Forest Simmons wrote: > Very well done!
Thanks. I was wondering about my definition for the monotonicity criterion: It seems right but it's limited to methods that base the result on numerical scores (just as the other definitions I've seen seem to be limited to positional voting methods). Is there a definition general enough to take in all classes of methods or does monotonicity have to be defined separately for each class? Also, I noticed a shortcoming in the MC definitions on various web sites. They all seem to be worded along the lines of, "If X wins and you increase the support for X then X still wins," but this seems to require that even if you increase the support for X and Y at the same time, Y will not win. Of course this definition, taken literally, is too strict for any method to meet. I know this is nit-picking, but this definition should include words such as "without increasing the support for any other candidate" after "increase the support for X". I included this condition in my definition. Finally, regarding the Cal IRV site I posted the link to: They claim IRV is monotonic when adding preferences to the end of an incomplete list of preferences. But they are confusing monotonicity over a limited region with compliance to the monotonicity criterion. The monotonicity criterion is not met unless the method is *universally* monotonic. Every definition of the criterion has some words to this effect: For any possible set of ballots, there is no way to modify any subset of those ballots in a way that produces a non-monotonic response. Richard
