutil.googlecode.com/svn/sim_one_seat

On Nov 12, 2008, at 5:56 PM, fsimmons at pcc.edu wrote:

> It recently occurred to me that in the case of three-candidate  
> elections, Yee-Bolson Diagrams can be
> generalized to lotteries:
>
> In the three candidate case the traditional Yee-Bolson Diagram of a  
> method is a coloring of voter/candidate
> space in which each point of the space is assigned the color (red,  
> green, or blue, say) assigned to the
> candidate that would be elected if the mean of the (standard normal)  
> distribution of voters were at the point
> in question.
>
> To adapt this to lotteries we generalize the color possibilities to  
> all possible hues in the RGB system of
> colors.  In this system  RGB(p,q,r)  is the (full intensity color)  
> that is made up of red, green, and blue in the
> proportion p:q:r .  The respective pure red, green, and blue colors  
> that go with deterministic methods are
> given by RGB(1,0,0), RGB(0,1,0), and RGB(0,0,1).
>
> Ideal deterministic methods yield Yee-Bolson diagrams wherein the  
> colored regions are Dirichlet/Voronoi
> regions relative to the candidate positions.
>
> These ideal diagrams are benchmarks for comparison with diagrams  
> based on other methods.
>
> It seems to me that the (generalized) Yee-Bolson diagram of the  
> Random Ballot method could serve as
> another benchmark.
>
> This idea could be the basis of a good master's degree project.
>
> By the way, for me the most convincing case against IRV is the  
> original paper by Ka-Ping Yee.
>
> See
>
> http://zesty.ca/voting/sim/
>
> Forest