2010/6/8 Kevin Venzke <[email protected]> > Hi Warren, > > --- En date de : Mar 8.6.10, Warren Smith <[email protected]> a écrit : > > comments by WDS > > > > 1. I think using utility=-distance > > is not as realistic as something like > > utility=1/sqrt(1+distance^2) > > > > I claim the latter is more realistic both near 0 distance > > and near > > infinite distance. > > Why would that be? Do you mean it's more intuitive? > > > 2. It has been argued that L2 distance may not be as > > realistic as L1 distance. > > L2=euclidean > > L1=taxicab > > That's interesting. I wonder what arguments were used. >
I haven't seen anyone else argue this, but I've always found taxicab distance more reasonable. Separate issue dimensions add linearly. If somebody's going to put/take $3 in/from my left pocket and $4 in/from my right pocket, that's a total of $7, not $5. > > > 3. Your "candidates bolted in place" (in locations selected > > manually) > > at some point needs to be replaced by an outer loop which > > chooses > > their locations from some distribution, and finds average > > bayesian > > regret over all candidate locations. > > If I manually choose locations, I can probably make nearly > > any method look like > > "the best" or "worst" method... that is > > kind of anecdotal evidence > > versus real evidence. > > (Not that the anecdotes are uninteresting.) > > Well, it would be better to cycle over some of the locations, but taking > the average over all possible locations would not be very good evidence > either, since not all locations are equally likely. > OK, so you need to have some probability density function. But systematically, not just by picking scenarios that seem reasonable. > > On the other hand if you select a scenario that seems likely to occur > in practice, I think that is good and useful evidence, especially if you > can't refute your conclusion by changing the scenario slightly. > > If you stick to reasonably realistic scenarios I really doubt you could > find a way to make any method you like best or worst. > > > 4. your results look interesting but I do not know what a > > lot of your > > voting methods are, e.g. QR, VFA, SPST, C//A, etc. > > Too abbreviated. > > Need to supply a key. > > Of these: > C//A: Elect the CW if extant, else the Approval winner. > (Condorcet//Approval) > VFA: This is what you have called Venzke Disqualified Plurality. > Elect the FPP winner except that when more than half of the voters > rank this candidate strictly last, instead elect the second-place FPP > candidate. > SPST: This is the same as VFA except that when the FPP winner is > disqualified, his supporters' preferences are transferred, instead of > simply electing the second-place candidate. > QR: This is a new method by me called Quick Runoff. Elect the candidate > with the most first preferences who does not have a full majority pairwise > loss to the very next candidate in first-preference order. > > There is also CdlA (Conditional Approval) which is a method where voters > gradually add more of their preferences as a result of disliked options > being the vote leader in a "round." > > > 5. some conclusions, like RangeNS is better than IRV and > > IRV-tr and C//A, look > > fairly solid (happen in all your sims*); others, like > > Bucklin is > > better than RangeNS, > > look inconclusive (happen in some of your sims, but reverse > > happens in > > other sims) > > > > *There was one exception, but it had very small regret for > > all methods > > other than MMPO and ApprZIS. > > I don't try to draw many conclusions at this point simply because not > many scenarios have been analyzed. I mean four of the scenarios I posted > were only 1D. And most of the utility differences were very small. > > Kevin Venzke > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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