Re: [EM] SEC quickly maximizes total utility in spatial model
Jobst Heitzig wrote: Dear folks, earlier this year Forest and I submitted an article to Social Choice and Welfare (http://www.fair-chair.de/some_chance_for_consensus.pdf) describing a very simple democratic method to achieve consensus: I looked at it, and have to admit that my math knowledge is not enough to follow it fully in reasonable time. Simple Efficient Consensus (SEC): = 1. Each voter casts two plurality-style ballots: A consensus ballot which she puts into the consensus urn, and a favourite ballot put into the favourites urn. 2. If all ballots in the consensus urn have the same option ticked, that option wins. 3. Otherwise, a ballot drawn at random from the favourites urn decides. This method (called the basic method in our paper) solves the problem of how to... make sure option C is elected in the following situation: a% having true utilities A(100) C(alpha) B(0), b% having true utilities B(100) C(beta) A(0). with a+b=100 and a*alpha + b*beta max(a,b)*100. (The latter condition means C has the largest total utility.) Still, I have the very strong feeling that that claim is not part of your above mentioned paper and also it is not true. Counter-example: a = 40 b = 60 alpha = 10 beta = 99 the condition is true: max(a,b)*100 = 60*100 = 6000 a*alpha + b*beta = 40*10 + 60*99 = 400 + 5940 = 6340 So C does have the largest total utility. Can be sure option C is elected? As far as I remember, the paper doesn't say anything about the decision-making mechanisms in such situations. It always assumes that enough participants prefer this or that above the lottery. But here in your post you didn't say above the lottery, you said has the largest total. And I think in such situation many A voters including myself would prefer the lottery with 40% chance to the 100 value option over the sure 10 value. So C wouldn't be elected. Since then I looked somewhat into spatial models of preferences and found that also in traditional spatial models, our method has the nice property of leading to a very quick maximization of total utility (the most popular utilitarian measure of social welfare): Assume the following very common spatial model of preferences: Each voter and each option has a certain position in an n-dimensional issue space, and the utility a voter assigns to an option is the negative squared distance between their respective positions. Also assume that voters can nominate additional options for any in-between position (to be mathematically precise, any position in the convex hull of the positions of the original options). Traditional theory shows that, given a set of voters and options with their positions, total utility is maximized by the option closest to the mean voter position, but many traditional voting methods fail or struggle to make sure this option is picked. With our method SEC, however, total utility will be maximized very quickly: If the optimal option X located at the mean voter position is already nominated, every voter will have an incentive to tick X on her consensus ballot since she will prefer X to the otherwise realized fall-back lottery that picks the favourite of a randomly drawn voter. If X is not already nominated, every voter will have an incentive to nominate X for the same reason. This makes sure X is elected and thus total utility is maximized. Still I can't comprehend the full mathemathic background, but look at this example: An economic community with a common wealth decides about their future: Option Dismiss: dismiss the community by sharing equally the wealth, and everyone does what she wants with it. Option Salary: work as a cooperative, still common wealth, but members get different payment by their work. Option Equality: work as a classic kibbutz, equal living conditions, no money. The utility for the 40 Dismissists: Dismiss(100) Salary(10) Equality(0) For the 20 Salarists: Dismiss(10) Salary(100) Equality(30) For the 40 Equalists: Dismiss(0) Salary(80) Equality(100) For me it looks here the Salarists are the median voters, and also the Salary option has the largest total. And again, it looks that a typical Dismissist will go for the 40% lottery instead of accepting the low-value compromise. All these don't make the proposals necessarily look bad in my eyes. It looks promising wherever high-value compromises exist, and it looks logical they often do. Peter Barath brbrbra href= http://bookline.hu/news/news!execute.action?id=2942tabname=bookaffiliate=frekaakar9970utm_source=freemail_karakteres_level_aljautm_medium=level_alja_karakteres_kortars_szepirodalomutm_campaign=0910_kortars_szepirodalom; A nagy fogás - kortárs szépirodalom hete - 25-50% kedvezmény /a Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] SEC quickly maximizes total utility in spatial model
Dear Peter, I claimed that SEC... make sure option C is elected in the following situation: a% having true utilities A(100) C(alpha) B(0), b% having true utilities B(100) C(beta) A(0). with a+b=100 and a*alpha + b*beta max(a,b)*100. (The latter condition means C has the largest total utility.) ...to which you correctly replied: Still, I have the very strong feeling that that claim is not part of your above mentioned paper and also it is not true. Obviously, I made a typical copy-and-paste error from an earlier post here. The correct condition under which SEC makes sure that C is elected in the above situation is instead the following: alpha a and beta b This means that all voters prefer C to the Random Ballot lottery. All these don't make the proposals necessarily look bad in my eyes. It looks promising wherever high-value compromises exist, and it looks logical they often do. I think they do exist usually. In the described spatial model they do. Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SEC quickly maximizes total utility in spatial model
Dear folks, earlier this year Forest and I submitted an article to Social Choice and Welfare (http://www.fair-chair.de/some_chance_for_consensus.pdf) describing a very simple democratic method to achieve consensus: Simple Efficient Consensus (SEC): = 1. Each voter casts two plurality-style ballots: A consensus ballot which she puts into the consensus urn, and a favourite ballot put into the favourites urn. 2. If all ballots in the consensus urn have the same option ticked, that option wins. 3. Otherwise, a ballot drawn at random from the favourites urn decides. This method (called the basic method in our paper) solves the problem of how to... make sure option C is elected in the following situation: a% having true utilities A(100) C(alpha) B(0), b% having true utilities B(100) C(beta) A(0). with a+b=100 and a*alpha + b*beta max(a,b)*100. (The latter condition means C has the largest total utility.) Since then I looked somewhat into spatial models of preferences and found that also in traditional spatial models, our method has the nice property of leading to a very quick maximization of total utility (the most popular utilitarian measure of social welfare): Assume the following very common spatial model of preferences: Each voter and each option has a certain position in an n-dimensional issue space, and the utility a voter assigns to an option is the negative squared distance between their respective positions. Also assume that voters can nominate additional options for any in-between position (to be mathematically precise, any position in the convex hull of the positions of the original options). Traditional theory shows that, given a set of voters and options with their positions, total utility is maximized by the option closest to the mean voter position, but many traditional voting methods fail or struggle to make sure this option is picked. With our method SEC, however, total utility will be maximized very quickly: If the optimal option X located at the mean voter position is already nominated, every voter will have an incentive to tick X on her consensus ballot since she will prefer X to the otherwise realized fall-back lottery that picks the favourite of a randomly drawn voter. If X is not already nominated, every voter will have an incentive to nominate X for the same reason. This makes sure X is elected and thus total utility is maximized. Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] SEC quickly maximizes total utility in spatial model
At 07:28 AM 10/26/2009, Jobst Heitzig wrote: Dear folks, earlier this year Forest and I submitted an article to Social Choice and Welfare (http://www.fair-chair.de/some_chance_for_consensus.pdf) describing a very simple democratic method to achieve consensus: Simple Efficient Consensus (SEC): = 1. Each voter casts two plurality-style ballots: A consensus ballot which she puts into the consensus urn, and a favourite ballot put into the favourites urn. 2. If all ballots in the consensus urn have the same option ticked, that option wins. 3. Otherwise, a ballot drawn at random from the favourites urn decides. Well, I find it hard to believe how wrong-headed this is. I won't achieve consensus, ever, unless the society is so connected that it doesn't need to vote! I've found the logic of consensus inexorable: if we want to maximize consensus in a democracy, we must have a society which values consensus. I have no doubt that the method described, in its logic, is quite clever. Unfortunately, people don't play game theory, that's well known; the game-theoretical predictions don't work. In a real society that is large enough, the consensus urn will never choose a winner unless there is a true consensus process already in operation, people will not naturally agree on a large scale, and, while in small organization, 100% consensus is attainable, attaining it in very large ones is next to impossible. With 100,000 voters, at least one of them, even if they all agreed, would accidentally mark the wrong choice. Are write-in votes allowed? In any case, I've come to the conclusion that collective decision-making must be deliberative except as to one aspect, consent. It is traditional in democracies that no collective action can be taken without the consent of a majority. Nothing. Election under Roberts Rules of Order requires a truer majority of marked ballots cast, and the voter can mark on the ballot None of these jerks, and it's a valid ballot even if there is no candidate by that name. It counts in the basis for a majority, *as it should*. It's a No vote on all the candidates on the ballot. And the voter can, similarly, vote for any eligible candidate; normal small-organization ballots don't have names printed on them anyway, they are just blank pieces of paper. (Hence if you don't mark the ballot, it is 'scrap paper' and isn't counted as a ballot, though it may be reported as blank. So Robert's Rules, unless a bylaw permits otherwise, requires repeated balloting until a majority is found. IRV is claimed to simulate this, but actually it simulates repeated elimination, which is not what RR recommends. Voting reformers, I suggest, must understand that Runoff Voting is the most advanced system that is in actual use, it is much better than shallow analysis suggests, and Roberts Rules says why: voters may base their votes in subsequent balloting based on the earlier results. RR does not allow elimination, period. And, in fact, some Runoff Voting implementations allow write-ins. California took this away in a recent decision that voting theorists seem to have completely overlooked, so little attention is paid to Runoff Voting. San Francisco, for the last runoff election, decided to outlaw write-in votes. Very bad idea, and probably politically motivated. Candidate -- who might actually have won the election -- sued. California law requires that write-in votes be allowed in all elections. They decided that a runoff was just an extension of the original election, so that write-ins were allowed in the first round meant that the law was satisfied, so cities were free to prohibit them in the runoff. A loss for democracy, and very bad analysis. All of us know the big flaw of runoff voting, the possible elimination of a compromise winner in the first round, which winner would beat all others in direct face-offs, even by a landslide. Write-ins make it possible for the public to fix the problem. With better election methods, there wouldn't be a spoiler risk in that runoff. But aren't runoffs unnecessary if you have a good method? And there, my friends, lies the real problem. The holy grail has been the best single-ballot method. The method described is best only if it is used by an electorate sufficiently knowledgeable to make the best choices. I might point out that such an electorate could do the same with plurality. The electorate needs to know, to adjust individual preferences to choose the ideal compromise, what everyone else prefers. And how does it do that? It does it with a poll. A poll is another name for an election, only we tend to think of polls as non-binding. There is no single-ballot polling method that will choose a winner approved by a majority, without coercing voters, that's the bottom line. And a winner not approved by a majority may, indeed, be the best possible choice, given
Re: [EM] SEC quickly maximizes total utility in spatial model
Dear Abd ul-Rahman, you wrote: Well, I find it hard to believe how wrong-headed this is. Well, thank you very much. In a real society that is large enough, the consensus urn will never choose a winner unless there is a true consensus process already in operation, people will not naturally agree on a large scale, and, while in small organization, 100% consensus is attainable, attaining it in very large ones is next to impossible. With 100,000 voters, at least one of them, even if they all agreed, would accidentally mark the wrong choice. Of course. The method is not suggested for large groups. The cited paper includes suitable variations for that case (using thresholds and the like). It is traditional in democracies that no collective action can be taken without the consent of a majority. And that precisely makes those democracies undemocratic since it gives majorities the power to ignore minorities. While random choice has an appeal, where deliberation is impossible and where results over many elections will average out, what if 1% of the electorate wants to elect a crazy who will start a nuclear war? Could we afford to take a 1% chance of that? Of course not. But such an option must never appear on a ballot in ANY voting method, since such options could easily reach majority support as well, as history has proven over and over again. Exclusion of such options is a different topic which in my view cannot be addressed by voting methods but must be addressed with legal measures. The rest of your post does not seem to be related to mine, and I wonder how you were able to write this much in such short time. Sorry if I don't have the time to read it. Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] SEC quickly maximizes total utility in spatial model
At 08:58 AM 10/26/2009, Jobst Heitzig wrote: Dear Abd ul-Rahman, you wrote: Well, I find it hard to believe how wrong-headed this is. Forest is no slouch, either. Well, thank you very much. Don't take it personally. You are in the company of experts, too many of them. In a real society that is large enough, the consensus urn will never choose a winner unless there is a true consensus process already in operation, people will not naturally agree on a large scale, and, while in small organization, 100% consensus is attainable, attaining it in very large ones is next to impossible. With 100,000 voters, at least one of them, even if they all agreed, would accidentally mark the wrong choice. Of course. The method is not suggested for large groups. The cited paper includes suitable variations for that case (using thresholds and the like). The method seems simple. It's not. It's quite complex for the voter! I do suggest a possible application. Ballot after ballot has resulted in majority failure. So, this method. That's after voters know the general position of the electorate. Now, if the method requires a majority in the first box, might work. Don't come to a compromise, it's random ballot. (It seems that a factor in the system was misstated. If the threshold for the first box is majority, or possibly some supermajority, it could work, particularly for representation, if there must be single winners. It is a probable improvement on what Alchoholics Anonymous uses for delegation.) Alcoholics Anonymous requires a supermajority for the election of delegates to the World Service Conference from the Regions. 2/3 vote. If, after repeated balloting, they don't get it, the delegate is chosen by lot from the top two. Yes, in some ways it might not seem fair. But consider it a form of proportional representation; minorities get some representation that way. AA is seeking consensus; the Conference is where fellowship-wide consensus is expressed, and a vote there isn't considered to be consensus until it has at least a two-thirds vote, and, according to Bill Wilson, anyway, they will discuss well beyond that point and, in any case, the Conference is only advisory, it doesn't control anything except its record. It is traditional in democracies that no collective action can be taken without the consent of a majority. And that precisely makes those democracies undemocratic since it gives majorities the power to ignore minorities. Sigh. If the majority has the power to ignore minorities without harming itself, it will, and no structure you impose will prevent it. How is this ideal voting method going to be implemented? Against the will of the majority by the technocracy? That is *not* precisely what causes ignorance of minorities, it is ignorance about the value of consensus that causes that. The work of democracy is in the deliberative process, and voting is actually a detail. For efficiency, a majority *may* make a decision by as little as a half-vote margin. It's been claimed that this is arbitrary, but that's not true. Suppose you come to a fork in the road, and you and your company have to decide to turn left or turn right. You could also sit down, jump up and down, or turn back, of course, or start building a new road, there are an infinite number of possibilities, in fact, and it would take an infinite time to consider them all. So what do you do? Well, standard democratic process. It is moved to take one of the forks. If the motion passes by a majority, that's the decision. If the motion fails, it's off the table for the moment. If you have a required supermajority, then you create a bias against the first motion and, as well, a bias in favor of the status quo. I've seen it in consensus organizations. After quite a bit of experience and thought, both with the power of consensus and with the problems, I've concluded that it is the right of the majority to decide when it is ready to decide, and that the majority always has the right of decision. Typically, where not all the eligible voters are assembled, and they might be affected by a decision, there are supermajority rules limiting the power of a majority; generally, the majority cannot close off debate without a supermajority, generally 2/3. In systems that become partisan and that oscillate, there is constant pressure to move that margin down, to increase the power of the majority. But, in the end, the only thing actually restraining the majority is its own wisdom. And if the majority is stupid, the only thing you can do is to try to persuade them. If you try to force them, you become a dictator. The so-called nuclear option in the U.S. Senate proceeds from the rights of the majority over its own process, over interpretation of the rules. Any time a member of a deliberative body considers that the chair has ruled improperly, the member may immediately appeal, and this is a
