Hi, Daniel Radetsky wrote: > On Jan 1, 2008 1:15 PM, Steve Eppley <[EMAIL PROTECTED]> wrote: > > >> Are monotonic methods less manipulable than non-monotonic methods? I've >> never heard any evidence of that. >> > > I'm going to assume that you are not asking something like "For all possible > voting methods and some reasonable manipulability metric, is the average > manipulability of the monotonic methods lower than the average > manipulability of the non-monotonic methods?" For if a method is > non-monotonic, this means that there is a way to manipulate it.
I am not aware of any such cause and effect, since monotonic methods too are manipulable. (For our purposes we can neglect trivial scenarios: dictatorship, fewer than 3 candidates, special cases of voter preferences, etc. The Median Vote method, for example, is feasible only if the alternatives are mapped to a single dimension and is non-manipulable only if the voters' preferences fall within a particular domain sometimes called "single-peakedness.") I asked about "less manipulable." Are monotonic methods less manipulable? Right, I did not have averages in mind. But I don't want to ask the question too narrowly, since I can't predict which lines of thought might shed light on the issue. > If you are > asking whether given the choice between (say) a monotonic, > non-clone-independent method and a non-monotonic, clone-independent method, > all else being equal, then perhaps as you suggest, clone-independence is > more important. However, I was under the impression that one of the goals of > studying voting methods was to avoid having to make this choice. > That was a goal decades ago, until it was concluded there is no perfect voting method. (Take a look at the Gibbard-Satterthwaite manipulability theorem.) For the particular question of whether methods can be both monotonic and independent of clones, the answer is yes. (For instance, MAM, my favorite method.) > In any case, resistance to manipulability is not the only reason to desire a > particular property for a voting system. Another important quality is > transparency: does casting a vote do what the voter thinks it does? A voter > thinks that when he increases his vote for X (whatever "increases" means in > the system in question), he is helping X win. In a non-monotonic system, > he's wrong, or at least not guaranteed to be right. This is bad. Right? > Imperfect, not bad. All else being equal, it's better to be monotonic than non-monotonic. But it does not follow that the best method is monotonic (since all else is not equal). All else being equal, it's more transparent to be monotonic than non-monotonic. It does not follow that the most transparent method is monotonic. Regards, Steve ---- Election-Methods mailing list - see http://electorama.com/em for list info
