[EM] Unmanipulable Majority strategy criterion (Kristofer)
Kristofer Munsterhjelm wrote (Sat.Nov.29): -snip- I don't know of any method that meets the MDQBR you refer to that isn't completely invulnerable to Burial (do you?), so I don't see how that criterion is presently useful. That's odd, because the example I gave in a reply to Juho was yours. http://listas.apesol.org/pipermail/election-methods-electorama.com/2006-December/019097.html Note that the method of that post (which I've been referring to as first preference Copeland) ... -snip- Kristofer, Yes,sorry, that was a not-well-considered posting of mine that I'd forgotten. That method, the basic version of which was introduced by Forest Simmons as Clone-proofed Copeland, doesn't meet Mutual Dominant Quarter Burial Resistance (MDQBR). 26: AB 25: CA 02: CB 25: BA 22: BC AB 51-49, AC 51-49, BC 73-27. FPs: A26, B47, C27. A is the CW and wins with the penalty score of total FPs of candidates pairwise beaten by of zero. With over a quarter of the FPs A is a mutual dominant quarter candidate. Say two of the 25 BA change to BC: 26: AB 25: CA 02: CB 23: BA 24: BC AB 51-49, CA 51-49, BC 73-27 Now the penalty scores are A27, B26, C47. The Burial has worked, the new winner is B. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion
Kristofer, You wrote addressing me: You have some examples showing that RP/Schulze/etc fail the criterion. By my lazy etc. I just meant 'and the other Condorcet methods that are all equivalent to MinMax when there are just 3 candidates and Smith//Minmax when there are not more than 3 candidates in the Smith set'. Do they show that Condorcet and UM is incompatible? Or have they just been constructed on basis of some Condorcet methods, with differing methods for each? My intention was to show that all the methods that take account of more than one possible voter preference-level (i.e. not Approval or FPP) (and are well-known and/or advocated by anyone on EM) are vulnerable to UM except SMD,TP. I think I remember that you said Condorcet implies some vulnerability to burial. Is that sufficient to make it fail UM? Probably yes, but I haven't tried to prove as much. Returning to this demonstration: 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. Working in exactly the same way as ICA (because no ballots have voted more than one candidate top), this also applies to Condorcet//Approval and Smith//Approval and Schwartz//Approval. So those methods also fail UM. I did a bit of calculation and it seems my FPC (first preference Copeland) variant elects B here, as should plain FPC. Since it's nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure whether that can be fixed at all. My impression is/was that in 3-candidates-in-a-cycle examples that method behaves just like IRV. The demonstration that I gave of IRV failing UM certainly also applies to it. Chris Benham Kristofer Munsterhjelm wrote (Thurs.Dec.4): Chris Benham wrote: Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make Bthe winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* To have any point a criterion must be met by some method. It is met by my recently proposed SMD,TR method, which I introduced as 3-slot SMD,FPP(w): *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* [snip examples of methods failing the criterion] You have some examples showing that RP/Schulze/etc fail the criterion. Do they show that Condorcet and UM is incompatible? Or have they just been constructed on basis of some Condorcet methods, with differing methods for each? I think I remember that you said Condorcet implies some vulnerability to burial. Is that sufficient to make it fail UM? I wouldn't be surprised if it is, seeing that you have examples for a very broad range of election methods. 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. I did a bit of calculation and it seems my FPC (first preference Copeland) variant elects B here, as should plain FPC. Since it's nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure whether that can be fixed at all. Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Unmanipulable Majority strategy criterion (newly amended version)
Chris Benham wrote: Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* To have any point a criterion must be met by some method. It is met by my recently proposed SMD,TR method, which I introduced as 3-slot SMD,FPP(w): *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* [snip examples of methods failing the criterion] You have some examples showing that RP/Schulze/etc fail the criterion. Do they show that Condorcet and UM is incompatible? Or have they just been constructed on basis of some Condorcet methods, with differing methods for each? I think I remember that you said Condorcet implies some vulnerability to burial. Is that sufficient to make it fail UM? I wouldn't be surprised if it is, seeing that you have examples for a very broad range of election methods. 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. I did a bit of calculation and it seems my FPC (first preference Copeland) variant elects B here, as should plain FPC. Since it's nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure whether that can be fixed at all. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion (newly amended version)
Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* To have any point a criterion must be met by some method. It is met by my recently proposed SMD,TR method, which I introduced as 3-slot SMD,FPP(w): *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* Referring to the UM criterion: (a) if candidate A has a higher TR score than B then the BA strategists can only make B win by causing A to be disqualified. But in this method it isn't possible to vote x above y without approving x, so we know that just on the AB ballots A has majority approval. It isn't possible for a majority-approved candidate to be disqualified, and the strategists can't cause A's approval to fall below majority-strength. And the criterion specifies that none of the BA voters who don't top-rate B can raise their rating of B to increase B's TR score. (b) if on the other hand B has a higher TR score than A but B is disqualified there is nothing the BA strategists can do to undisqualify B. So SMD,TR meets the UM criterion. 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. 25: AB 26: BC 23: CA 26: C BC 51-49, CA 75-25, AB 48-26 Schulze/RP/MM/River (WV) and Approval-Weighted Pairwise and DMC and MinMax(PO) and MAMPO and IRV elect B. Now say 4 of the 26C change to AC (trying a Push-over strategy): 25: AB 04: AC 26: BC 23: CA 22: C BC 51-49, CA 71-29, AB 52-26 Now Schulze/RP/MM/River (WV) and AWP and DMC and MinMax(PO) and MAMPO and IRV all elect C. Since B had/has a majority-strength pairwise win against C, all these methods also fail Unmanipulable Majority. If scoring ballots were used and all voters score their most preferred candidate 10 and any second-ranked candidate 5 and unranked candidates zero, then this demonstration also works for IRNR so it also fails. Who knew that such vaunted monotonic methods as WV and MinMax(PO) and MAMPO were vulnerable to Push-over?! 48: AB 01: A 03: BA 48: CB BA 51-49. Bucklin and MCA elect B, but if the 48 AB voters truncate the winner changes to A. So those methods also fail UM. 49: A9, B8, C0 24: B9, A0, C0 27: C9, B8, A0 Here Range/Average Ratings/Score/CR elects B and on more than half the ballots B is voted above A, but if the 49 A9, B8, C0 voters change to A9, B0, C0 the winner changes to A. So this method fails UM. 48: ABCD 44: BADC 04: CBDA 03: DBCA Here Borda elects B and B is voted above A on more than half the ballots, but if the 48 ABCD ballots are changed to ACDB the Borda winner changes to A, so Borda fails UM. This Unmanipulable Majority criterion is failed by all well known and currently advocated methods, except 3-slot SMD,TR! Given its other criterion compliances and simplicity, that is my favourite 3-slot s-w method and my favourite Favourite Betrayal complying method. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Unmanipulable Majority strategy criterion
At 01:21 PM 11/26/2008, Chris Benham wrote: I have a suggestion for a new strategy criterion I might call Unmanipulable Majority. *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A.* Does anyone else think that this is highly desirable? Compared to what? Chris, you know I have a high level of suspicion about all the election criteria, though monotonicity seems pretty basic, I mean it is highly offensive to me that one could cause a candidate to lose by voting for the candidate. The Majority Criterion and the Condorcet Criterion, once consider no-brainers, turn out to be quite defective, preventing an optimal election outcome, i.e., there are situations, fairly easy to describe, where all of us would agree that there was a better outcome than the first preference of a majority or the pairwise winner. It is, of course, a different question as to whether or not these criteria are important for large public elections, but voting systems theory is about *all* elections, not just public ones. However, what are the implications of this criterion? Here is what it does. Range ballot, the only kind that can get around Arrow's Theorem (in substance). The only kind that directly expresses preference strength. I can modify the Range method to satisfy the criterion, but it then becomes a non-deterministic method. WTF are we always wanting a deterministic method, when this is the major stumbling block to finding democratically ideal winners? Anyway, let's just look at two candidates. There are others which explain the range of votes, but we only need to look at two. 51: A 5, B 4 49: A 4, B 5 A is rated (equivalent to ranked) above B on a majority of ballots. Alter the 49% to 49: A 0, B 10. B wins, by a landslide, actually. Was this a better result than if A continued to win? Elections like this, with realistic examples behind them, are the reason why the Majority Criterion, which this is a variation on, are suspect. Let's assume that those ratings are sincere, in both cases. In the first case A is, from the votes, a reasonable winner, but it is close. In the second case, A is *not* a reasonable winner, and there is a high likelihood that a majority of voters, in a real runoff, would vote for B. I've explained elsewhere why. Allowing weak preferences to overcome strong preference is an obvious error! It is *not* what we do in real deliberative process or in making personal decisions, particularly in small groups. Range does not satisfy the Majority Criterion, and no method which considers and uses preference strength can, except by a trick. In the election I described, because preference analysis shows that a majority preferred a candidate other than the Range winner, I'd have the election fail. Further process is necessary. The common way is with a runoff election, where the top two are listed on the ballot. There are possible variations on this; I have, for example, proposed that the runoff between the Range winner and a candidate who is preferred by a majority to the Range winner (if there exist more than one such -- that should be extraordinarily rare -- I'd make it be between the Range winner and the highest sum-of-ratings Condorcet winner or member of the Smith set. I.e., I'd use the ratings to resolve any Condorcet cycle. These runoffs would be rare, usually Range chooses the Condorcet winner. I have also argued that, usually, the Range winner would beat the Condorcet winner in a real, delayed runoff, because of preference strength considerations, which affect turnout and which also affect how many voters change their minds. Have a weak preference -- which is the situation here -- and it's more likely you will change your mind. Both of these effects favor the Range winner. Only if the Range results were distorted, perhaps by unwise strategic voting, would the Condorcet winner prevail. This trick turns the overall method into one which satisfies the Majority Criterion, because that criterion applies, properly, to the runoff. The first election, really, failed. But it guided ballot placement in the second, perhaps, and the majority favorite was guaranteed position on that ballot. All the majority has to do is persist a little. But they will usually, in a healthy society, I'd submit, step aside. They will collectively say, well, if you want that outcome so badly, be our guest. I'm sure you will return the favor someday. And that is how real elections in real societies that value unity and cooperation actually work. Fortunately, the world doesn't run only by the kind of political division and confrontation that we are accustomed to. Election-Methods mailing list -
[EM] Unmanipulable Majority strategy criterion definition amended
I propose to amend my suggested Unmanipulable Majority criterion by simply adding a phrase beginning with without.. so that it now reads: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* (Later I might rephrase it just to make it more succinct and polished). The effect of the alteration is to preclude Compromise strategy. When I first suggested the original version I knew that many methods fail it due to Burial and/or Push-over, but I mistakenly thought that my recent 3-slot method suggestion (defined below) meets it. *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* My preferred name for that method is now Strong Minimal Defense, Top Ratings (SMD,TR). 45: A 03: AB 47: BA 02: XB 03: YA Approvals: A98, B52, Y3, X2 Max. AO: A2, B48, Y95, X95 Top Ratings: A48, B47, Y3, X2. X and Y are disqualified, and A wins. A is voted above B on more than half the ballots, but if all the ballots on which B is voted above A are altered so that they all plump for B (top-rate B and approve no other candidates) then B wins. 45: A 03: AB 49: B 03: YA Approvals: A51, B52, Y3, X0 Max. AO: A49, B48, Y52, X52 Top Ratings: A48, B49, Y3, X0 As before only X and Y are disqualified, but now B has the highest Top Ratings score. I will soon post more on the subject of which methods meet or fail the (newly amended) Unmanipulable Majority criterion. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion
Kristofer, ...your Dominant Mutual Quarter Burial Resistance property. I don't remember reading or hearing about anything like that with Quarter in the title anywhere except in your EM posts. A few years ago James Green-Armytage coined the Mutual Dominant Third criterion but never promoted it. I took it up, but sometimes mistakenly reversed the order of the first two words. I now think the original order is better, because MDT is analogous with the better-known older Mutual Majority criterion. I do remember suggesting what is in effect MDT Burial Resistance, because there is an ok method that meets it while failing Burial Invulnerability: namely Smith,IRV. I don't know of any method that meets the MDQBR you refer to that isn't completely in invulnerable to Burial (do you?), so I don't see how that criterion is presently useful. In response to my question is Unmanipulative Majority desirable? you wrote: In isolation (not affecting anything else), sure. It's desirable because it limits the burying tricks that can be done. I'm glad you think so. The mention of pushover strategy there would mean that the method would have to have some degree of monotonicity, I assume. Yes. If AX voters can cause A to win by rearranging their ballots, then that would be a form of constructive burial. If, for instance, some subset of the voters who place X fifth can keep X from winning by rearranging their first-to-fourth preferences, then that would be destructive burial. If those voters are sincere in ranking X fifth, i.e they sincerely prefer all the candidates they rank above X to X; then I can't see that that qualifies as Burial strategy at all. Normally the strategy you refer to would qualify as some form of Compromise strategy. (Do you have an example that doesn't?) Chris Benham Kristofer Munsterhjelm wrote (Fri.Nov.28) wrote: Chris Benham wrote: Kristofer, Thanks for at least responding. ...I won't say anything about the desirability because I don't know what it implies;.. Only judging criteria by how they fit in with other criteria is obviously circular. That's true. If we're going to judge criteria by how they fit in with other criteria, we should have an idea of how relatively desirable they are. It may also be the case that it the tradeoff would be too great, by reasoning similar to what I gave in the reply to Juho about your Dominant Mutual Quarter Burial Resistance property. But if we consider this in more detail, we don't really know whether such tradeoffs are too great for, for instance, cloneproof criteria (though I think they are not). Do you (or anyone) think that judged in isolation this strategy criterion is desirable? It is true that some desirable/interesting criteria are so restrictive (as you put it) that IMO compliance with them can only be a redeeming feature of a method that isn't one of the best. (I put Participation in that category.) In isolation (not affecting anything else), sure. It's desirable because it limits the burying tricks that can be done. If you're asking whether I think it's more important than being, say, cloneproof, I don't think I can answer at the moment. I haven't thought about the relative desirability of criteria, though I prefer Condorcet methods to be both Smith and cloneproof. Maybe some people would like me to paraphrase this suggested criterion in language that is more EM-typical: 'If candidate A majority-strength pairwise beats candidate B, then it must not be possible for B's supporters (pairwise versus A) to use Burial or Pushover strategy to change the winner from A to B.' The mention of pushover strategy there would mean that the method would have to have some degree of monotonicity, I assume. Destructive burial would be trying to make X not win,... Your destructive burial looks almost synonymous with *monotonicity*. Hm, not necessarily. Without qualifications on the criterion, destructive burial would be constructive burial for *any* candidate, but also more than that. If AX voters can cause A to win by rearranging their ballots, then that would be a form of constructive burial. If, for instance, some subset of the voters who place X fifth can keep X from winning by rearranging their first-to-fourth preferences, then that would be destructive burial. Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Unmanipulable Majority strategy criterion
I think you have alot of redundant language, is the criterion effectively the following? If the winner is preferred to another candidate on the majority of the ballots, it must not be possible to make any such candidate win by modifying the ballots where that candidate is preferred to the winner. By requiring that at least 3 levels are possible, you are effectively forcing lots of methods to fail. Also, just because most methods would meet the criterion in the 2 candidate case isn't a reason to exclude that case. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Unmanipulable Majority strategy criterion
Hi Chris, --- En date de : Mer 26.11.08, Chris Benham [EMAIL PROTECTED] a écrit : I have a suggestion for a new strategy criterion I might call Unmanipulable Majority. *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A.* Does anyone else think that this is highly desirable? Is it new? [end quote] I think it's probably new. I have a reservation about how desirable it is, because you're guaranteeing that this A (preferred by a majority to B) can hang on to his win, but only when A would win in the first place. It's hard for me to judge whether A ought to be able to continue to win when I don't know why he won in the first place. It seems to me I'd rather state why A's original win should be guaranteed. (I think this direction may lead to SFC or votes-only SFC.) All things being equal it is desirable, of course. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Unmanipulable Majority strategy criterion
Chris Benham wrote: Kristofer, Thanks for at least responding. ...I won't say anything about the desirability because I don't know what it implies;.. Only judging criteria by how they fit in with other criteria is obviously circular. That's true. If we're going to judge criteria by how they fit in with other criteria, we should have an idea of how relatively desirable they are. It may also be the case that it the tradeoff would be too great, by reasoning similar to what I gave in the reply to Juho about your Dominant Mutual Quarter Burial Resistance property. But if we consider this in more detail, we don't really know whether such tradeoffs are too great for, for instance, cloneproof criteria (though I think they are not). Do you (or anyone) think that judged in isolation this strategy criterion is desirable? It is true that some desirable/interesting criteria are so restrictive (as you put it) that IMO compliance with them can only be a redeeming feature of a method that isn't one of the best. (I put Participation in that category.) In isolation (not affecting anything else), sure. It's desirable because it limits the burying tricks that can be done. If you're asking whether I think it's more important than being, say, cloneproof, I don't think I can answer at the moment. I haven't thought about the relative desirability of criteria, though I prefer Condorcet methods to be both Smith and cloneproof. Maybe some people would like me to paraphrase this suggested criterion in language that is more EM-typical: 'If candidate A majority-strength pairwise beats candidate B, then it must not be possible for B's supporters (pairwise versus A) to use Burial or Pushover strategy to change the winner from A to B.' The mention of pushover strategy there would mean that the method would have to have some degree of monotonicity, I assume. Destructive burial would be trying to make X not win,... Your destructive burial looks almost synonymous with *monotonicity*. Hm, not necessarily. Without qualifications on the criterion, destructive burial would be constructive burial for *any* candidate, but also more than that. If AX voters can cause A to win by rearranging their ballots, then that would be a form of constructive burial. If, for instance, some subset of the voters who place X fifth can keep X from winning by rearranging their first-to-fourth preferences, then that would be destructive burial. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Unmanipulable Majority strategy criterion
Chris Benham wrote: I have a suggestion for a new strategy criterion I might call Unmanipulable Majority. *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A.* Does anyone else think that this is highly desirable? Is it new? I think it's new. I won't say anything about the desirability because I don't know what it implies; it could be too restrictive (like Consistency) for all I know. It would be possible to extend this to a set. For instance: if the method elects from a set w, then it must not be possible to make a candidate X outside w the winner by modifying ballots on which X is ranked above all in w. Or a more general case, with constructive and destructive burial. Constructive burial would be trying to make Y win instead of X. Destructive burial would be trying to make X not win, though in that case you would have to consider what kind of ballots could be changed, since there's no equivalent of B in the destructive burial case. Destructive burial also sounds too strict, that no useful method could fulfill it (unless only very specific ballots were permitted to be changed, e.g those who rank X last). Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion
I have a suggestion for a new strategy criterion I might call Unmanipulable Majority. *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A.* Does anyone else think that this is highly desirable? Is it new? Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
