[EM] Simple Election Methods and Geometry

[Alex Small]

Kevin Venzke wrote:
>Thanks to information from Forest, I was able to write a program that plots winners
>in a pyramid (a slice of which can be viewed at a time), for three candidates and
>4 of the 6 ballot types at one time.
 
I'd be interested in trying that program if it's available.
 
>In my program, I have implemented this rule as "Approval." (There is no requirement
>to vote for a 2nd, correct?)

I should have been more explicit in my definition of the method:  You indicate a complete ranking of all 3 candidates and the top 2 candidates each get 1 point.  I specified at the beginning of the post, for simplicity, that equal rankings aren't allowed.  This isn't a value judgement about whether it's better to have a method that allows equal rankings (I've seen too many debates about that on this list), it's just a way to simplify the analysis.  I figure if I can first get a handle on the geometry in 6 dimensions, then it will be easier to add in equal rankings (add more dimensions).
 
>Actually, "If no CW, Random Candidate" is probably the best.
 
Well, the geometric approach that I'm using to analyze elections isn't really capable of handling "random candidate" because my approach assumes that the winner is uniquely and deterministically specified by the number of people submitting each type of ranked ballot.
 
Again, there are people on this list who would argue that my analysis does not encompass every conceivable question or election method that one might be interested in, and I agree.  In particular, it is useless for analyzing Approval Voting (well, standard Approval Voting anyway) because Approval Voting is not a ranked method in the sense of my geometric approach.
 
Anyway, I'd be interested in seeing your software if it's available.
 
 

Alex

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