At 09:01 AM 8/25/2007, Jobst Heitzig wrote: >Dear Steve, > > > Although Jobst may not have intended this assumption, I will continue to > > make the assumption that the B minority's preference intensity for the > > compromise C over A is much greater than the A majority's preference > > intensity for A over C. > >Sorry, I had just not read carefully the first time. Of course that >interpretation is consistent with what I had in mind, although I do >not believe that preference "intensities" belonging to different >persons can be compared.
Yet by asserting that C is the best winner, the "just" winner was the word you used, you are doing just that. The problem is that strong preference for one voter may be weak preference for another, particularly when ratings (or utilities) have been normalized such that, for a specific candidates set, max rating and min rating are the same for all voters. Humans are not necessarily rational, but the only theory we have for rational behavior is utility theory, and supposedly irrational behavior may be explainable by hidden utilities. That is, if I have a strong value, as an example, for being "sincere" and "honest," I might vote against my own apparent interests in order to vote "sincerely" or "honestly." Some game theory that does not take into account the matter of being sincere or honest might judge my behavior irrational. Not necessarily. It is fairly obvious that humans do have some kind of utility scaling, it shows in our language about making choices, we "weigh" them. And the experience of making choices can feel very much like hefting objects to see which is heaviest. Most of us would not sit down and calculate, for example, dollar values for various candidates winning an election, but we *could*, and if there were a system in place where votes were bids, having a cost, we *would*. And economic return is, by far, not the only consideration that can nevertheless be measured in, say, dollars. How much would you pay for an election outcome? Suppose you knew that if enough people voted like you, and you got what you voted for, you would have to pay the cost associated with it. That cost could include actual implementation cost plus compensation for losses incurred by others. (If we decide to seize land by eminent domain and build a school, the costs certainly will include compensation for the seized property.) Now, utilities are, by custom around here, stated in positive units. If we are seeking to maximize individual utility or overall utility, that functions well enough. But, in reality, our impression of choices is bipolar, we are attracted by a choice -- and thus would be willing to pay for it, or we are repelled by it, and thus, to accept the choice voluntarily, we would require compensation. Which, for some choices, could be a *lot* of compensation (probably, collectively, dwarfing the resources of the wealthiest person on the planet). (If you knew that you could, with the collective compensation obtained, save millions of lives by, say, allowing the election of Bush at a time like 2000, even though you knew, let's say, that what he will do will cost hundreds of thousands of lives, how would you choose? If you think the answer is obvious, think again. We make choices all the time that involve loss of life for a few, at least. How much do we put into neonatal medical care? We use automobiles, when it is known that there will be a certain level of accidents, and on and on. Actually taking responsibility for the choices we make as a society is *difficult*, which is one reason why, I suspect, people are averse to realizing how much power they have. If we think it is all controlled by *them*, why, we aren't responsible for all the bad stuff that comes down. It's *their* fault.) In any case, a more realistic statement of utilities would be one a scale that includes negative numbers; zero then represents a neutral point, where one is neither attracted nor averse to an outcome. One would not pay for this outcome, nor would one need compensation to accept it. (Except by comparison, which is another matter). This kind of discussion often brings up a huge red herring: that some people can afford to pay more than others, and, allegedly, a Clarke tax would essentially create a plutocracy. The flaw in this is that, almost by definition, the wealthy are few. The wealthy are wealthy precisely because the stand atop a pyramid of people of lesser means. Without that pyramid, their wealth would be meaningless. What would a million dollars, or a billion dollars, mean if there were not people of lesser means willing to work for you or sell you things for that money? Money is a social convention, a means whereby we allocate and distribute power and control. If someone has obtained money, they can then mobilize, with it, certain resources of society as they see fit. We do not, in general, have any agreement, any social contract, that requires us to recognize the value of money, except for debts stated in specific currency. If nobody is willing to shave the Barber of Seville, he cannot compel it with money, he can only offer it. The price someone would charge for that shave is not fixed, in general. (It can be in places, and those are places where there is no democracy, there is, instead, repression and oligarchy and coercion. The actual payment for the shave is in two parts: one, an exchange of currency, and, two, we won't put you in jail.) Studying utility in elections through utilities does not mean that we should actually encourage "sincere voting" by attaching some proportional cost to the votes. Rather, I bring up such things as a Clarke tax and bidding for votes to point out that there *can* be commensurable utilities, and that, indeed, it is these utilities which are maximized by fully sincere, non-normalized votes in a Range system. It is not necessarily the normalized utilities that Jobst fed us. Those are utilities which have been modified to expand the preference strengths for a particular candidate set into a single vote span, the Range in a Range election. > > (I am NOT saying there is a way to measure or > > compare sincere preference intensities or utilities suitable for input > > into a good vote tallying algorithm.) Without an assumption like this, > > we would have no reason to believe C is better than A for the society. Eppley is almost entirely correct. When you say "no way," it raises my hackles a little. There is a way. Not perfect, but a way, and that way is to, precisely, assume that the scales are commensurable, because, on average, they will be. But that does not mean that they are commensurable *in this election*, unless we make the assumption, which is what he did. >I think we have! The reasoning is this: 55% like A best, 45% like B best. Yes. We have that. > Therefore the "democratic benchmark" solution with which we should > compare prospective solutions is the lottery that elects A with 55% > probability and B with 45% probability. The algorithm has not been explained. I'm going to guess that its a pure preference election, and the percentages are assigned to the first preference of that percentage of voters. > Now, all voters prefer C to this benchmark, but only 55% prefer A > to this benchmark and only 45% prefer B to the benchmark. From this > point of view C is a better solution than A is. Do all voters prefer C to the benchmark? It's true that we can neglect the commensurability of utilities here, all that matters is that the utilities are internally useful. The A voters look at this: return for A, 100. Return for B, 0 Return for benchmark, 55 average, Return for C, 80. The B voters look at this: return for A, 0. Return for B, 100. Return for benchmark, 45 average. Return for C, 80. Yes, C is definitely a good bet for all voters. I wouldn't take the risk, myself. "From this point of view," is the kicker, though. The point of view is one which assigns the benchmark based on the number of first preference votes. The result is, certainly, that C is the best choice, *but* we have elsewhere shown that with some real utility patterns, i.e, absolute costs or benefits, C is quite unjust. All voters prefer C to the benchmark, but that does not mean that the outcome is the best outcome. Only if you can establish that the benchmark is fair would this actually work. And clearly it is not, if the normalization of utilities has caused a major loss of information. If the utilities are equally normalized, that is, the full range of preference is the same for all the voters, then the benchmark is indeed fair. But if the B voters, for example, really have very little at stake, overall, and what we are seeing with their utilities is really a small preference range, overall -- as might become visible if there were two more candidates that everyone disliked, one the one side, and that everyone loved, on the other -- and then the A voters actually have a much larger preference range, C could be a very bad choice. In a previous response, I have the example of a choice of site for some public facility. If the votes are distances (inverted Range, lowest total wins), and the A voter ratings were A 0, B 100, C 20, whereas the B voter ratings were A 10, B 0, C 2, we would have the same relative ratings as what Jobst gave us. But the absolute ratings would be quite different. And the optimum choice, overall, would be A. Totals: 55 A 0, B 5500, C 1100 45 A 450, B 0, C 90 ------------------------ A 450, B 5500, C 1190. A is clearly the optimal choice for the community. Sure, the A voters would prefer C to the benchmark. Because the benchmark is quite unfair. >But I hope that also without this kind of reasoning it should be >obvious that a compromise which everybody likes almost as most as >her favourite is a better election outcome than one of the polar favourites... Depends on what "almost" means. Please consider the site choice election I described. It just happens to be a way of describing utilities that makes them commensurable, and it shows how normalization distorts them, making small preferences equal to large ones, sometimes. > > In other words, I believe > > we should confine ourselves to solving the "Tyranny of the Nearly > > Indifferent Majority" but not try to solve the "Tyranny of the > > Passionate Majority." Of course. But the solution is already with us. It is full deliberative process, undertaken in a small group that represents the whole society. Because of various flaws in the system, it does not always work under current conditions, but it *does* work much more often than simple preference analysis would indicate. In a functioning legislature, members *do* work out compromises that bring broad support. This doesn't make for such entertaining news as the issues where they duke it out, eking out a small victory for one side or the other, which is sometimes a pyrrhic victory. But its normal business for most legislatures, most of the time. Recent years have been bad for the U.S. Congress in this respect, though. No election method is going to take the place of this; however, deliberative process can choose and use *any* election method it considers helpful. I've seen polling used to quite good effect, bringing a result where the clear preference of a majority was passed over to select an option that enjoyed, in the end, unanimous consent. It's even possible, here, that the final choice was not the S.U. optimizer, in a simple sense, this was an organization where group unity was highly valued. That is, making a choice that had universal acceptance had *extra* value. So what happened was that the majority shifted its preference when impacted by the knowledge of preference strengths (and the reasons behind the preferences). >You suggest not to solve the problem of the "Tyranny of the >Passionate Majority"? Why? Shouldn't problems be solved? The solution to that problem is education of the majority, and good leadership, not substituting some hidden higher authority, which is the bottom line if election method trumps the consent of the majority. > > In the real world, it is much easier to elect a compromise than Mr. > > Lomax seems to be saying below, because in the real world the set of > > alternatives is not fixed to {A,B,C} by nature (nor by Jobst). "Seems to be" was a correct hedge. It is *often* true that the problems I note with election methods are ameliorated in the "real world" by various factors, typically ones that introduce elements of deliberation. For example, we do not spring elections on voters with no preparation. There is, first of all, the nomination process, which is part of the *real* election system (one which some want to eliminate, thus moving toward pure aggregation, a bad move on principle). And then there is the campaign and public debate. All of this means that there is more than meets the eye, there is no just the final poll to analyze. And then, of course, many voters do vote strategically. They take into account poll information as well as their general sense of how their friends and acquaintances feel. > Most > > procedures allow a very small minority to add an alternative to the set > > being voted on. (Under Robert's Rules of Order, for instance, only two > > people are required: one to propose alternative D and the other to > > "second" the proposal.) Of course, I've noted similar many times. Eppley is referring to the standard process for nomination, in some peer organizations. In others, petitions are required, and it gets dicier, sometimes the "small minorith" is too large, or the process too cumbersome. More often, I mention that standard deliberative process for election by ordinary motion not only allows the equivalent of nomination as mentioned (it just takes two to insert a candidate into the process), but it is also Condorcet compliant. If not for problems of scale, we would not need election methods at all, beyond being able to participate in deliberative process and vote Yes or No on the motions as they appear and are modified to their final form. Since I'm proposing that representation does not require elections, indeed, elections for representation, in the sense of contests where there are winners and losers, guarantee loss of representation; under the current system, it is a reasonable assertion that most people are not represented in our legislatures, other than by representatives chosen by someone other than them. So, if I had my druthers, and I think ultimately I will, though not necessarily in my lifetime, which is getting fairly short, I would make almost all of what we call "election methods" footnotes in history, what people did when they didn't know better. What would remain are two things: pure and full chosen representation in process, where only the most intransigent and isolated of individuals are not represented, *and* direct voting for those who are willing to vote in public (Asset Voting for the rest). Because of the direct voting option, even highly isolated voters are not deprived of their right to consent or not consent to any public action. The other thing that would remain is voting on issues, and among the issues is the election of officers. While election methods can be used to create a nomination, in the end any election must be ratified -- i.e., accepted -- by a majority, as a minimum. Healthy societies would strive to see them accepted by much more than that. >It seems you and Adb ul-Rahman try to convince us that the problem I >posed does not exist in the real world. Well, if you really think >so, I can't help it. No, I think we are pointing out to Jobst some things that he has overlooked, some assumptions that he has made which are distorting. Further, the comment about the real world problems not being so bad was not intended, I'm sure, to say that there was no problem, only that the real situation is not as bad as we might think just from the analysis that has been presented so far. The "tyranny of the majority" is ameliorated by many factors, in actual practice. Logrolling is only part of this. >Anyway, it would be nice if you could still give a hint what kind of >method you would suggest to solve the stated problem *assuming* that >the problem exists :-) Certainly I think I have done that. ---- Election-Methods mailing list - see http://electorama.com/em for list info