2012/9/6 Michael Ossipoff <[email protected]> > On Thu, Sep 6, 2012 at 9:49 AM, Jameson Quinn <[email protected]> > wrote: > > > MJ's chicken dilemma is incontrovertibly less serious than Score's, and > > arguably less than Approval's. > > Maybe that depends on one's arbitrary choice among the sets of elaborate > bylaws. > > But let's take an obvious and natural interpretation, and try it in > the original Approval bad-example: > > Suppose a majority rate A at 0, and the rest rate A at s100. What's > A's median score? Well, if the right number of those zero-raters had > been a little more generous, and had given A a millionth, and one had > given A 1/2 of a millionth, you could establish A's median at 1/2 a > millionth. > > Therefore, if a majority of the voters rate A at an extreme, then it's > obviously fair and right to call that extreme hir median. > > What if a not quite a majority rate B at zero, and a sub-majority rate > B at max, and the rest rate B at N? > > An argument similar to that above shows that B's median should be taken as > N. > > Now, let's try that in the original, standard Chicken Dilemma: > > Sincere preferences: > > 27: A>B > 24: B>A > 49: C > > Actual MJ ratings: > > 27: A100, BN, C0 > 24: B100, A0, C0 > 40: C100, A0, B0 > > What are the candidates' MJ scores, by the above interpretation? Who wins? > > MJ scores: > > A: 0 > B: N > C: 0 > > B wins. The B voters' defection has worked. The B voters have easily > taken advantage of the A voters' co-operativeness. >
This defection would "work" in Score (or probabilistic approval) as well. That is, if the B voters commit to defect, the A voters have a choice of making N high enough to elect B (submit to the extorsion) or not (retaliate spitefully). In general, scenarios with solid blocs of voters are convenient for illustrating the possibility of a pathology, but not good for comparing the likeliness of that pathology. For that, you need a more sophisticated model, like http://rangevoting.org/MedianAvg1side.html. This shows median doing better. In practice, in MJ both factions could rate each other's candidate at 1 (the second-from-bottom rating). This would mean that any further defection would be risky, and yet the correct candidate (A in this case) would win naturally. >> For computations in the count: I'd argue that it's actually easier to > carry > > out in practice than Score. Even more so if you consider CMJ. > > With Score, you add each ballot's rating of X to X's total. > > With MJ, if one or two newly-counted ballots rate X above hir current > median, then you must raise X's MJ score to hir rating on the ballot > with the lowest X-rating above X's median (or maybe to the mean of two > such ballots?). > > That means you have to go through the ballots again, to find the one > with the lowest X-rating above X's median. ...unless you've sorted > all of the ballots, by their ratings, for each candidate. > > You don't think that's a lot more computation-intensive than Score? (see > above). > > Yes, but that's totally the wrong way to do it. You don't keep a running track of the median as you count, you simply tally each rating for each candidate. (Note that part of the definition of MJ is that you use a limited number of non-numeric ratings, so it's more like A-F than 100-0; a manageable number of tallies.) Once you have the tallies, computing the median (and the MJ or CMJ tiebreakers) is easy. And tallying is easier, less error-prone, and more informative, than a running total as in Score. > Michael Ossipoff >
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