Re: [Election-Methods] Challenge: Elect the compromise
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.
(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.
I think we have! The reasoning is this: 55% like A best, 45% like B best.
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. 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.
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...
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.
You suggest not to solve the problem of the Tyranny of the Passionate
Majority? Why? Shouldn't problems be solved?
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). 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.)
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.
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 :-)
Yours, Jobst
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Re: [Election-Methods] Challenge: Elect the comprom ise when there're only 2 factions
Dear Abd ul-Rahman, Okay, here is my solution. The B voters gain some very substantial advantage for the election of C over the favorite of the A voters, who have only a substantially smaller preference for A over C. So the B voters offer something of value to the A voters to compensate them for their loss. That is certainly an interesting proposal. It seems to be based on the assumption that the just solution is to elect A and that in order to get the compromise, the minority should pay for it. Although that would probably solve the problem, this is not how I think society should work: I don't think nearly half of the electorate should pay the other half for getting what is the more just solution in my eyes. Perhaps that is a difference in culture? The original conditions assume commensurability of utilities, No, definitely not! I would never propose such a thing! I only said that those who believe in such measures may interpret the given numbers in that way... Yours, Jobst __ Erweitern Sie FreeMail zu einem noch leistungsstärkeren E-Mail-Postfach! Mehr Infos unter http://produkte.web.de/club/?mc=021131 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Elect the Compromise
Dear Forest, The main thing I overlooked was vote trading. So there are two main devices for solving the challenge: vote trading and randomness. There is a third one! One of the oldest voting methods that have been studied can also solve it at least in part. I wonder who will first see what I mean :-) Jobst suggested a way of combining them: asset voting with random ballot as the base method, so that probabilities are traded. Right. That could solve the problem: With Random Ballot, A and B will win with 55% and 45% probability, respectively. If Candidates A and B agree to trade their power by transferring their complete share of the probability to C, both factions will gain. There is only one problem left: If candidates are allowed to trade also parts of their power, C will not be elected with certainty since then A and B will only offer to transfer a part of their probability large enough so that the other faction will still gain somewhat (details to come). We could also combine them into a DYN version of D2MAC. The basic ballots are DYN ballots. Voters decide Yes/No for each candidate that they feel sure about, and then Delegate the remaining Y/N votes to one of the candidates, presumably their favorite. After all of the Y/N votes have been completed by the proxies, two ballots are drawn at random. If there is a candidate that was (either directly or by proxy) voted Yes on both ballots, then the common Yes candidate with the greatest number of Y's (from the other voters or their proxies) is elected. Otherwise the favorite (i.e. proxy candidate) of the first drawn ballot chooses the winner. That's just an idea meant to stimulate exploration of further possibilities. A very nice idea in my view! One could even let the candidates know what the direct votes are and communicate with each other and let them sign contracts what candidates they will approve of. This would give them also some means of asset trading... Yours, Jobst _ Der WEB.DE SmartSurfer hilft bis zu 70% Ihrer Onlinekosten zu sparen! http://smartsurfer.web.de/?mc=100071distributionid=0066 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Elect the Compromise
Dear Kevin, Hi, It seems to me there might be a use for something like the method that was proposed awhile ago that had to do with offering voters incentives to give sincere ratings. For example, the majority would give the sincere score to their compromise in exchange for their vote having greater effect in reducing the win odds of their least favorite candidate. If they rate their compromise too high, the loss of win odds from favorite to compromise outweighs the value of the corresponding lessened odds of the worst candidate. And vice versa for rating the compromise too low. Hmm, I don't think I understand how this works, either. It would have to be a non-majoritarian method in order to solve the problem, of course. Yours, Jobst ___ Jetzt neu! Schützen Sie Ihren PC mit McAfee und WEB.DE. 3 Monate kostenlos testen. http://www.pc-sicherheit.web.de/startseite/?mc=00 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there're only 2 factions
At 09:16 AM 8/25/2007, Jobst Heitzig wrote: I don't think nearly half of the electorate should pay the other half for getting what is the more just solution in my eyes. Perhaps that is a difference in culture? No. It's an understanding of what utilities mean. If A does not win, the supporters of A lose something. They are in the majority. If each of them grabs a B supporter and wrestles with him, or her, I suppose, the excess A supporters can then arrange things the way they like. A drastic picture, but actually part of the theory behind majority rule. If C wins, the B supporters gain 60% utility, that's large. If they pay the A voters the equivalent of the A loss, 20%, they are still way ahead. It is a very good deal for the B voters and, in fact, the A voters might hold out for more, knowing this. Why shouldn't everyone benefit from the improved result? A free negotiation would effectively generate a bid based on the *real* utilities, and these have been posited as stated. A free negotiation collapses what might be incommensurable utilities into whatever medium of exchange is used. Money is only one option, others are possible. (And, strictly speaking, if it were a Clarke tax, the payment is a reduction in taxes, effectively.) I'm not suggesting that this is practical, but rather pointing out that it is far more fair than we might, with certain knee-jerk responses, assume. We think of plutocracy when proposals like this are floated, but the scale is such that the truly large sums of money that are available to be transferred are mostly contributed by the average person. Jobst regards it as unjust that the majority should be paid by the minority to get an outcome he regards as more just. However, he isn't looking at the utilities, he is simply regarding these numbers as representing, perhaps, some degree of consent. The actual consequences of the election are irrelevant to him. Suppose this is not candidates for office being considered, but actual choices for the community. There are three projects, and it is considered that the community can only afford to build one. Let's even say that there is one project but three *sites*. Which site shall be chosen? If site A is chosen, the majority will find it maximally convenient, site C is almost as good, and site B is terrible. The B faction, the minority faces the reverse situation, Sure, if we have an assumption of equal taxes and all the rest, and if the stated ratings are based, say, on travel cost and value of time spent driving, then site C is the best choice. But this is a democracy. Sure, one can imagine systems where majority rule is not sufficient for making decisions, and many communities use them. Contrary to what Jobst might assume, I have a lot of experience with consensus communities, both positive and negative. My comments about majority rule proceed from that experience, they are not merely theory. However, when you get down to the nuts and bolts of a system, *including how the system is implemented,* majority rule has proven itself to be practical *and* sustainable. Consensus systems get people all excited at first, particularly when they discover that obtaining full consent is not as difficult as many would think, it is exhilarating to sufficiently satisfy *everyone*. However, over years, going through what becomes tedious meeting process to do it gradually exhausts many members of the community, and, further, they start to discover what happens when the status quo favors a minority. Perhaps a decision was made some years back that did not anticipate the full impact it would have. It can't be changed without full consensus. I have seen this be literally oppressive, causing direct harm to a substantial minority (I've never seen it seriously harm the majority, probably because there are certain natural restraints. People can walk away from consensus communities and create standard ones, and sometimes the consensus rules are not legally enforceable. But I'm not aware of any legal tests of that.) Point is, when you don't have majority rule, you have decisions being made by something *other* than the majority, even if it is only the default decision to change nothing. And a determined minority can then hold its right to withhold consent over the rest of the community, in order to get what it wants. Again, it would never, in that context, blatantly do this, but it happens, social dynamics do not disappear in consensus communities. There is nothing magic about 50%, it is simply the point where there are more people on one side than another, there are more saying Yes to a motion than No. Or the reverse. In real communities, other than seriously unhealthy ones, the majority is restrained. It does not make decisions based on mere majority, ordinarily, it seeks broader consent, and deliberative process makes this happen. As an example of how majority rule is modified in
Re: [Election-Methods] Challenge: Elect the compromise
At 09:09 AM 8/25/2007, Jobst Heitzig wrote: Dear Abd ul-Rahman! Range *is* a majoritarian method since a majority can elect whomever it wants by bullet voting. That does not contradict what I wrote. Being a majoritarian method does not make the method Majority Criterion compliant. I did not claim that is does. But the relevant question in the situation I specified is whether the majority 55% can elect A no matter what the B-supporters do or not. No matter what is a pretty big condition. Part of my question is this, and it is often neglected in discussions of election method theory. How will the method itself be determined for this election? What vote is required to choose an election method? Someone like Jobst will imagine, I suspect, that the election method is *imposed* by some benevolent dictator. It isn't a democracy -- majoritarian or otherwise -- if the rules are not subject to free choice. And choice by what standard? Is total consent required, for example, on the rules? What if total consent is required for the election? Again, it's fairly easy to get C. This might, indeed, be Jobst's secret method. Consensus, or some high supermajority, required to complete the election. 60% would do in this election, and, in fact, standard deliberative process is even stronger, requiring a two-thirds majority under normal rules to proceed to a vote, and the C faction would not rest until the motion were amended to choose C. So standard deliberative process would, in fact, satisfy the conditions of the problem. But supermajority consent is itself hazardous for other reasons, and I've mentioned them. Standard rules do give the majority tools that, if it cares enough, it could use to overcome the determined opposition of a minority like 45%. But it won't use them in a situation like this, if the preferences are accurately stated and commensurable. I gave an example where they would not be, but if we assume that they are, then generally the majority would not care enough to take the risky move of bypassing the normal rules. The majority knows that those rules are there to protect everyone, not just this particular minority, this time. Majority rule in aggregative systems is oppressive, which is why few seriously propose pure aggregative, direct democracy. However, in the context of full deliberative context, it is crucial, for, in fact, the alternative to majority rule is not supermajority rule or consensus, it is minority rule, where the status quo favors the minority. How do you come to that conclusion? Experience and theory. Well, if the status quo favors the minority, it is obvious. If a minority can block decision, no matter how important, then the majority is powerless to rectify what may be even severely oppressive, as the situation has developed. And who decides what is important? Some consensus communities incorporate a circuit breaker to ameliorate the problem. One, for example, provided that, after certain process had been exhausted, 80% of the property owners (it was a cohousing community) could vote to bypass the consensus rule. But, of course, this merely requires that the faction holding out is not 20%. It ameliorates the problem, but does not fix it. There are of course other alternatives, as the solution of the stated problem will show. We'll see. Majority rule is the foundation of deliberative democracy. No. Democracy means the people rule, not a mere 51% of the people. I wrote deliberative democracy, which means that the *deliberation of the people rules*. Not the people simply voting. Deliberation requires process and process requires constant decision-making. How are these decisions made? Is consensus or supermajority required for all of them? This is difficult enough when there are only, say, twenty people in the community. Try this trick with 200 or 2000. Without DP, forget it. And with DP, how would the assembled proxies make process decisions? Would they have to debate every decision? Robert's Rules are the operating foundation of deliberative democracy, they are a codification of common law, based on the actual practice of deliberative assemblies -- peer assemblies, with the freedom to make their own rules -- the world over, though, mostly from western culture, to be sure. If you have to debate the question of whether or not to close debate and proceed to whatever decision-making process is going to be used, well, Robert's Rules does not allow debating Previous Question. To do so would defeat the purpose. Similarly, there are other motions that are not debatable. A majority is the *bare minimum* by which a deliberative body makes certain decisions. Some decisions, including the very important Previous Question, require a two-thirds majority. The relative guarantee of full deliberative process, and the procedural protections involved in Previous Question, mean that a vote is not taken until a
Re: [Election-Methods] Challenge: Elect the compromise
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
Re: [Election-Methods] [EM] A more efficient strategy-free ratings-based method than Hay voting
Jobst, It was Hay Voting that I was referring to. Maybe this post contains the desired answer to your puzzle? Kevin Venzke --- Jobst Heitzig [EMAIL PROTECTED] a écrit : Dear Forest, you wrote: I have one question, though. If best strategy is to report true utilities, then what do you mean by encouraging compromise? You must mean compromise in the outcome as opposed to compromise in the ballots. That's true. By compromise I mean the transfer of two voters' share of the winning probability from their favourite options to a common compromise option in case that transfer increases both voters' expected utility according to the ratings they provided. In other words, you want the lottery to favor centrist candidates as much as possible without giving incentive for the voters to compromise through distorted ratings. Is that right? I'm not sure. My intention was just to construct a democratic (in the sense of equal power for all voters) method under which it was optimal to reveal true utilities and which was hopefully more efficient than both Hay voting and Random Ballot. Having studied D2MAC before, the idea was natural to use two randomly drawn ballots for this. The third drawn ballot is only used for providing the potential compromise option in a clone-proof way, so that the whole method becomes clone-proof (another advantage over Hay voting). Of course, it would be even more efficient to not draw the potential compromise option at random (by means of a third randomly drawn ballot) but try to find a best compromise given the first two randomly drawn ballots, and also to try to find optimal instead of random numbers x,y for the probability transfers. That would however destroy the incentive to vote sincerely and introduce strategy. Jobst From: Jobst Heitzig Dear friends, Hay voting was supposedly the first known method under which it is always optimal (as judged from expected utility) to vote sincere ratings (i.e. ratings proportional to true utility). However, it seems that it is a rather inefficient method (as judged from total expected utility), even less efficient than Random Ballot. Here's a different, more efficient method under which it is also always optimal (as judged from expected utility) to vote sincere ratings. It is also based on Random Ballot, but in a very different way. It is essentially a Random Ballot method with an added mechanism of automatic cooperation for compromise. The basic idea is that when there is a pair of ballots showing preferences A...C...B and B...C...A, those two voters can profit from cooperating and transferring part of their share of the winning probability from A and B to the compromise option C. Here's the method, I call it... RANDOM BALLOT WITH AUTOMATIC COOPERATION, Version 1 (RBAC1): Voters rate each option. Three ballots i,j,k and two numbers x,y between 0 and 1/2 are drawn at random. Assume that the top-ranked options of i,j,k are A,B,C, and that i and j have assigned to A,B,C the ratings ri(A),ri(B),ri(C) and rj(A),rj(B),rj(C), respectively. Now check whether the inequalities y * (ri(C) - ri(B)) x * (ri(A) - ri(C)) and x * (rj(C) - rj(A)) y * (rj(B) - rj(C)) both hold. If so, elect A, B, or C with probabilities 1/2 - x, 1/2 - y, x + y, respectively. Otherwise, elect A or B each with probability 1/2. Why should it be optimal to vote sincere ratings under this method? Consider an arbitrary voter i with favourite option A, and some arbitrary options B,C and numbers x,y between 0 and 1/2. Let us designate the A,B,C-lottery with probabilities 1/2 - x, 1/2 - y, x + y by L, and the A,B-lottery with probabilities 1/2 and 1/2 by M. The only thing i can do about the election outcome is by influencing whether or not her inequality y * (ri(C) - ri(B)) x * (ri(A) - ri(C)) holds, and the only situations in which this matters at all are those in which i is among the first two drawn ballots, the other of the two has B top-ranked, and the third has C top-ranked. As it is equally likely for i's ballot to be drawn as the first or the second ballot, and as i cannot influence whether or not the other inequality x * (rj(C) - rj(A)) y * (rj(B) - rj(C)) holds, i would therefore want her inequality y * (ri(C) - ri(B)) x * (ri(A) - ri(C)) to hold if and only if she prefers lottery L to lottery M. But the latter is the case if and only if y * (ui(C) - ui(B)) x * (ui(A) - ui(C)) where ui(A),ui(B),ui(C) are i's evaluations of the true utility of the options A,B,C. Now x and y were arbitrary numbers, so the only way to get this equivalence is to put ri(A),ri(B),ri(C) proportional to ui(A),ui(B),ui(C), and perhaps adding some irrelevant constant. Q.E.D. Note that it doesn't matter from which precise
