[EM] Yee-Bolson Diagrams for Lotteries

[fsimmons at pcc.edu]

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