Re: [EM] The structuring of power and the composition of norms by communicative assent
Juho Laatu wrote: > What would be a typical case where you > recommend public votes to be used? Where the voting system is intended to be in the public sphere, and to serve as the voice of the public - but in that case, there's no alternative. Public opinion can only be expressed in and through the public. As far as votes are part of that expression, the votes must also be public. Habermas relates this anecdote, from history: ^[2] The exclusion of the public from the parliamentary deliberations could no longer be maintained at a time in which "Memory" Woodfall was able to make the Morning Chronicle into the leading London daily paper because he could reproduce verbatim sixteen columns of parliamentary speeches without taking notes in the gallery of the House of Commons, which was prohibited. A place for journalists in the gallery was officially provided by the Speaker only in the year 1803; for almost a century they had to gain entry illegally. But only in the House of Parliament newly constructed after the fire of 1834 were stands for reporters installed - two years after the first Reform Bill had transformed Parliament, for a long time the target of critical comment by public opinion, into the very organ of this opinion. It subsequently lost that role, as mass democracy took hold. It wasn't just the publication of the votes that mattered, but the debates leading up to them. The debates retreated into private negotiations between the parties, and the votes in the house were whipped. Parliament became a theatre once again, with lots of critics and a disinterested audience. > I believe the practice/principle of having > secret votes also often implies interest > in allowing people to vote as they > privately think. Difference between public > and private opinions is thus often seen to > mean some sort of unwanted pressure that > makes people vote some other way than they > really would like to vote. If private and public opinions differ, then which is the manipulated one? Consider state electoral systems that are based on private voting. Every 4 years or so, the state must legitimize its authority. So it takes a poll, sums up the private votes, and presents them as "public opinion". But despite being expressed *in* public, the resulting synthetic opinion is not an expression *of* the public. It's not clear who it belongs to (in its aggregate form), but it seems closer to mass opinion, as characterized by C. W. Mills: ^[4] In a public, as we may understand the term, (1) virtually as many people express opinions as receive them. (2) Public commununications are so organized that there is a chance immediately and effectively to answer back any opinion expressed in public. Opinion formed by such discussion (3) readily finds an outlet in effective action, even against - if necessary - the prevailing system of authority. And (4) authoritative institutions do not penetrate the public, which is thus more or less autonomous in its operation. In a mass, (1) far fewer people express opinions than receive them; for the community of publics becomes an abstract collection of individuals who receive impressions from the mass media. (2) The communications that prevail are so organized that it is difficult or impossible for the individual to answer back immediately or with any effect. (3) The realization of opinion in action is controlled by authorities who organize and control the channels of such action. (4) The mass has no autonomy from institutions; on the contrary, agents of authorized institutions penetrate this mass, reducing any autonomy it may have in the formation of opinion by discussion. > > You and Kristopher went on to discuss how you might solve this > > problem [of coersion] by precluding the possibility of public > > expression entirely (as far as votes go), and falling back to a > > medium of private expression. > > Yes. Or at least by keeping the lowest > layers secret. Even if that design path were a good one, it wouldn't be open to us. We may certainly *allow* for private voting at the perhipery. Some people will want it (maybe many), I agree. But we cannot force it on everyone. We cannot force anything in the public sphere. The most we can do is *omit* to facilitate. But where we omit, others will come along to make up the shortfall. > I don't see how secret voting would > particularly limit public participation. > Public voting maybe automatically > forces/encourages public participation but > secret votes allow that too. People are > also free to tell how they voted even if > their vote was secret. One limitation is > that the voter can not prove to the > candidate that she voted that she really > voter for her. But that also does not > limit public participation. It's true, private voting imposes no effective limits. And mass democracy allows us complete freedom. What's crucial is not what it imposes, b
Re: [EM] language/framing quibble
Good Morning, Juho re: "If there is a common understanding that this (or some other plan) should be implemented then you can do it." That's wishful thinking. Every perversion extant, political or otherwise, runs counter to the 'common understanding'. Optimism is a wonderful trait; an unrealistic expectation is not. Glenn Miller's beautiful rendition to the contrary notwithstanding, wishing will NOT make it so. re: "There have been also idealistic revolutions that have not led to positive results in the long run." I'm not sure what that assertion is intended to mean (it may contain a typographical error). In any case, idealistic revolutions can lead to widely different changes in society. We've mentioned the disastrous results of fascistic and communistic revolts, while, on the positive side, my country prides itself on the major advance in democratic governance that flowed from its revolution. The results of revolutions tend to be dictated by their leaders. As I said in a recent message, "The American Revolution was unusual because its nominal leader had no aspirations beyond the stated aim of the revolution." Unfortunately for all of us, that is the exception rather than the rule. re: "Parties have the potential to be destructive. But I don't see that they would necessarily become destructive at some point." Of course they don't 'necessarily' become destructive. They need a catalyst ... a demagogue ... to send them careening down the path of extremism and destruction. Building on such a foundation is building on quicksand. It guarantees failure, if not because of your party, because of someone else's. It is my opinion that giving any subset of our society greater influence in our government than any other subset is inherently wrong. Unless one is committed to advancing some point of view over other points of view, the purpose of considering political systems must always be to ensure that everyone has an opportunity to participate in the decision-making process. Whether any or all of them are Liberal, Conservative, Catholic, Protestant, Communist, Capitalist, or of any other ideological bent is not important. The important thing is that they, all of them, have an equal opportunity to participate ... whatever their biases. Juho, you and I examined the elements of partisanship in detail several months ago. If you can not see the deleterious effect partisanship has on our world, if you didn't recognize the cause of my homeland's invasion of a sovereign nation, if you are unaware of the politically sanctioned excesses that led to the economic collapse engulfing us, if you haven't noticed the poison flowing out of the middle east for more than 50 years, I don't believe there's anything I can say that will change your mind about a fundamentally flawed approach to democratic government. Fred Gohlke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Generalizing "manipulability"
Hi, Manipulability by voter strategy can be rigorously defined without problematic concepts like preferences or sincere votes or how a dictator would vote or or how a rational voter would vote given beliefs about others' votes. Let X denote the set of alternatives being voted on. Let N denote the set of voters. Let V(X,N) denote the set of all possible collections of admissible votes regarding X, such that each collection contains one vote for each voter i in N. For all collections v in V(X,N) and all voters i in N, let vi denote i's vote in v. Let C denote the vote-tallying function that chooses the winner given a collection of votes. That is, for all v in V(X,N), C(v) is some alternative in X. Call C "manipulable by voter strategy" if there exist two collections of votes v,v' in V(X,N) and some voter i in N such that both of the following conditions hold: 1. v'j = vj for all voters j in N-i. 2. vi ranks C(v') over C(v). The idea in condition 2 is that voter i prefers the winner given the strategic vote v'i over the winner given the sincere vote vi. That definition works assuming all possible orderings of X are admissible votes. I think it works for Range Voting too (and Range Voting can be shown to be manipulable). The following may be a reasonable way to generalize it to include methods like Approval (and if this is done then Approval can be shown to be manipulable): Call C "manipulable by voter strategy" if there exist two collections of votes v,v' in V(X,N) and some voter i in N and some ordering o of X such that all 3 of the following conditions hold: 1. v'j = vj for all j in N-i. 2. o ranks C(v') over C(v). 3. For all pairs of alternatives x,y in X, if vi ranks x over y then o ranks x over y. The idea in condition 3 is that vi is consistent with the voter's sincere order of preference. For example, approving x but not y or z is consistent with the 2 strict (linear) orderings "x over y over z" and "x over z over y." It's also consistent with the weak (non-linear) ordering "x over y,z." Approving x and y but not z is consistent with "x over y over z" and "y over x over z" and "x,y over z." Interpreting o as the voter's sincere order of preference, condition 2 means the voter prefers the strategic winner over the sincere winner. Another kind of manipulability is much more important in the context of public elections. Call the voting method "manipulable by irrelevant nominees" if nominating an additional alternative z is likely to cause a significant number of voters to change their relative vote between two other alternatives x and y, thereby changing the winner from x to y. We observe the effects all the time given traditional voting methods. It explains why so many potential candidates drop out of contention before the general election (Duverger's Law). It explains why the elites tend not to propose competing ballot propositions when asking the voters to change from the status quo using Yes/No Approval. I expect this kind of manipulability to be a big problem given Approval or Range Voting or plain Instant Runoff or Borda, but not given a good Condorcet method. The reason manipulability by irrelevant nominees is more important than manipulability by voter strategy is that it takes only a tiny number of people to affect the menu of nominees, whereas voters in public elections tend not to be strategically minded--see the research of Mike Alvarez of Caltech. Regards, Steve -- On 1/17/2009 10:38 PM, Juho Laatu wrote: --- On Sun, 18/1/09, Jonathan Lundell wrote: On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote: The mail contained quite good definitions. I didn't however agree with the referenced part below. I think "sincere" and "zero-knowledge best strategic" ballot need not be the same. For example in Range(0,99) my sincere ballot could be A=50 B=51 but my best strategic vote would be A=0 B=99. Also other methods may have similarly small differences between "sincere" and "zero-knowledge best strategic" ballots. My argument is that the Range values (as well as the Approval cutoff point) have meaning only within the method. We know from your example how you rank A vs B, but the actual values are uninterpreted except within the count. The term "sincere" is metaphorical at best, even with linear ballots. What I'm arguing is that that metaphor breaks down with non-linear methods, and the appropriate generalization/abstraction of a sincere ballot is a zero-knowledge ballot. I don't quite see why ranking based methods (Range, Approval) would not follow the same principles/definitions as rating based methods. The sincere message of the voter was above that she only slightly prefers B over A but the strategic vote indicated that she finds B to
Re: [EM] IRV and Brown vs. Smallwood
Markus, Do you have any example of FairVote suggesting Condorcet methods might be unconstitutional? I have worked with FairVote for many years, and I don't think they ever made that argument, or that Later-No-Harm failure makes any method unconstitutional (the widely used block plurality method fails L-N-H). I would certainly support a referendum for adopting Condorcet Voting compared to plurality. A nutshell summary of FairVote's position, I believe, would be that PR is the most significant reform, but that for single-seat elections, Condorcet is a theoretically much better method than Plurality, Bucklin or Approval, but like Range Voting, Condorcet has characteristics that make it unappealing to most Americans, and it probably has no chance of being adopted for governmental elections in the U.S., and that the best single-seat reform that has any realistic chance of adoption is IRV. Terry Bouricius - Original Message - From: "Markus Schulze" To: Sent: Saturday, January 17, 2009 9:47 PM Subject: Re: [EM] IRV and Brown vs. Smallwood Hallo, FairVote always argued that Brown vs. Smallwood declared Bucklin unconstitutional because of its violation of later-no-harm. FairVote always claimed that, therefore, also Condorcet methods were unconstitutional. However, the memorandum of the district court doesn't agree to this interpretation of Brown vs. Smallwood. This means that this memorandum is a progress at least in so far as FairVote cannot use Brown vs. Smallwood anymore as an argument against Condorcet methods. Markus Schulze 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: [EM] Condorcet - let's move ahead
Your promotion of IRV discourages for, while its ballots would be valid Condorcet ballots, its way of counting sometimes fails to award the deserved winner (even when there is no cycle making the problem more complex). That the indicated winner could withdraw does not really help, for that candidate does not necessarily know whether IRV has erred. Therefore I still wait to hear from others as to whether MAM deserves backing, though it properly handled your simple cycle example. DWK On Sat, 17 Jan 2009 19:40:35 -0800 Steve Eppley wrote: > Hi, > > [I'm not subscribed to rangevot...@yahoogroups.com, so I won't see > replies posted only there.] > > On 1/9/09 Dave Ketchum wrote: > >> Extended now to EM - I should have started this in both. >> On Fri, 09 Jan 2009 15:40:58 - Bruce R. Gilson wrote: >> >>> --- In rangevot...@yahoogroups.com, Dave Ketchum wrote: >>> We need to sort thru the possibilities of going with Condorcet. I claim: Method must be open - starting with the N*N matrix being available to anyone who wants to check and review in detail. If the matrix shows a CW, that CW better get to win. Cycle resolution also better be simple to do. We need to debate what we document and do here such as basing our work on margins or vote counts. >>> >>> >>> Yes. My biggest gripe with Condorcet is that cycle resolution in many >>> systems is so complex that it does not seem that a typical voter (as >>> opposed to people like us who are personally interested in electoral >>> systems) could understand what is being done. >> > -snip- > > I think there's no need to gripe or fret. Resolving cycles doesn't need > to be complex. Here are 2 solutions. > > 1) The "Maximize Affirmed Majorities" voting method (MAM) is an > excellent Condorcet method and is very natural. Here's a simple way to > explain how it works and why: > > The basis of the majority rule principle is that the more people there > are who think candidate A is better than candidate B, the more likely > it is that A will be better than B for society. (Regardless of whether > they think A is best.) > > Since majorities can conflict like "rock paper scissors" (as shown > in the > example that follows) the majority rule principle suggests such > conflicts > should be resolved in favor of the larger majorities. > > Example: Suppose there are 3 candidates: Rock, Paper and Scissors. > Suppose there are 9 voters, who each rank the candidates from best > to worst (top to bottom): > > 432 > Rock Scissors Paper > Scissors PaperRock > PaperRock Scissors > > 7 voters (a majority) rank Scissors over Paper. > 6 voters (a majority) rank Rock over Scissors. > 5 voters (a majority) rank Paper over Rock. > > By paying attention first to the larger majorities--Scissors over > Paper, > then Rock over Scissors--we establish that Scissors finishes over Paper > and then that Rock finishes over Scissors: > > Rock > Scissors > Paper > > It can be seen at a glance that Rock also finishes over Paper. > The smaller majority who rank Paper over Rock are outweighed. > > Since Rock finishes over both Scissors and Paper, we elect Rock. > > I think that's not too complex. (How did anyone reach the dubious > conclusion that beatpaths or clone-proof Schwarz sequential dropping > will be easier than MAM to explain?) I think the only operational > concept that will take work to explain is that there is more than one > majority when there are more than two alternatives. (Analogous to a > round robin tournament, common to all Condorcet methods, and not really > hard to explain.) Most people already know what an order of finish is, > and I think most people are familiar enough with orderings that they > will recognize the transitive property of orderings when it's presented > visually. > > Jargon terms such as "Condorcet winner," "beats pairwise" and "winning > votes" are unnecessary. Their use may interfere with moving ahead. > > Top-to-bottom orderings are more intuitive than the left-to-right > orientation many other writers use in their examples. Two common > meanings of "top" are "best" and "favorite." Two common meanings of > "bottom" are "worst" and "least favored." In those contexts, "over" > means "better" or "more preferred." Left-to-right offers no such > friendly connotations (except to the "leftist" minority, and the > opposite to the "rightist" minority). Left-to-right becomes even worse > when symbols like the "greater than" sign (>) are used, since a lot of > people are repelled by math symbols. Left-to-right rankings may > interfere with moving ahead. > > 2) One could promote the variation of Instant Runoff (IRV) that allows > candidates to withdraw from contenti
Re: [EM] IRV and Brown vs. Smallwood
Dear Terry Bouricius, you wrote (18 Jan 2009): > Do you have any example of FairVote suggesting Condorcet > methods might be unconstitutional? See appendices 3 and 4 of this study: http://www.lwvmn.org/LWVMNAlternativeVotingStudyReport.pdf Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Schulze ("Approval-Domination prioritised Margins")
I have an idea for a new defeat-strength measure for the Schulze algorithm (and similar such as Ranked Pairs and River), which I'll call: "Approval-Domination prioritised Margins": *Voters rank from the top however many candidates they wish. Interpreting ranking (in any position, or alternatively above at least one other candidate) as approval, candidate A is considered as "approval dominating" candidate B if A's approval-opposition to B (i.e. A's approval score on ballots that don't approve B) is greater than B's total approval score. All pairwise defeats/victories where the victor "approval dominates" the loser are considered as stronger than all the others. With that sole modification, we use Margins as the measure of defeat strength.* This aims to meet SMD (and so Plurality and Minimal Defense, criteria failed by regular Margins) and my recently suggested "Smith- Comprehensive 3-slot Ratings Winner" criterion (failed by Winning Votes). http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html Here is an example where the result differs from regular Margins, Winning Votes and Schwartz//Approval. 44: A 46: B>C 07: C>A 03: C A>B 51-46 = 5 * B>C 46-10 = 36 C>A 56-44 = 12 Plain Margins would consider B's defeat to be the weakest and elect B, but that is the only one of the three pairwise results where the victor "approval-dominates" the loser. A's approval opposition to B is 51, higher than B's total approval score of 46. So instead my suggested alternative considers A's defeat (with the next smallest margin) to be the weakest and elects A. Looking at it from the point of view of the Ranked Pairs algorithm (MinMax, Schulze, Ranked Pairs, River are all equivalent with three candidates), the A>B result is considered strongest and so "locked", followed by the B>C result (with the greatest margin) to give the final order A>B>C. Winning Votes considers C's defeat to be weakest and so elects C. Schwartz//Approval also elects C. Margins election of B is a failure of Minimal Defense. Maybe the B supporters are Burying against A and A is the sincere Condorcet winner. I have a second suggestion for measuring "defeat strengths" which I think is equivalent to Schwartz//Approval, and that is simply "Loser's Approval" (interpreting ranking as approval as above, defeats where the loser's total approval score is higher are considered to be weaker than those where the loser's total approval score is lower). Some may see this as more elegant than Schwartz//Approval, and maybe in some more complicated example it can give a different result. Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] The structuring of power and the composition of norms by communicative assent
Michael Allan wrote: Kristofer Munsterhjelm wrote: The general problem is that if there's a way of finding out what a certain person voted, or whether a certain person voted in a particular way, one can apply pressure to get that person to vote a desired way (to the one applying the pressure). That can be simple coercion, be it formal (in "democratic" countries that aren't fully democratic yet), semi-formal (mob bosses, or "vote this way or you're fired"), or informal (social pressure). The coercion is "do it my way or something bad happens" - it can also easily be changed into "do it my way and something good happens", as with vote buying. If coercion is a problem in this case, then it is strictly a social problem. If the private sphere of individuals, families, employers, and so forth, is restricting the public communications of individuals wrongly, in defiance of the norms, then society itself has a problem in the relations between its private and public spheres. It is not a problem for a voting medium that functions exclusively in the public sphere. The purpose of the medium is to accurately mirror public opinion, and so it must also mirror the distortions, including those caused by private coercion. If people cannot *speak* their minds freely, they ought not to *vote* them either. This connection between speech and voting is especially crucial to a voting system that is based on communicative assent, as I propose here. It is essential that the voters, delegates and candidates all be engaged in mutual discussion. If the votes were not public, then the discussion would die out, and voter behaviour would cease to be informed by communicative reason. You may put it that way, but I think that goes the other direction as well: if it is true that distortions (by carrot or by stick, e.g vote-buying or coercion) degrade the public sphere so that one have to use a secret ballot in ordinary elections, then the distortions will remain when using a method that relies on public sphere information (that is, what you call communicative assent), yet the means of masking that distortion no longer applies, because it's no longer a private matter of voting, but a public one of discussion. Or to phrase it in another way: the distortions of action can be called corruption, since this is really what happens when you're letting the distortions govern how you act when you're supposed to be acting either in accordance to your own opinion, or as an agent of someone else. For obvious reasons, we don't want corruption, and we would seek to minimize it, but it's still a problem. The secret ballot came into use to protect voters from the distortion. Presumably the distortion was real and sufficiently severe to need such measures. If we remove the protection, the distortion will again be uncovered. It may be a problem with society, or with the method, but it'll be there, whatever the cause. None of the above applies to traditional voting mechanisms, of the sort normally discussed here in election-methods. Those mechanisms are not designed for the public sphere. They are designed for the private sphere, opening a private communication channel from individuals to the government. Traditionally, the only communications that become public are those of the reverse channel, in which the voters are informed via the mass media, as a passive audience. Any sort of voter-reconfigurable proxy democracy has the kind of feedback that enables coercion or vote-buying. ... Re vote buying: Although the vote is public and compliance may easily be verified by the buyer, there is no guarantee of *continued* compliance. The voter may take the money from one side, then shift her vote and take it from the other. Vote buying is likely to be a poor investment. The vote-buying effort would, of course, be a this-for-that endeavor. I provide money, you provide the vote - I "buy" your vote. After you've voted, I got what I bought, and I may buy another vote later. Alternately, it can be continual: for as long as you, as a proxy, mirror me, I'll pay you. Stop doing it and I stop paying. In both cases, the vote is the commodity. ... if the conspirators assume law X has near-majority support, they can buy the votes of enough to get a majority, and then pay them if X does indeed pass ... Such a deferred and contingent payment will be unattractive to someone who is selling her vote for a few dollars. She probably wants the money right away. If her payment is contingent on subsequent administrative action by the government - what the buyer really cares about - then the delay is apt to be too long. In a legislative context, for example, the assembly must schedule a separate, in-house vote. The vote buyer must then engineer a massive shift in public votes, just prior to the in-house vote. But caveat emptor, because of the: i) cost of buying votes in vast numbers; ii) risk of discovery in such
Re: [EM] Generalizing "manipulability"
On Jan 17, 2009, at 10:38 PM, Juho Laatu wrote: --- On Sun, 18/1/09, Jonathan Lundell wrote: On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote: The mail contained quite good definitions. I didn't however agree with the referenced part below. I think "sincere" and "zero-knowledge best strategic" ballot need not be the same. For example in Range(0,99) my sincere ballot could be A=50 B=51 but my best strategic vote would be A=0 B=99. Also other methods may have similarly small differences between "sincere" and "zero-knowledge best strategic" ballots. My argument is that the Range values (as well as the Approval cutoff point) have meaning only within the method. We know from your example how you rank A vs B, but the actual values are uninterpreted except within the count. The term "sincere" is metaphorical at best, even with linear ballots. What I'm arguing is that that metaphor breaks down with non-linear methods, and the appropriate generalization/abstraction of a sincere ballot is a zero-knowledge ballot. I don't quite see why ranking based methods (Range, Approval) would not follow the same principles/definitions as rating based methods. The sincere message of the voter was above that she only slightly prefers B over A but the strategic vote indicated that she finds B to be maximally better than A (or that in order to make B win she better vote this way). (I'd use rating/ranking opposite to that. No?) I was making a smaller point, that the actual values in Range and the approval cutoff point in Approval are hard to interpret as "sincere" or not. On the other hand, we need a voter's "sincere" linear ordering of the candidates (ranking?) in order to be able to say whether an *outcome* is better or worse. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hi, On 1/18/2009 10:52 AM, Dave Ketchum wrote: Your promotion of IRV discourages for, while its ballots would be valid Condorcet ballots, its way of counting sometimes fails to award the deserved winner (even when there is no cycle making the problem more complex). I do not promote IRV. IRV+Withdrawal is not IRV. The withdrawal option allows candidates to correct for IRV's tendency to undermine centrist compromise. Candidates would have the incentive to withdraw because they and their supporters would prefer centrist compromises over "greater evils." See the example below. That the indicated winner could withdraw does not really help, for that candidate does not necessarily know whether IRV has erred. I don't see why Dave wrote about the "indicated winner" withdrawing. The point of withdrawal is to allow *spoilers* to withdraw after the votes are cast. Also, it would quickly become clear whether IRV has "erred." The votes would be published soon after the election day polls close. Then the candidates would be given days after the votes are published to decide whether to withdraw. During that period of time, the candidates (and other interested people) can download the published votes and privately tally who will win if no one withdraws and who will win if they and/or other candidates do withdraw. Here's an example to illustrate. Suppose there are 3 candidates: Left, Center and Right. Suppose the voters vote as follows: 40% 5% 10% 45% LeftCenter Center Right Center LeftRight Center Right Right LeftLeft When the votes are published, everyone can see that IRV will elect Right if no one withdraws, and will elect Center if Left withdraws. Since Left and Left's supporters prefer Center over Right, Left has a strong incentive to withdraw, electing the Condorcet winner. Left is not the "indicated winner." The only way Left could win is if both Center and Right withdraw or do not run, which would be crazy. Left is just a spoiler. If Left didn't compete, Center would win outright with 55% of the votes (neglecting the effect of possible changes in voter turnout). Therefore I still wait to hear from others as to whether MAM deserves backing, though it properly handled your simple cycle example. MAM satisfies all the desirable criteria satisfied by Beatpath Winner (aka Cloneproof Schwartz Sequential Dropping--CSSD for short--aka Schulze's method). It also satisfies some criteria that Beatpath Winner fails: Immunity from Majority Complaints (IMC, which is satisfied only by MAM), Immunity from 2nd-Place Complaints (I2C) and Local Independence of Irrelevant Alternatives (LIIA). Furthermore, simulations by several people have shown that over the long run, more voters rank MAM winners over Beatpath winners than vice versa, and a majority rank the MAM winner over the Beatpath winner more frequently than a majority rank the Beatpath winner over the MAM winner. (Those simulations suggest MAM comes a little closer than Beatpath Winner to satisfying Arrow's Independence of Irrelevant Alternatives criterion.) See www.alumni.caltech.edu/~seppley for more information about MAM and criteria it satisfies or fails. An alternate description of MAM is to find the order of finish that minimizes the size of the largest "thwarted" majority, where a thwarted majority is defined as a majority who ranked x over y when the order of finish does not rank x over y. It's been proved that the 2 different descriptions of MAM are equivalent. I'm mentioning this alternate description just in case there are some people who will find it easier to understand. I prefer describing MAM in terms of constructing the order of finish a piece at a time by considering the majorities one at a time from largest to smallest, since I think more people will understand it and that's how MAM is actually implemented in software. (It's computationally much quicker than finding the best order of finish by comparing all possible orders of finish.) As far as I can tell, the reason some groups have adopted Beatpath Winner rather than MAM is because there used to be a website co-written by Mike Ossipoff in which he claimed it will be easier to explain CSSD than MAM. (Mike used the name Ranked Pairs instead of MAM, but he definitely meant MAM, not the pairwise margins-based voting method that Nicolaus Tideman invented and named Ranked Pairs in 1987/1989.) Mike based his conclusion on a few personal anecdotes, which I think can be attributed to his own greater familiarity with the Schwartz set that made him more comfortable explaining in terms of subsets of candidates. (I could forward emails from Mike where he acknowledges MAM is at least as good as Beatpath Winner.) As my previous message about the ease of explaining MAM illustrated, Mike was mistaken about which is easier to
Re: [EM] Generalizing "manipulability"
Jonathan Lundell wrote: On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote: The mail contained quite good definitions. I didn't however agree with the referenced part below. I think "sincere" and "zero-knowledge best strategic" ballot need not be the same. For example in Range(0,99) my sincere ballot could be A=50 B=51 but my best strategic vote would be A=0 B=99. Also other methods may have similarly small differences between "sincere" and "zero-knowledge best strategic" ballots. My argument is that the Range values (as well as the Approval cutoff point) have meaning only within the method. We know from your example how you rank A vs B, but the actual values are uninterpreted except within the count. The term "sincere" is metaphorical at best, even with linear ballots. What I'm arguing is that that metaphor breaks down with non-linear methods, and the appropriate generalization/abstraction of a sincere ballot is a zero-knowledge ballot. Wouldn't it be stricter than this? Consider Range, for instance. One would guess that the best zero info strategy is to vote Approval style with the cutoff at some point (mean? not sure). However, it would also be reasonable that a sincere ratings ballot would have the property that if the sincere ranked ballot of the person in question is A > B, then the score of B is lower than that of A; that is, unless the rounding effect makes it impossible to give B a lower score than A, or makes it impossible to give B a sufficiently slightly lower score than A as the voter considers sincere (by whatever metric). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why the concept of "sincere" votes in Range is flawed.
Juho Laatu wrote: Are you looking for the English language meaning of sincerity or some technical definition of it (e.g. some voting related criterion)? What is the problem with sincerity in Plurality? I'm not Abd, but I think the reasoning goes like this: If people vote according to VNM utilities, then they'll vote their preference among the candidates their vote has some chance of influencing. From such a point of view, "lesser of two evils" would not be strategy, since one would only be able to influence a decision between those "evils" in the first place. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hallo,
Steve Eppley wrote (18 Jan 2009):
> MAM satisfies all the desirable criteria satisfied
> by Beatpath Winner (aka Cloneproof Schwartz Sequential
> Dropping--CSSD for short--aka Schulze's method).
Many people consider the Simpson-Kramer MinMax method
to be the best single-winner election method because it
minimizes the number of overruled voters. The winner of
the Schulze method is almost always identical to the
winner of the MinMax method, while the winner of the
ranked pairs method differs needlessly frequently from
the winner of the MinMax method.
For example, Norman Petry made some simulations and
observed that the number of situations, where the
Schulze method and the MinMax method chose the same
candidate and the ranked pairs method chose a different
candidate, exceeded the number of situations, where the
ranked pairs method and the MinMax method chose the same
candidate and the Schulze method chose a different
candidate, by a factor of 100:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html
Jobst Heitzig made a thorough investigation of the
4-candidate case. In no situation, the Schulze method
and the MinMax method chose different candidates.
("Beatpath and Plain Condorcet are unanimous in all
these examples!") But in 96 situations, the ranked
pairs method and the MinMax method chose different
candidates:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html
There are even situations where the winner of the
ranked pairs method differs from the winner of the
MinMax winner without any plausible reason. See
section 9 of my paper:
http://m-schulze.webhop.net/schulze1.pdf
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hallo, the links to Norman Petry's and Jobst Heitzig's mail have changed. Norman Petry's mail is now here: http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004541.html Jobst Heitzig's mail is now here: http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012838.html Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hi,
I haven't confirmed the results in the articles by Jobst and Norm cited
by Markus, but clearly he has misrepresented their results, since Minmax
(aka Simpson-Kramer) was not one of the methods they simulated in those
articles. They simulated Smith//Minmax, which is a different method
that does NOT minimize the number of voters who prefer a different winner.
Markus also erred when he wrote that Minmax and Beatpath Winner always
pick the same winner when there are 4 candidates. Recall the classic
example that shows Minmax fails clone independence is a 4 candidate
scenario. In that scenario, Minmax elects the candidate outside the top
cycle because the 3 candidates in the top cycle are in a "vicious" cycle
of large majorities. Beatpath Winner elects within the top cycle (as
does MAM).
Minmax's best feature, I think, is its simplicity. Minmax+Withdrawal
would be a fine method, since any of the candidates in the vicious cycle
could withdraw to defeat the candidate outside the top cycle, and at
least one of them would be pressured to do so.
I don't see any validity in Markus' argument that Beatpath Winner is
better than MAM because BeatpathWinner elects the Smith//Minmax winner
more often than MAM does. Simulations support the conclusion that MAM
is better than both: More voters rank MAM winners over Beatpath winners
than vice versa, and more voters rank MAM winners over Smith//Minmax
winners than vice versa. Norm was one of the people whose simulations
corroborated these results.
By the way, http://m-schulze.webhop.net/schulze1.pdf didn't load
properly for me using either Firefox or Internet Explorer. It quickly
crashed Firefox and displayed nothing in IE.
Regards,
Steve
On 1/18/2009 1:18 PM, Markus Schulze wrote:
Hallo,
Steve Eppley wrote (18 Jan 2009)
MAM satisfies all the desirable criteria satisfied
by Beatpath Winner (aka Cloneproof Schwartz Sequential
Dropping--CSSD for short--aka Schulze's method).
Many people consider the Simpson-Kramer MinMax method
to be the best single-winner election method because it
minimizes the number of overruled voters. The winner of
the Schulze method is almost always identical to the
winner of the MinMax method, while the winner of the
ranked pairs method differs needlessly frequently from
the winner of the MinMax method.
For example, Norman Petry made some simulations and
observed that the number of situations, where the
Schulze method and the MinMax method chose the same
candidate and the ranked pairs method chose a different
candidate, exceeded the number of situations, where the
ranked pairs method and the MinMax method chose the same
candidate and the Schulze method chose a different
candidate, by a factor of 100:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html
Jobst Heitzig made a thorough investigation of the
4-candidate case. In no situation, the Schulze method
and the MinMax method chose different candidates.
("Beatpath and Plain Condorcet are unanimous in all
these examples!") But in 96 situations, the ranked
pairs method and the MinMax method chose different
candidates:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html
There are even situations where the winner of the
ranked pairs method differs from the winner of the
MinMax winner without any plausible reason. See
section 9 of my paper:
http://m-schulze.webhop.net/schulze1.pdf
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet - let's move ahead
Hallo, Steve Eppley wrote (18 Jan 2009): > I haven't confirmed the results in the articles > by Jobst and Norm cited by Markus, but clearly > he has misrepresented their results, since Minmax > (aka Simpson-Kramer) was not one of the methods > they simulated in those articles. They simulated > Smith//Minmax, which is a different method that > does NOT minimize the number of voters who prefer > a different winner. When the MinMax method chooses a candidate from outside the Smith set, then the winners of both methods, the Schulze method and the ranked pairs method, differ from the winner of the MinMax method. Therefore, such instances have no impact on the result of Norman Petry's simulations. Steve Eppley wrote (18 Jan 2009): > Markus also erred when he wrote that Minmax and > Beatpath Winner always pick the same winner when > there are 4 candidates. Recall the classic example > that shows Minmax fails clone independence is a > 4 candidate scenario. In that scenario, Minmax > elects the candidate outside the top cycle because > the 3 candidates in the top cycle are in a "vicious" > cycle of large majorities. Beatpath Winner elects > within the top cycle (as does MAM). I didn't write that the MinMax method and the Schulze method always pick the same candidate. I only wrote that, in all of Heitzig's instances, the MinMax method and the Schulze method chose the same candidate (Jobst Heitzig: "Beatpath and Plain Condorcet are unanimous in all these examples!") while, in 96 instances, the ranked pairs method chose a different candidate. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Generalizing "manipulability"
On Jan 18, 2009, at 9:56 AM, Steve Eppley wrote:
Manipulability by voter strategy can be rigorously defined without
problematic concepts like preferences or sincere votes or how a
dictator would vote or or how a rational voter would vote given
beliefs about others' votes.
I appreciate the formalism, and I think we're on the same page. I
note, though, that concepts like preferences or sincere votes are
implicit in the formalism, or at least its consequences, indeed as you
mention below ("… vi is consistent with the voter's sincere order of
preference").
Your second definition requires a little work, or at least we qualify
ballot admissibility to be more restrictive than the voting rule
itself might be. For the purposes of applying the second definition to
approval, we need to rule out (for purposes of the definition) ballots
approval all or none of the alternatives X. Such a ballot satisfies
(3), but it makes approval trivially manipulable (though it's
manipulable anyway).
Likewise, for the generalization to apply to ranked methods, we need
to restrict truncation, perhaps by adding a condition that vi rank
C(v) and better. But that introduces difficulties for the generalizing
to approval.
Let X denote the set of alternatives being voted on.
Let N denote the set of voters.
Let V(X,N) denote the set of all possible collections of admissible
votes regarding X, such that each collection contains one vote
for each voter i in N. For all collections v in V(X,N) and all
voters i in N, let vi denote i's vote in v.
Let C denote the vote-tallying function that chooses the winner
given a collection of votes. That is, for all v in V(X,N), C(v) is
some alternative in X.
Call C "manipulable by voter strategy" if there exist two
collections
of votes v,v' in V(X,N) and some voter i in N such that both of
the following conditions hold:
1. v'j = vj for all voters j in N-i.
2. vi ranks C(v') over C(v).
The idea in condition 2 is that voter i prefers the winner given the
strategic vote v'i over the winner given the sincere vote vi.
That definition works assuming all possible orderings of X are
admissible votes. I think it works for Range Voting too (and Range
Voting can be shown to be manipulable). The following may be a
reasonable way to generalize it to include methods like Approval
(and if this is done then Approval can be shown to be manipulable):
Call C "manipulable by voter strategy" if there exist two
collections
of votes v,v' in V(X,N) and some voter i in N and some ordering o
of X
such that all 3 of the following conditions hold:
1. v'j = vj for all j in N-i.
2. o ranks C(v') over C(v).
3. For all pairs of alternatives x,y in X,
if vi ranks x over y then o ranks x over y.
The idea in condition 3 is that vi is consistent with the voter's
sincere order of preference. For example, approving x but not y or
z is consistent with the 2 strict (linear) orderings "x over y over
z" and "x over z over y." It's also consistent with the weak (non-
linear) ordering "x over y,z." Approving x and y but not z is
consistent with "x over y over z" and "y over x over z" and "x,y
over z." Interpreting o as the voter's sincere order of preference,
condition 2 means the voter prefers the strategic winner over the
sincere winner.
Another kind of manipulability is much more important in the context
of public elections. Call the voting method "manipulable by
irrelevant nominees" if nominating an additional alternative z is
likely to cause a significant number of voters to change their
relative vote between two other alternatives x and y, thereby
changing the winner from x to y. We observe the effects all the
time given traditional voting methods. It explains why so many
potential candidates drop out of contention before the general
election (Duverger's Law). It explains why the elites tend not to
propose competing ballot propositions when asking the voters to
change from the status quo using Yes/No Approval. I expect this
kind of manipulability to be a big problem given Approval or Range
Voting or plain Instant Runoff or Borda, but not given a good
Condorcet method.
The reason manipulability by irrelevant nominees is more important
than manipulability by voter strategy is that it takes only a tiny
number of people to affect the menu of nominees, whereas voters in
public elections tend not to be strategically minded--see the
research of Mike Alvarez of Caltech.
Regards,
Steve
--
On 1/17/2009 10:38 PM, Juho Laatu wrote:
--- On Sun, 18/1/09, Jonathan Lundell wrote:
On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote:
The mail contained quite good
definitions.
I didn't however agree with the
referenced part below. I think "sincere"
and "zero-knowled
Re: [EM] The structuring of power and the composition of norms by communicative assent
--- On Sun, 18/1/09, Michael Allan wrote:
> > I believe the practice/principle of having
> > secret votes also often implies interest
> > in allowing people to vote as they
> > privately think. Difference between public
> > and private opinions is thus often seen to
> > mean some sort of unwanted pressure that
> > makes people vote some other way than they
> > really would like to vote.
>
> If private and public opinions differ, then which is the
> manipulated
> one?
If they deviate it is hard to imagine
that the private opinion would not be
the sincere one.
> > > You and Kristopher went on to discuss how you
> might solve this
> > > problem [of coersion] by precluding the
> possibility of public
> > > expression entirely (as far as votes go), and
> falling back to a
> > > medium of private expression.
> >
> > Yes. Or at least by keeping the lowest
> > layers secret.
>
> Even if that design path were a good one, it wouldn't
> be open to us.
> We may certainly *allow* for private voting at the
> perhipery. Some
> people will want it (maybe many), I agree. But we cannot
> force it on
> everyone.
I think the common practice is to force
privacy on everyone in order to allow
the weakest of the society to keep
their privacy.
> > I don't see how secret voting would
> > particularly limit public participation.
> > Public voting maybe automatically
> > forces/encourages public participation but
> > secret votes allow that too. People are
> > also free to tell how they voted even if
> > their vote was secret. One limitation is
> > that the voter can not prove to the
> > candidate that she voted that she really
> > voter for her. But that also does not
> > limit public participation.
>
> It's true, private voting imposes no effective limits.
> And mass
> democracy allows us complete freedom. What's crucial
> is not what it
> imposes, but what it omits to facilitate.
>
> We can make up for some of its shortfalls by adding a
> voting system to
> the public sphere. A well designed voting facility will:
It is true that public votes help
implementing some features, but in
most typical ("low level") elections
privacy has been considered to be
essential.
Juho
>
> a. reveal the fact of agreement (and disagreement) on
> issues - what
> other people are agreeing to
>
> b. report the quantity of agreement - for and against -
> in definite
> numbers
>
> c. characterize the *quality* of agreement, especially
> the concrete
> options under discussion - exactly what people are
> agreeing to,
> and how the consensus (and dissensus) is distributed
>
> d. open participation to everyone in the community, with
> no formal
> restrictions on age, mental ability, citizenship, etc.
>
> e. help newcomers to join in the discussion by revealing
> the
> existing participants, and showing easy points of
> entry at the
> periphery
>
> f. keep the proximal scale of discussion to a humanly
> mangageable
> size, by organizing it in a tree structure, like the
> votes
>
> g. promote consensus without forcing it, or limiting it
>
> h. provide assurance of ultimate action - a conduit for
> consensus
> votes to cross into legislative assemblies and general
> elections
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] language/framing quibble
--- On Sun, 18/1/09, Fred Gohlke wrote: > Good Morning, Juho > > re: "If there is a common understanding that this (or > some other > plan) should be implemented then you can do it." > > That's wishful thinking. Every perversion extant, > political or otherwise, runs counter to the 'common > understanding'. Optimism is a wonderful trait; an > unrealistic expectation is not. Glenn Miller's > beautiful rendition to the contrary notwithstanding, wishing > will NOT make it so. OK. If it is not possible to make the change then there maybe is no widespread mutual understanding behind the change. > > > re: "There have been also idealistic revolutions that > have not > led to positive results in the long run." > > I'm not sure what that assertion is intended to mean > (it may contain a typographical error). In any case, > idealistic revolutions can lead to widely different changes > in society. My intention was to say that sometimes revolutions may lead to positive changes but it is also very common that the changes are not good or the end result is not what the people originally hoped for. > > We've mentioned the disastrous results of fascistic and > communistic revolts, while, on the positive side, my country > prides itself on the major advance in democratic governance > that flowed from its revolution. The results of revolutions > tend to be dictated by their leaders. As I said in a recent > message, "The American Revolution was unusual because > its nominal leader had no aspirations beyond the stated aim > of the revolution." Unfortunately for all of us, that > is the exception rather than the rule. Yes, there are good and bad revolutions. Revolutions are a risky business. > > > re: "Parties have the potential to be destructive. > But I don't > see that they would necessarily become destructive at > some > point." > > Of course they don't 'necessarily' become > destructive. They need a catalyst ... a demagogue ... to > send them careening down the path of extremism and > destruction. Building on such a foundation is building on > quicksand. It guarantees failure, if not because of your > party, because of someone else's. > > It is my opinion that giving any subset of our society > greater influence in our government than any other subset is > inherently wrong. Unless one is committed to advancing some > point of view over other points of view, the purpose of > considering political systems must always be to ensure that > everyone has an opportunity to participate in the > decision-making process. Whether any or all of them are > Liberal, Conservative, Catholic, Protestant, Communist, > Capitalist, or of any other ideological bent is not > important. The important thing is that they, all of them, > have an equal opportunity to participate ... whatever their > biases. > > > Juho, you and I examined the elements of partisanship in > detail several months ago. If you can not see the > deleterious effect partisanship has on our world, if you > didn't recognize the cause of my homeland's invasion > of a sovereign nation, if you are unaware of the politically > sanctioned excesses that led to the economic collapse > engulfing us, if you haven't noticed the poison flowing > out of the middle east for more than 50 years, I don't > believe there's anything I can say that will change your > mind about a fundamentally flawed approach to democratic > government. I think I agree with you that political parties may take stronger role than what they ideally should have, and that would be harmful. On the other hand a representational democracy needs some structure to handle different political opinions, and having parties is not a bad approach for taking care of this need. I'd thus rather say that one should watch out and keep the system (with or without parties) sound. Juho > > Fred Gohlke > > 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: [EM] Generalizing "manipulability"
OK, roughly agreed. Some problems that I had: - Why was the first set of definitions not good enough for Approval? (I read "rank" as referring to the sincere personal opinions, not to the ballot.) - Also Condorcet is *slightly* vulnerable to "irrelevant nominees". Imagine an election with 100 candidates from one party and voters that prefer to mark only a limited number of candidates in the ballot. Juho --- On Sun, 18/1/09, Steve Eppley wrote: > From: Steve Eppley > Subject: Re: [EM] Generalizing "manipulability" > To: election-meth...@electorama.com > Date: Sunday, 18 January, 2009, 7:56 PM > Hi, > > Manipulability by voter strategy can be rigorously defined > without problematic concepts like preferences or sincere > votes or how a dictator would vote or or how a rational > voter would vote given beliefs about others' votes. > > Let X denote the set of alternatives being voted on. > Let N denote the set of voters. > > Let V(X,N) denote the set of all possible collections > of admissible > votes regarding X, such that each collection contains > one vote > for each voter i in N. For all collections v in V(X,N) > and all > voters i in N, let vi denote i's vote in v. > > Let C denote the vote-tallying function that chooses > the winner > given a collection of votes. That is, for all v in > V(X,N), C(v) is > some alternative in X. > > Call C "manipulable by voter strategy" if > there exist two collections > of votes v,v' in V(X,N) and some voter i in N such > that both of > the following conditions hold: > 1. v'j = vj for all voters j in N-i. > 2. vi ranks C(v') over C(v). > > The idea in condition 2 is that voter i prefers the winner > given the strategic vote v'i over the winner given the > sincere vote vi. > > That definition works assuming all possible orderings of X > are admissible votes. I think it works for Range Voting too > (and Range Voting can be shown to be manipulable). The > following may be a reasonable way to generalize it to > include methods like Approval (and if this is done then > Approval can be shown to be manipulable): > > Call C "manipulable by voter strategy" if > there exist two collections > of votes v,v' in V(X,N) and some voter i in N and > some ordering o of X > such that all 3 of the following conditions hold: > 1. v'j = vj for all j in N-i. > 2. o ranks C(v') over C(v). > 3. For all pairs of alternatives x,y in X, > if vi ranks x over y then o ranks x over y. > > The idea in condition 3 is that vi is consistent with the > voter's sincere order of preference. For example, > approving x but not y or z is consistent with the 2 strict > (linear) orderings "x over y over z" and "x > over z over y." It's also consistent with the weak > (non-linear) ordering "x over y,z." Approving x > and y but not z is consistent with "x over y over > z" and "y over x over z" and "x,y over > z." Interpreting o as the voter's sincere order of > preference, condition 2 means the voter prefers the > strategic winner over the sincere winner. > > Another kind of manipulability is much more important in > the context of public elections. Call the voting method > "manipulable by irrelevant nominees" if nominating > an additional alternative z is likely to cause a significant > number of voters to change their relative vote between two > other alternatives x and y, thereby changing the winner from > x to y. We observe the effects all the time given > traditional voting methods. It explains why so many > potential candidates drop out of contention before the > general election (Duverger's Law). It explains why the > elites tend not to propose competing ballot propositions > when asking the voters to change from the status quo using > Yes/No Approval. I expect this kind of manipulability to be > a big problem given Approval or Range Voting or plain > Instant Runoff or Borda, but not given a good Condorcet > method. > The reason manipulability by irrelevant nominees is more > important than manipulability by voter strategy is that it > takes only a tiny number of people to affect the menu of > nominees, whereas voters in public elections tend not to be > strategically minded--see the research of Mike Alvarez of > Caltech. > > Regards, > Steve > -- > On 1/17/2009 10:38 PM, Juho Laatu wrote: > > --- On Sun, 18/1/09, Jonathan Lundell > wrote: > > > > > >> On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote: > >> > >> > >>> The mail contained quite good > >>> definitions. > >>> > >>> I didn't however agree with the > >>> referenced part below. I think > "sincere" > >>> and "zero-knowledge best strategic" > >>> ballot need not be the same. For example > >>> in Range(0,99) my sincere ballot could > >>> be A=50 B=51 but my best strategic vote > >>> would be A=0 B=99. Also other methods > >>> may h
Re: [EM] Generalizing "manipulability"
--- On Sun, 18/1/09, Jonathan Lundell wrote: > On Jan 17, 2009, at 10:38 PM, Juho Laatu wrote: > > > --- On Sun, 18/1/09, Jonathan Lundell > wrote: > > > >> On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote: > >> > >>> The mail contained quite good > >>> definitions. > >>> > >>> I didn't however agree with the > >>> referenced part below. I think > "sincere" > >>> and "zero-knowledge best strategic" > >>> ballot need not be the same. For example > >>> in Range(0,99) my sincere ballot could > >>> be A=50 B=51 but my best strategic vote > >>> would be A=0 B=99. Also other methods > >>> may have similarly small differences > >>> between "sincere" and > "zero-knowledge > >>> best strategic" ballots. > >> > >> My argument is that the Range values (as well as > the > >> Approval cutoff point) have meaning only within > the method. > >> We know from your example how you rank A vs B, but > the > >> actual values are uninterpreted except within the > count. > >> > >> The term "sincere" is metaphorical at > best, even > >> with linear ballots. What I'm arguing is that > that > >> metaphor breaks down with non-linear methods, and > the > >> appropriate generalization/abstraction of a > sincere ballot > >> is a zero-knowledge ballot. > > > > I don't quite see why ranking based > > methods (Range, Approval) would not > > follow the same principles/definitions > > as rating based methods. The sincere > > message of the voter was above that she > > only slightly prefers B over A but the > > strategic vote indicated that she finds > > B to be maximally better than A (or > > that in order to make B win she better > > vote this way). > > > (I'd use rating/ranking opposite to that. No?) Yes, sorry about the confusion. > > I was making a smaller point, that the actual values in > Range and the approval cutoff point in Approval are hard to > interpret as "sincere" or not. On the other hand, > we need a voter's "sincere" linear ordering of > the candidates (ranking?) in order to be able to say whether > an *outcome* is better or worse. OK. I think people are most often (e.g. on this list) expected to have an internal preference order of the candidates, also when the ballots of the method does not express it. I also think that most often people on this list assume that Approval votes are expected to be strategic while Range votes are expected to be sincere (except that many assume votes to be normalized, and that can already be seen to be a strategy). Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Why the concept of "sincere" votes in Range is flawed.
--- On Sun, 18/1/09, Kristofer Munsterhjelm wrote: > Juho Laatu wrote: > > Are you looking for the English language > > meaning of sincerity or some technical > > definition of it (e.g. some voting related > > criterion)? What is the problem with > > sincerity in Plurality? > > I'm not Abd, (Nor Jobst Heitzig ;-) > but I think the reasoning goes like this: > If people vote according to VNM utilities, then they'll > vote their preference among the candidates their vote has > some chance of influencing. From such a point of view, > "lesser of two evils" would not be strategy, since > one would only be able to influence a decision between those > "evils" in the first place. OK. This sounds like strategic voting (in a situation where all are expected to check the very basic strategic options/risks). Juho Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Generalizing "manipulability"
On Jan 18, 2009, at 4:11 PM, Juho Laatu wrote: OK, roughly agreed. Some problems that I had: - Why was the first set of definitions not good enough for Approval? (I read "rank" as referring to the sincere personal opinions, not to the ballot.) "vi ranks", and vi is by definition the ballot. That's why the second definition introduces o. - Also Condorcet is *slightly* vulnerable to "irrelevant nominees". Imagine an election with 100 candidates from one party and voters that prefer to mark only a limited number of candidates in the ballot. Juho --- On Sun, 18/1/09, Steve Eppley wrote: From: Steve Eppley Subject: Re: [EM] Generalizing "manipulability" To: election-meth...@electorama.com Date: Sunday, 18 January, 2009, 7:56 PM Hi, Manipulability by voter strategy can be rigorously defined without problematic concepts like preferences or sincere votes or how a dictator would vote or or how a rational voter would vote given beliefs about others' votes. Let X denote the set of alternatives being voted on. Let N denote the set of voters. Let V(X,N) denote the set of all possible collections of admissible votes regarding X, such that each collection contains one vote for each voter i in N. For all collections v in V(X,N) and all voters i in N, let vi denote i's vote in v. Let C denote the vote-tallying function that chooses the winner given a collection of votes. That is, for all v in V(X,N), C(v) is some alternative in X. Call C "manipulable by voter strategy" if there exist two collections of votes v,v' in V(X,N) and some voter i in N such that both of the following conditions hold: 1. v'j = vj for all voters j in N-i. 2. vi ranks C(v') over C(v). The idea in condition 2 is that voter i prefers the winner given the strategic vote v'i over the winner given the sincere vote vi. That definition works assuming all possible orderings of X are admissible votes. I think it works for Range Voting too (and Range Voting can be shown to be manipulable). The following may be a reasonable way to generalize it to include methods like Approval (and if this is done then Approval can be shown to be manipulable): Call C "manipulable by voter strategy" if there exist two collections of votes v,v' in V(X,N) and some voter i in N and some ordering o of X such that all 3 of the following conditions hold: 1. v'j = vj for all j in N-i. 2. o ranks C(v') over C(v). 3. For all pairs of alternatives x,y in X, if vi ranks x over y then o ranks x over y. The idea in condition 3 is that vi is consistent with the voter's sincere order of preference. For example, approving x but not y or z is consistent with the 2 strict (linear) orderings "x over y over z" and "x over z over y." It's also consistent with the weak (non-linear) ordering "x over y,z." Approving x and y but not z is consistent with "x over y over z" and "y over x over z" and "x,y over z." Interpreting o as the voter's sincere order of preference, condition 2 means the voter prefers the strategic winner over the sincere winner. Another kind of manipulability is much more important in the context of public elections. Call the voting method "manipulable by irrelevant nominees" if nominating an additional alternative z is likely to cause a significant number of voters to change their relative vote between two other alternatives x and y, thereby changing the winner from x to y. We observe the effects all the time given traditional voting methods. It explains why so many potential candidates drop out of contention before the general election (Duverger's Law). It explains why the elites tend not to propose competing ballot propositions when asking the voters to change from the status quo using Yes/No Approval. I expect this kind of manipulability to be a big problem given Approval or Range Voting or plain Instant Runoff or Borda, but not given a good Condorcet method. The reason manipulability by irrelevant nominees is more important than manipulability by voter strategy is that it takes only a tiny number of people to affect the menu of nominees, whereas voters in public elections tend not to be strategically minded--see the research of Mike Alvarez of Caltech. Regards, Steve -- On 1/17/2009 10:38 PM, Juho Laatu wrote: --- On Sun, 18/1/09, Jonathan Lundell wrote: On Jan 17, 2009, at 4:31 PM, Juho Laatu wrote: The mail contained quite good definitions. I didn't however agree with the referenced part below. I think "sincere" and "zero-knowledge best strategic" ballot need not be the same. For example in Range(0,99) my sincere ballot could be A=50 B=51 but my best strategic vote would be A=0 B=99. Also other methods may have similarly small differences between "sincere" and "zero-knowledge best strategic" ballots. My argument is that the Range values (as well as the Ap
Re: [EM] Generalizing "manipulability"
--- On Mon, 19/1/09, Jonathan Lundell wrote: > > - Why was the first set of definitions > > not good enough for Approval? (I read > > "rank" as referring to the sincere > > personal opinions, not to the ballot.) > > "vi ranks", and vi is by definition the ballot. > That's why the second > definition introduces o. OK. I should say that is the way I'd like to read it. Juho > >>Call C "manipulable by voter > strategy" if > >> there exist two collections > >>of votes v,v' in V(X,N) and some voter i in > N such > >> that both of > >>the following conditions hold: > >> 1. v'j = vj for all voters j in N-i. > >> 2. vi ranks C(v') over C(v). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV and Brown vs. Smallwood
Markus, The source you cite is a Minnesota League of Women Voters report that refers to an article with legal analysis in the Minnesota Bar Association's journal, dealing with the Minnesota statutes and Minnesota constitution. "Municipal Voting System Reform: Overcoming the Legal Obstacles." Bench and Bar of Minnesota. Vol. 59, No. 9, October 2002 FairVote is not responsible for reports by the League of Women Voters or lawyers writing scholarly articles. Again, I do not think FairVote has any position on the constitutionality of Condorcet Voting, and would probably defend its constitutionality. Terry Bouricius - Original Message - From: "Markus Schulze" To: Sent: Sunday, January 18, 2009 2:44 PM Subject: Re: [EM] IRV and Brown vs. Smallwood Dear Terry Bouricius, you wrote (18 Jan 2009): > Do you have any example of FairVote suggesting Condorcet > methods might be unconstitutional? See appendices 3 and 4 of this study: http://www.lwvmn.org/LWVMNAlternativeVotingStudyReport.pdf Markus Schulze 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: [EM] IRV and Brown vs. Smallwood
Dear Terry Bouricius, you wrote (18 Jan 2009): > FairVote is not responsible for reports by > the League of Women Voters or lawyers writing > scholarly articles. Tony Solgard was president of FairVote Minnesota when he wrote the quoted article in which he claims that Condorcet was unconstitutional in Minnesota. Also the report by the League of Women Voters of Minnesota refers to him as "Tony Solgard, President of Board of FairVote Minnesota". Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
