Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
Jobst Heitzig wrote: Dear Abd ul-Rahman, In a Range poll, social utility is maximized if everyone votes *absolute* utilities, accurately. Only if social utility is defined so that your statement becomes true by definition (and becomes a triviality thus). Absolute utilities means that the utilities are commensurable. Yes, it is a tautology. But it still should be said, because a great deal is written that ignores this. You mean, many people ignore that you choose to define social utility as the sum of individual utilities, while others define it otherwise? Welfare economics, however, does not define social utility as the sum of individual utility, it rather defines social welfare in some more sophisticated ways which we already discussed earlier several times. That is also true. There can be utilities that combine in a nonlinear way. But how complicated do you want to make it? We have enough trouble getting a method in place that will optimize, to the degree that Range does, linear utilities, and many forms of utility *are* commensurable linearly. What do you mean by commensurable linearly? The question is simple, is it better for society when one has 100 and the other 0 or when both have 50. If the latter is considered better for society, then social utility is obviously not the sum of individual utilities. That's what welfare economics is about. Not to insert myself in a private conversation. But, I was under the impression that that an individual utility (Ui) function was usually defined as the log of some trade-able commodity. example Ui = Log($) So by extension welfare economics would still have reason to exist if the social utility (SU)was defined as SU = Sum(Ui) The trick is in my opinion identifying the trade-able commodity, in relation to elections. My guess at place to start would be something like a Gaussian of the distance between a candidate and each voter...or something like that Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
Dear Abd ul-Rahman, I dislike, by the way, describing voters as selfish if they vote in their own interest. That's the default, they *should* vote in their own interest. That is probably a language problem again. I thought selfish was a synonym for acting in my own interest only, is it not? However, the latter was what I meant to say. Yes, it is a synonym for that. However, the implication here is that not only is one acting in one's own self-interest, it is a narrow self interest that does not care if nearly half the electorate ends up with a maximally unsatisfactory outcome, as long as they personally gain a dime. This is actually sociopathy, someone who truly thinks like this and who is not afraid of consequences would slit your throat for pocket change. And yet you think they *should* vote in their own interest? In a Range poll, social utility is maximized if everyone votes *absolute* utilities, accurately. Only if social utility is defined so that your statement becomes true by definition (and becomes a triviality thus). Welfare economics, however, does not define social utility as the sum of individual utility, it rather defines social welfare in some more sophisticated ways which we already discussed earlier several times. What I ended up suggesting was that the problem is resolved if the voters negotiate. It's possible to set up transfers of value (money?) such that the utilities are equalized, and that the benefit of selecting C is thus distributed such that the A voters do *not* lose by voting for C. If they vote for A, they get A but no compensation. If they vote for C, they get C plus compensation. If the utilities were accurate -- Juho claimed that they were *not* utilities, but that then makes the problem incomprehensible in real terms -- then overall satisfication is probably optimized by the choice of C with compensation to the A voters, coming from the C voters. Certainly the reverse is possible, that is, the A voters could pay the C voters compensation to elect A, but it would have to be much higher compensation! I understood this. But I consider it quite absurd that the A voters should be compensated for anything. This is because you refuse to look at the underlying utilities. Because you don't believe in utility, in particular in *commensurable* utilities, you have only preference left, and from the raw preferences it appears that C is the best compromise. I love to look at utilities. I did just that to infer that C is a good compromise in the example I gave. By the same reasoning (which I will not repeat again here) it also follows that C would be *no* good compromise had the ratings been 55 voters: A 100, C 20, B 0 45 voters: B 100, C 20, A 0 Do you still think only the rankings matter? I don't and never did. Indeed, if that is all the information we have, C is the best compromise. But what has been overlooked, which is precisely what makes the arguments about compensation mysterious to Jobst, is that compromise means that all parties lose something, compared to the ideal for them. Yes, *all* parties, that's exactly the point! So no one of them has to compensate the other, since neither can hope to get their will for certain. They have to compromise. After all, that's what societies are about. By the way, compensation is no mystery at all for me, it is simply not justified in the situation at hand. Suppose it is realized before the election that B is not a viable candidate, and we do not consider B at all. What we have left is 55: AC 45: CA What is the optimal outcome? For ranked methods, it is obvious. You think so? May I assume then that your obvious best outcome is the same as mine, namely electing A with 55% probability and C with 45%? Because this would make it quite attractive to all of them to search for a compromise that all would like better than this lottery. (This is how far I got into your post.) Yours, Jobst For Range and selfish voters, it is also obvious. Only the introduction of the irrelevent candidate makes it appear not obvious. But we do have more information than the ranks. *If* we assume commensurable utilities in the original votes, then we can say much more. There is a relative preference strength, commensurable, of 100:80 for the A voters and 80:0 for the original B voters. The majority has a weak preference and the minority a strong one. There is a complication, if this is a real election. The majority will have reduced motivation to turn out, so if we actually get a 55:45 preference in the final poll, the *real* preference would be greater than that, generally. Forcing all voters to turn out warps elections unnaturally, causing true weak preference to become equal to strong preference. The common argument that strong preference is somehow selfish is seriously flawed, because true knowledge will cause strong
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
At 04:19 PM 8/31/2007, Howard Swerdfeger wrote: I believe we have made an abrupt left hand turn with this analogy. buy destroying the eggs, I intended that would happen if you voted in a manner (on any bill) that you did not approve of. I think that instead of you voted he meant your representative voted Let's assume that we are talking about the Asset Voting with direct elector voting allowed proposal. If you don't trust that your proxy will vote in a trustworthy manner, then why not serve, yourself, as an elector, and vote for yourself? Any system where we have representatives who vote on issues will allow our representatives to vote contrary to our desires. What proxy systems allow is for some of us (the public voters, the electors) to vote directly, *and* to have someone to vote for us when we cannot vote ourselves. Not, that my first proxy got hit by the #96 bus going out to Kanata, or some such thing, and I needed a fall back proxy. If your proxy has named a proxy, you have one. Your proxy's proxy. Now, your proxy assignment to the first proxy might, indeed, have a provision that upon the incapacity of your proxy, a different proxy would serve. I don't recommend it, for various practical reasons that I don't care to describe at this point, and I'm not sure I would set up a functioning proxy system that would recognize such, because it *vastly* complicates it. What delegable proxy does is to essentially allow participation by *everyone* through a very simple system of collecting voting power. Make it complicated and well, complicated systems become more vulnerable to various problems. Other things being equal, KISS. You can name a new proxy at any time. With delegable proxy, your proxy has a stand-in, ready to go, at all times, unless your proxy has not named a proxy. Generally, your proxy's proxy will be higher in proxy rank than your proxy, but, at the top, obviously, there comes to be a proxy whose proxy is of lower rank. I would not name a proxy who does not maintain a proxy this is the backup in case of that wayward bus event. And if I don't like that substitution, why, I change my proxy. With Asset Voting / Direct Electors, the members with seats represent you in deliberation, but that is actually not a crucial function; i.e., you are not greatly harmed if something goes awry, for others can represent you in deliberation as well, there are parallel paths. Your member, the seat holding your default votes, will be relatively open to you. However, if we look at DP, which is *very* similar, we can see that voting for the big famous influential person would generally be a mistake. How sure are you of that voting for famous influential person would be a mistake in a liquid/proxy/asset voting system? What factors do you believe would lead to this being the best strategy for most voters? You mean not the best. What delegable proxy does is to set up a bidirectional communications network that centralizes intelligence and distributes advice. It also centralizes advice and distributes intelligence! If you choose the FIP, by definition you are choosing -- unless you are one of a few -- someone who *cannot* personally communicate with you. Thus you lose access. Now, as I've mentioned in the past, what the FIP will probably do is to assign you to someone, whether you know it or not. The FIP will have staff to handle communications with constituents, if they are accepting lots of proxies. So it might not work so badly, but this is the difference: if you choose your own proxy as someone closer to you in level, someone who only is collecting a relatively small number of proxies, not thousands or millions, you will have access, and through this proxy, access to higher levels as well. If you directly choose the FIP, you don't choose the access path, it is chosen for you. If it works, fine! My suggestion: if there is someone you can call, and they answer the phone or get back to you quickly, and you can talk, and you feel heard, and you can understand what they tell you, it's working. And, of course, you either like the results, or, when it is explained to you (you can call up and ask!), you agree that the vote was reasonable, then it is truly working. I just think that all of this is more likely if the proxy is *not* the FIP. Unless you are an almost-FIP yourself. Your vote can and will get there eventually, but it's far more effective to have someone you can talk to. What most people have is a model of a very isolating process, and they think of election methods in this context. They don't think about, Can I call up and talk to my representative? Once a month if I want to? Who do I tallk to if I have a idea that I think worth considering? Did you want me to answer that in context of liquid/proxy/asset voting, or my current democratic system (Westminster system, Canada) or yours? Both. That is, do you have access now, and would
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
This is being cc'd to [EMAIL PROTECTED], a new list for the discussion of FA/DP issues. Those interested in FA/DP, even if only to block this dangerous and unprecedented extension of power to the great unwashed, or, at the opposite end, to save us all from wasting our time with this ridiculous and impossible scheme, is welcome to join. I may have the list set for moderator approval, but, if so, that is only to stop spam. Approval will be routine if the request has a non-robot message in it, such as Give it up! FA-DP is insane and totally impractical. Membership approved. Of course, you are also welcome to join if you think the FA-DP ideas are interesting and just might work, particularly if they become based on something wider than Mr. Lomax's idiosyncratic opinions. In other words, the list is itself a Free Association. Welcome! It really is happening, I am starting to get reasonably common requests to help with setting up one of these beasties in the real world, hence the need to start the list. Thanks for all your support, you might start seeing me less here. And you might not, I don't know. At 08:21 AM 8/31/2007, Howard Swerdfeger wrote: There are two versions of the adage: Don't put all your eggs in one basket, and Put all your eggs in one basket and watch that basket like a hawk! General advise: If you do this, in any respect you must be reasonably certain that if some threat does come to your eggs you have 1. The ability to see the danger coming, 2. The ability to act and move your eggs to a safe location, before danger strikes. even if you watch it like a hawk. That's right. Now, if we have, as described in another post, assigned proxies for all electors -- that's simple, it is part of the required registration process -- then it's not true that all the eggs are in one basket, for if that basket is destroyed, there are clones of the eggs ready to step up They aren't exact clones, of course. As a background, Asset Voting allows you to do something you cannot do with standard election methods in large elections. You can vote for someone you personally know. You will have far more information, not dependent upon media and thus upon possibly manipulated information, about the trustworthiness of this person. And, again, if you don't trust anyone sufficiently, you have two choices that remain: spread the vote out, or vote for yourself. As I've described it, there is no registration fee, you just fill out the papers and are assigned a ballot code. You can use it, you can give it to others and they can use it. And if you pay a nominal charge to cover expenses, like it might be $5, you can have your name listed in a publication of available electors. In my original proposals, you *had* to have the name published in that way. I realized that this wasn't necessary, and it created a small burden for people intending to vote for themselves. The ballot codes of all electors would be available on-line, and they would be public information, the fee is just for costs of a print publication. If you have eggs in many baskets, you may not be able to watch them. FAAV allows you to make the choice, while the ballot remains very simple. I'd probably vote for one, though, because I think know who, quite precisely, represents me, and I can talk to this person. Now, with secret ballot, I could vote for five and then talk to one, it still works. But then I really only know how one fraction of my vote is working Someone who is relatively uninformed about all the possible candidates -- which is pretty braod in Asset, we assume that something very similar to write-in is allowed -- might indeed decide to spread the vote out among a number of candidates, not being sure about whom to trust. But, generally, in my view, the best strategy in asset is to pick the single candidate you most trust. If this is based on knowledge, it's safer than spreading it around. That a candidate is getting a *lot* of votes, though, is a mark against him in Asset! It does make him a target for possible corruption. So that, too, is a factor. I disagree, I would pick a candidate who I think will closely match my voting pattern and would either have direct influence in the debate and framing of the argument, or someone who has a large amount of direct influence over somebody who does. Sure, those are factors. You can vote that way. It's a democracy, purely implemented. However, if we look at DP, which is *very* similar, we can see that voting for the big famous influential person would generally be a mistake. Your vote can and will get there eventually, but it's far more effective to have someone you can talk to. What most people have is a model of a very isolating process, and they think of election methods in this context. They don't think about, Can I call up and talk to my representative? Once a month if I want to? Who do I tallk to if I
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
Sorry about The formatting Its a re post the first one got rejected by the server! Assume all Quotes are down one Level. thanks! Howard Swerdfeger wrote: Put all your eggs in one basket and watch that basket like a hawk! General advise: If you do this, in any respect you must be reasonably certain that if some threat does come to your eggs you have 1. The ability to see the danger coming, 2. The ability to act and move your eggs to a safe location, before danger strikes. even if you watch it like a hawk. That's right. Now, if we have, as described in another post, assigned proxies for all electors -- that's simple, it is part of the required registration process -- then it's not true that all the eggs are in one basket, for if that basket is destroyed, there are clones of the eggs ready to step up I believe we have made an abrupt left hand turn with this analogy. buy destroying the eggs, I intended that would happen if you voted in a manner (on any bill) that you did not approve of. Not, that my first proxy got hit by the #96 bus going out to Kanata, or some such thing, and I needed a fall back proxy. However, if we look at DP, which is *very* similar, we can see that voting for the big famous influential person would generally be a mistake. How sure are you of that voting for famous influential person would be a mistake in a liquid/proxy/asset voting system? What factors do you believe would lead to this being the best strategy for most voters? Your vote can and will get there eventually, but it's far more effective to have someone you can talk to. What most people have is a model of a very isolating process, and they think of election methods in this context. They don't think about, Can I call up and talk to my representative? Once a month if I want to? Who do I tallk to if I have a idea that I think worth considering? Did you want me to answer that in context of liquid/proxy/asset voting, or my current democratic system (Westminster system, Canada) or yours? I also think if you are going to choose someone who has a small number of votes that you are best to split it up, as you are farther down the decision tree and are thus more likely to have your vote perverted away from your desires. but then again after splitting it up my votes would again merge at a higher levelAll roads lead to Rome, after all. Again, I understand that people think this way. But if you really think that your own opinions are sufficiently researched that them being followed up to a high level is important (to you!), then you really should register as an elector and vote for yourself. Then, you might well cast your vote for that important influential fellow. But you might consider, it might be better to vote for someone who has *access* to that fellow, whereas you, with one vote, won't. er.. perhaps you did not understand me. In the above paragraph I never mentioned that I thought my own opinion would be sufficiently researched, on the contrary I would fully take advantage of the proxy nature of voting. I was stating that if I did choose to split my vote that both my proxies might choose not to vote and give there vote to the same person. thus It would have the same effect as if I did not split my vote and instead voted for that super proxy instead. Thus I would come back to the original problem I had or a single point of failure in my personal proxy chain. When the big important fellow votes a way that you don't like, wouldn't you want to be able to talk to him about it? *Maybe he had a reason* that would convince you if the opportunity were there.* Or are you rigid in your own ideas? You have a right to be but it is also dangerously foolish. Now, practically by definition, you can't call the big guy up. But you can call someone who can. which is why I would probably vote for a second rung guy. or a first rung guy if I found one that voted in a way that I approved of. I would not vote for a 3rd or 4th level guy. Cause calling Sue, to ask bob, to tell bill, to leave a message for God that he is not voting the way I like is not going to be effective. besides with 10 people on the first level and 100 on the second it is highly likely that I would find somebody in those 2 levels who vote in accordance with my wishes 95% of the time. I may not have direct access to Level 2 guys but I can switch my vote when I am not happy. Once again, what Asset is setting up is a deliberative system, but some persist in thinking of it as an election method. It's understandable, because if the candidate set is restricted, it looks somewhat like an election method. But it is much more -- and much less. It depends on being a public process, otherwise there would be no way to negotiate the vote transfers, and it is this negotiation and agreement that makes it work to not waste votes.
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
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
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
At 12:23 AM 8/30/2007, Paul Kislanko wrote: If I understand the meaning of the original example correctly, the answer is Asset voting. Give every voter 100 points. By the conditions given, both the A and B voters think C is 80% as good as their true favorite, so give 5/9 of their points to their favorite and 4/9 to C. A's total is 55 x 5/9 = 275/9 B's total is 45 x 5/9 = 225/9 C's total is 55 x 4/9 + 45 x 4/9 = 100 x 4/9 = 400/9 so C wins. Mr. Kislanko misunderstood the conditions of the problem. One of the conditions was that the voters were selfish. What is to stop tha A voters from giving all their points to A? Range handles the problem quite well if voters vote sincerely. But the A voters, voting sincerely, are voting against their own interests. That's the problem. If they are selfish, they will simply elect A. I dislike, by the way, describing voters as selfish if they vote in their own interest. That's the default, they *should* vote in their own interest. What I ended up suggesting was that the problem is resolved if the voters negotiate. It's possible to set up transfers of value (money?) such that the utilities are equalized, and that the benefit of selecting C is thus distributed such that the A voters do *not* lose by voting for C. If they vote for A, they get A but no compensation. If they vote for C, they get C plus compensation. If the utilities were accurate -- Juho claimed that they were *not* utilities, but that then makes the problem incomprehensible in real terms -- then overall satisfication is probably optimized by the choice of C with compensation to the A voters, coming from the C voters. Certainly the reverse is possible, that is, the A voters could pay the C voters compensation to elect A, but it would have to be much higher compensation! Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
At 08:19 AM 8/30/2007, [EMAIL PROTECTED] wrote: That isn't how asset voting works. You assign your vote to the elector that you most trust. The elector can then assign the vote to any candidate after negotitation. Actually, what Paul wrote about was the original Asset proposal. I proposed Fractional Approval Asset Voting (which might normally mean that voters would vote for one, but they are *allowed* to vote for more than one), to make the ballot practical and simple. In FAAV, if you vote for N, the vote is divided fractionally, as 1/N, to each candidate you vote for. But the original proposal allowed votes to be real numbers in the range of 0 to 1, with the restriction that they sum to one. If that is what we wanted, we would probably normalize the ballots, to avoid problems with math errors. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
At 09:48 AM 8/30/2007, Howard Swerdfeger wrote: In personal economics a diversified portfolio helps reduce risk, I see no reason why in fractional asset should not follow the same logic. by diversifying the people or groups you give your votes to you reduce risk of your vote being corrupted. Well, whether or not it reduces risk depends on the effort you can put into watching how your vote works. There are two versions of the adage: Don't put all your eggs in one basket, and Put all your eggs in one basket and watch that basket like a hawk! If you have eggs in many baskets, you may not be able to watch them. FAAV allows you to make the choice, while the ballot remains very simple. I'd probably vote for one, though, because I think know who, quite precisely, represents me, and I can talk to this person. Now, with secret ballot, I could vote for five and then talk to one, it still works. But then I really only know how one fraction of my vote is working Someone who is relatively uninformed about all the possible candidates -- which is pretty braod in Asset, we assume that something very similar to write-in is allowed -- might indeed decide to spread the vote out among a number of candidates, not being sure about whom to trust. But, generally, in my view, the best strategy in asset is to pick the single candidate you most trust. If this is based on knowledge, it's safer than spreading it around. That a candidate is getting a *lot* of votes, though, is a mark against him in Asset! It does make him a target for possible corruption. So that, too, is a factor. Asset turns traditional politics on its head. Voting for one person is quite practical in Asset, you can even simply vote for yourself, in which case you become a public elector and can participate in the direct democracy of electors. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
I finally figured out what was wrong with this question. The notion that C is a compromise, and even that electing the compromise is desirable, is based upon gathering ballots range-style. I'd suggest that the zeroes in the last column are improbable if C is acceptable to both A and B voters. That all A-first voters like C almost as much as A but don't like B (or all B voters like C almost as much as B but don't like A) is so improbable I can't believe it would happen. Present 100 separate ranked ballots that result in this semi-counted conclusion. -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Jobst Heitzig Sent: Wednesday, August 22, 2007 1:55 AM To: election-methods@lists.electorama.com Subject: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions A common situation: 2 factions 1 good compromise. The goal: Make sure the compromise wins. The problem: One of the 2 factions has a majority. A concrete example: true ratings are 55 voters: A 100, C 80, B 0 45 voters: B 100, C 80, A 0 THE CHALLENGE: FIND A METHOD THAT WILL ELECT THE COMPROMISE (C)! The fine-print: voters are selfish and will vote strategically... Good luck have fun :-) Jobst _ In 5 Schritten zur eigenen Homepage. Jetzt Domain sichern und gestalten! Nur 3,99 EUR/Monat! http://www.maildomain.web.de/?mc=021114 Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
At 07:31 PM 8/29/2007, Paul Kislanko wrote: I'd suggest that the zeroes in the last column are improbable if C is acceptable to both A and B voters. That all A-first voters like C almost as much as A but don't like B (or all B voters like C almost as much as B but don't like A) is so improbable I can't believe it would happen. On the contrary, I gave a travel example that explained the ratings as relative utilities. Then I showed how different absolute utilities underlying the relative utilities could lead to the conclusion that A was the best choice, B was the best choice, or C was the best choice. It's not common that we can determine absolute utilities so easily, but it *is* possible in some cases. And it gives us, I think, valuable information about how election methods behave. For example, where absolute utilities can be known, the majority criterion is almost preposterous. It happens to *usually* indicate the best winner, if a majority winner exists, but it can fail spectacularly. The most cogent objection to Range is not that it can fail MC. It is that it can fail to do what it is purported to do, which is to maximize social utility, and not only from strategic voting, but merely from the normalization that we generally allow as still being sincere. Only if we have a way of encouraging voters to vote *absolute* utilities could we then be assured that Range would reliably elect the social utility winner. However, the extremes I have described are not the usual case. This is where Warren's simulations come in. With reasonable assumptions about absolute utilities for candidates would be formed (I think he has used an issue space model, the point is not whether or not that model is accurate, but only whether or not the utility distributions it generates are reasonably similar to those present in real elections, and that seems likely), we can then use these absolute utilities to judge the performance of election methods. Contrary to what so many claim about Warren's simulations of Range, he does not simply assume sincere votes. Range still performs quite well with various mixes of strategic voters, and, of course, in the extreme, the election has been reduced to Approval, which is not a bad outcome, Approval also performs well, though not as well as Range. So, to me, the interesting question becomes whether or not we can detect what could be called S.U. failure in a Range election. I don't think there is any way to be sure of it, but there are, I strongly suspect, certain signs, and majority failure or the existence of a candidate who beats the Range winner pairwise, would be one. This is *not* a proof of SU failure, it is, however, something that can be associated with it. And so it becomes interesting, then, to test the preferences... by setting up a minor inconvenience in holding a runoff election. Voters with small preference strengths will be less likely to go to the trouble of voting, voters with strong preferences will be highly motivated, and there is more that I've described elsewhere. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions
If I understand the meaning of the original example correctly, the answer is Asset voting. Give every voter 100 points. By the conditions given, both the A and B voters think C is 80% as good as their true favorite, so give 5/9 of their points to their favorite and 4/9 to C. A's total is 55 x 5/9 = 275/9 B's total is 45 x 5/9 = 225/9 C's total is 55 x 4/9 + 45 x 4/9 = 100 x 4/9 = 400/9 so C wins. Election-Methods mailing list - see http://electorama.com/em for list info
