2011/6/25 Kristofer Munsterhjelm <km_el...@lavabit.com> > Jameson Quinn wrote: > > Wait.... is that a global randomization, used across all votes? If it >> is... or in fact, even if it isn't... I suggest you do what Warren >> suggested, and run it several times, with different random seeds, to see if >> the results are reasonably stable. >> > > The way my program works, it deals with candidate numbers instead of names. > The standard way to map numbers to names is to call the first named > candidate 0, the second candidate 1, and so on. What I did was populate an > array idx with 0...n, randomly permute it, then the first named candidate is > idx[0], the second named candidate is idx[1] and so on. > > That's a global randomization because the program just sees numbers. If > it's being unfair based on the numbers, it won't be unfair based on the > candidate names since the mapping has been randomized. > > I could try reseeding many times, but I'd have to find a way of presenting > the outcome. Say, for instance, that we have a multiwinner situation where > six candidates are to be elected out of ten. The outcome is so that A and B > are always in the result, but then the other four are randomly picked from > [C-J] with every combination equally likely. How would I output that result? > Printing them all would take a lot of space (8 choose 4 = 70). Should I just > pick the outcome that happens most often, and break randomly if there's a > tie? > > More interesting would be statistics on how many results you got, how common the most-common one was, and similar. (How common the second-most-common one, the median one...)
Actually better would be to randomly break the ties on each ballot before feeding it into your algorithm. I suspect that this would be more stable than your global randomization, because there are more potential permutations and thus a greater chance that they cancel each other out. 20-100 runs should be enough to start to get a feel for how stable the results are. (Of course, I don't know how easy that change would be in your program... but if you wanted, I could make and send you a file where I do those permutations 100 times.) JQ
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