>WDS: Eventually the candidate as he moves away approaches the worst > he can be for you, which is, say, advocating your death, > and then > moving the candidate twice as far away doesn't make him twice as bad > from your perspective, and 10X as far doesn't make him 10X worse. It > only makes him a little worse.
>RBJ: i dunno, Warren. maybe if the candidate advocates for starving, torturing, and then killing your kids and other descendants, relatives. a holocaust for your ethnic group. then fouls the entire environment of your homeland to extract resources for he and his unworthy buddies. but i agree, there might be a limit. --WDS: I think it is clear there is a limit. If he moves a trillion times further away than the cnddt advocating your death, does that make him a trillion times worse? Seems to me it is simply not possible to get a trillion times worse. OK, not convinced? Replace "trillion" with "10^100." The behavior at infinity was wrong. >Venzke: A difficulty with this is that you have to know where this reduction in effect (of distance) occurs in comparison to where the voters are. In other words are there really voters who advocate policies so bad for me that I can't feel any difference among them, while they can? ...Maybe 1 meter isn't twice as good as 2 meters. But maybe 1 mile is twice as good as 2 miles. Within a simulation it's not clear what we're talking about. --WDS: right. That is why I suggest using util=A/sqrt(B+distance^2) where choose the positive constants A,B to get reasonable behavior. I admit "reasonable behavior" is somewhat subjective and depends on the scenarios you are setting up... you've inherently introduced a length scale the minute you actually set up any scenario..., but you can try a few scenarios and make sure to use A,B that do something reasonably sane in them, given the length scale you chose. And by the way, there really IS a length scale, set by the parameters defining "a human life." I contend human utility simply is not scale-free. Let me elaborate a little since not enough people seem to have "got it." In issue space, you are assuming there is some utility that depends only on candidate-voter distance. Once you assume that, there are two questions: (a) What is the right notion of "distance"? (b) Utility is clearly a MONOTONE DECREASING function f of distance, but which f to use? One can make a case L1 distance seems a good answer to (a), at least better answer than L2 distance. Or maybe it ought to be L(1.1). Now I argued re (b) that the function ought to asymptote to a constant at infinite distance and further I even feel it should behave like const/x+const at large distance x. Somebody might complain infinity is not a place of great concern in the real world -- which may or may not be true (actually it might matter a lot) -- but even if we dodge that debate, just getting the right QUALITATIVE behavior for f seems important at the least to prevent you from looking like a total moron. And also I argued utility ought to be a SMOOTH (e.g. everywhere differentiable) function of location. My selection of the formula f(x) = A / sqrt(B+x^2) for some constants A>0, B>0 was not because it was written on a gold tablet from God, it was simply because this was the simplest formula I could think of that obeys the desiderata I just mentioned about behavior at infinity, smoothness, and monotone decreasing. The attempted formulas f2(x) = A/(B+x^2) f3(x) = exp(-x^2) f4(x) = A/(B+x) f5(x) = -x f6(x) = -x^2 f7(x)=sin(x) would fail to satisfy because of too-fast asymptotic at infinity, ditto, nonsmooth corner at 0 distance, wrong behavior at infinity and corner, wrong at infinity, and nonmonotone respectively. IEVS by the way uses my f-formula and also has Lp distance with user-choosable p. I'd recommend Venzke also do that, plus if he wanted to keep his present thing he could rename it "expected distance" rather than "utility." In a sense Venzke is redoing IEVS his own way independently. That's good since it is good to have independence and also he's putting in different voting methods and different strategizing/polling. Hopefully his results will mostly agree with mine/IEVS, but hopefully also he will find something new. >Venzke: It's pretty clear to me that if you just toss out candidates randomly, RangeNS will usually win. It just happens that in the scenarios I pick out as being of interest to me, RangeNS isn't usually winning. So I would like to investigate this to find exactly what are the circumstances that cause methods like Bucklin or DAC to prevail. --well, if you can somehow understand what is "interesting" and bias your distribution toward interestingness (and somehow justify that biasing as being realistic, otherwise it is just data fudging) then you might find RangeNS is no longer best. I cannot say at present. I still think at some point you have to settle on some distribution also you can make a recommendation of some voting system. IEVS include an option to use what I call "reality based distributions." That is, there is a database of about 100 real world rank-ballot elections. You can download my dataset to make your own yourself, see http://rangevoting.org/TidemanData.html and if you do it'd be nice to place whatever cleaner nicer bigger set you get, back on that CRV webpage. Anyhow, IEVS uses a somewhat cheesy hack to generate "randomized perturbations" of the real elections to get an infinite set of reality-based fake elections equipped with reality-based utilities. Anyhow, roughly speaking, using the reality based distribution rather than more simpleminded distributions (which IEVS also has) in practice does not seem to make much difference to my BR results. Roughly speaking the same results come out. But anyway, glad to hear Venzke's sort-of-endorsement of range voting. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
