Mr. Kislanko wrote directly to me, which I prefer not be done unless there is a specific reason for a personal communication, immediately disclosed. I'm responding to the list.
At 12:35 AM 8/31/2007, Paul Kislanko wrote: >Any question about what method works that is turned into how a question >about how humans behave is per-force an exercise in navel-gazing. In a word, nonsense. How humans behave is relevant to election methods, or else we'd just do Range and leave it at that. Or Plurality, for that matter (if humans simply talk to each other and agree on what they want, Plurality is generally adequate as a test). >No. The question was what method can elect C if all voters vote their >natural selfishness, which is 55% A 100 C 80, 45 percent B 100 C 80. I generally consider election methods in the contexts where they are used. There is no question about what happens with various methods if people vote according to known algorithms. However, they don't, at least not according to a single fixed algorithm. People use various algorithms to turn preferences into votes, they do it with various degrees of knowledge of the election context (i.e., election probabilities), etc. The problem did not describe the "natural selfishness" of the voters as those ratings. Rather, it described this as their sincere preferences, and that was further clarified using comparison with a lottery, i.e., if we assume rational behavior, then those values would explain their choices in picking a certainty of an outcome against a lottery with those odds. What "selfish" refers to would be the behavior of any faction of the voters in attempting to secure their favorite outcome, by voting "selfishly," i.e., strategically, *not* by voting their sincere preferences, unless strategy indicates that. Thus the problem boils down to selecting a method which would encourage them to vote their sincere preferences, or to otherwise respond such as to discover those preferences, even in the face of a majority attempting to defeat picking the compromise C in order to gain some preferential benefit for themselves, in the face of an apparent strong preference by a minority. >If they vote as described in the (highly unlikely) conditions, then any >method that allows them to split votes 5/9 favorite 4/9 second favorite >solves the problem. > >All of the rest of the discussion related to this problem is noise. No, though if Mr. Kislanko is correct, it would be error. Error is not noise. In fact, if you cannot express an error condition (and discover it, of course), you cannot correct your course. When we write erroneously to this list, it is not noise, it is *information* about our own incorrect understandings, and thus highly useful. It's only noise if you don't care about human beings, but only election methods. That may be true for Mr. Kislanko, but it's not true for me. Is he correct? If the A voters know their position, why would they give 4/9 of a vote to their second choice? As I've pointed out, the gap between the A voters' first choice and second choice could be quite large, in absolute terms. B would be practically suicidal (so to speak), and C is only proportionally better. The 20% reduction in preference suffered by the A voters in the selection of C might be greater in absolute terms, for each member of the A faction, than the 80% gain in utility for each of the B voters. What this means is that C might *not* be the just outcome, in spite of the apparent situation, even if the ratings given are sincere and rational. The lottery method of testing the ratings will confirm sincere *relative* ratings, not absolute ones. On the other hand, a Clarke tax, on the one hand, or, on the other, free negotiation between the factions for compensation to a faction which loses value from an outcome, would determine commensurable utilities. If these means, or similar, confirm that the ratings given may be treated as commensurable (that is, not absolute, necessarily, but covering the same range of absolute utilities for each faction), then we could say, indeed, that C would be the just outcome. Another way to put this is that if the outcome of the method, with the given relative preferences, is C, it *could* be unjust, a poor outcome. Far from being "highly unlikely," the meaning of which is, however, unclear, the ratings given would be appropriate and sincere for some physical layout of voter locations; perhaps there are two population centers in the town, and a layout of roads such that travel distances to a proposed public facility explain the ratings. A, B, and C, are, of course, locations for the facility. The A voters have travel distances, in km., of A 0, B 100, C 20 and the B voters have travel distances of A 10, B 0, C 2, to give an example where the utilities are sincere but the C outcome is unjust. If we can arrange for the voters to vote absolute utilities in a Range election, the outcome will be just; however, it will not be *fully* just, all by itself, for it this choice does not distribute the benefit of making an optimal choice to all voters. Rather, we can say about the Range winner with these sincere absolute utilities is that this winner is *efficient*, one possible meaning of which is that compensation described to distribute the benefit would be minimized. In the absolute example I gave, there is no C faction. That, by the way, is a rather strong refutation of the IRV proponent's argument that Core Support is an important criterion. C, with commensurable utilities, is clearly the optimal choice, but has no "core support." In this example, A is in the majority, and, as it happens, its choice is optimal for reducing overall travel distance, assuming equal usage of the facility by all voters. Justice, however, would be increased if the A voters were to compensate the B faction for their increased travel time. Majoritarian systems often ignore this. But suppose the utilities are not arranged in this way, suppose that the travel distances are as implied by the original statement of ratings, i.e, 100, 0, 80 and 0, 100, 80, in the same units; i.e., these ratings are commensurable as given. In this case C is the best choice, so the question then becomes, how do we coerce or induce the A voters, as the majority, to given up their preference and suffer a loss? Since I'd prefer to avoid coercion, there is, then, an obvious solution: the B voters offer compensation for the choice of C. Put it another way, a set of payments is negotiated such that, for each outcome, the voters who benefit from that outcome are compensated by the voters who lose value. If we assume that the utilities are inverse from travel costs, including the value of time, then we can determine a matrix of compensations to be paid for all the outcomes, and it will be seen that the choice of C reduces the necessary compensation, since it is the most efficient choice. And I gave an example of how compensation like that is actually arranged in a real organization, Alcoholics Anonymous; there is, for delegates to the annual Conference, a travel equalization plan, where all delegates pay the same travel cost, no matter where they live, into a fund, which is then distributed according to distance or other measure, I'm not sure of the details. Again, that would not be difficult to arrange in a real example as that described, though the political practicality might be another matter; it would, in fact, be simple: all citizens would be paid a subsidy, perhaps as a credit against their taxes, depending on place of residence and the travel distance to the facility, calculated to equalize the rational utilities. Taxes, of course, would be increased and the increase would be borne by all. Thus, other things being equal, such a scheme would distribute the maximized benefit of making the optimal choice, or, more accurately, the reduced overall cost of making the optimal choice. However, the problem with the tax plan is that "other things" are generally not equal. Different citizens may have different values for their time, for example. So a free negotiation, if efficiently done, should be better able to balance true utilities, rather than a central planning kind of approach, unless the latter could somehow deal fairly with the more complex individual utilities. A Clarke tax type of scheme may be one means of doing this, but I pointed out how, even with Plurality, the citizens could negotiate the equivalent, inducing the majority to choose some loss in utility in order to give a minority a greater net improvement. After compensation, all factions would have the same cost or benefit *within their own estimation*, and they would, rationally, sincerely choose the optimal outcome, since that would provide them with minimal cost or maximum benefit over any of the other outcomes. Is it necessary to detail the compensation necessary, or is it enough to provide the basic principles of how it would be done, i.e., equalization of cost or benefit? The problem with the tax-based equalization ---- Election-Methods mailing list - see http://electorama.com/em for list info