[EM] Path Voting Algorithm

[Markus Schulze]

Dear Paul,

you wrote (11 Jun 1999):
> Does anyone have a path voting algorith that they could post here? I'm
> trying to code a MatLab program that runs path voting and Dumais voting
> algorithms. I've just about got the Dumais algorithm figured out. It
> seems that building a pair wise matrix is difficult. Dumais doesn't need
> to build a pair wise matrix so, I've done it a different way.
>     The difficulty in building a pair wise matrix is that even if you have
> a vector (of size C! - almost 40 million with just C=11 candidates)
> which represents the votes how do you code using loops etc so that you
> can add the right elements that produce a particular pair wise entry? It
> might be simpler to have an input matrix where the elements are the
> margins or the borda scores. The columns could represent the candidates
> while the rows would represent each vote. I'm doing it this way for
> Dumais voting (but not creating a pair wise matrix). To get the
> pair-wise matrix, we would iterate over the C(C-1)/2 possible pairs,
> compare and sum. The matrix could then be used compute the (many?!)
> paths to each opponent for each candidate. OK, I'm getting lost now. How
> do you write an algorith that computes all possible paths? Path voting
> seems really hard to code. I hope I'm wrong.
>     I'll work on it this weekend. If anyone has done this work already,
> please e-mail me on this list or at pdumais at powersurfr.com.

What is wrong with that algorithm I have posted yesterday?

Markus Schulze