[EM] Complete MMT definition
Mike, I think this fails the FBC. Say sincere is: 45: C 06: D>A 39: A>B 20: B>A There is no "mutual majority set" (by your latest definition) so C wins. That is also true if the 6 D>A voters change to D=A or D=A=B or D=A>B or anything else except A>B or A=B or B>A in which case the winner changes to A. It also fails Mono-add-Plump. 49: C 27: A>B 24: B>A Your latest version of MMT elects A, but if we add between 2 and 21 ballots that plump for A then there is no longer a "majority candidate set" and so the MMT winner changes from A to C. 49: C 21: A (new voters, whose ballots switch the MMT winner from A to C) 27: A>B 24: B>A (121 ballots, majority threshold = 61) I think all reasonable methods will elect A in both cases. Electing C in the second case will have voters wondering why they bothered switching from FPP, and is a very bad case of failing Condorcet and Mutual Dominant Third (DMT). A is voted above all other candidates on nearly 40% of the votes, and A>C 72-49 and A>B 48-24. Chris Benham Mike Ossipoff wrote (6 Dec 2011): Complete new definition of Mutual-Majority-Top (MMT): A mutual-majority candidate set is a set of candidates who are each rated above-bottom by each member of the same majority of voters--where that set of candidates contains every candidate rated above bottom by any member of that majority of the voters. If there are one or more mutual-majority candidate sets, then the winner is the most top-rated candidate who is in a mutual-majority candidate set. If there are no mutual-majority candidate sets, then the winner is the most top-rated candidate. [end of latest definition of MMT] Election-Methods mailing list - see http://electorama.com/em for list info
[EM] How to vote in IRV
Mike, Similar to the good Approval strategy "approve the candidate A you would vote for in FPP, plus all the candidates you like as much or better than A" as an IRV strategy guide is "vote in first place the candidate A you would vote for in FPP and in second place the candidate B that you would vote for in FPP if A wasn't on the ballot and in third place the candidate C you would vote for in FPP if neither A or B was on the ballot, and so on." So barring rare and risky Push-over strategy opportunities, I don't see how IRV voting strategy is qualitatively more difficult than FPP strategy. When there are completely unacceptable candidates who might win (I call that condition u/a, for “unacceptable/acceptable”) IRV, like many methods, has a relatively simple strategy: When the voter's over-riding priority is to prevent the election of an unacceptable candidate, the voter should rank the acceptable candidates in order of estimated pairwise strength versus the likely unacceptable finalist (i.e. the unacceptable candidate that isn't eliminated before the final virtual run-off). Ideally, then rank the unacceptables in order of some complicated combination of their disutility and (some guessed or complicatedly-calculated measure of) their popularity. Actually, ignore that last paragraph. There is no reason at all to not rank the unacceptables sincerely. If your ranking among the unacceptables is ever counted it means that your strategy (aimed at preventing the election of an unacceptable candidate) has failed, and if any are even slightly less bad than the very worst you might as well help the lesser evil (unless you are concerned about your vote's symbolic gesture and want to deny any unacceptable winner "legitimacy"). What’s that you say? You might get lucky, even if you don’t top-rank a compromise? I think the voter very probably will, and most of the time will have sufficient information to "know" that s/he can safely vote hir sincere ranking. “Step right up, folks, and pick a card!” IRV, a game of chance, should only be allowed in states that allow gambling. I won't bother, but I think it is at least as easy to argue that Approval is "a game of chance". Chris Benham Mike Ossipoff wrote (6 Dec 2011): How to vote in IRV: When there are completely unacceptable candidates who might win (I call that condition u/a, for “unacceptable/acceptable”) IRV, like many methods, has a relatively simple strategy: Rank the acceptable candidates in order of (some guessed or complicatedly-calculated measure of) their popularity. Ideally, then rank the unacceptables in order of some complicated combination of their disutility and (some guessed or complicatedly-calculated measure of) their popularity. Actually, ignore that last paragraph. In u/a, all the unacceptables are just unacceptable. What matters is the election of an acceptable instead of an unacceptable. In u/a, IRV is just ranked Plurality. In Plurality you vote for the acceptable candidate who is most popular (most likely to get the most votes). The difference is that the needed measure of popularity is simpler in Plurality (Which of the acceptables will be the best votegetter?). In that (decisive) regard, Plurality is better than IRV. Oh, and, by the way, our public political elections are u/a. IRV’s LNHa and LNHe: Some boast that IRV meets those two criteria. Well, if your 2nd choice gets your vote, your favorite, by that time, is beyond help or harm, isn’t s/he. Let’s protect hir from harm from your 2nd choice vote, by expelling hir from the election. :-) …A sort of electoral euthanasia. In IRV, you don’t have to be afraid to vote your 2nd choice necessary compromise at least in 2nd place. In fact you have to be afraid to not rank hir alone in 1st place. So, you see, IRV takes LNHa one step farther :-) What’s that you say? You might get lucky, even if you don’t top-rank a compromise? “Step right up, folks, and pick a card!” IRV, a game of chance, should only be allowed in states that allow gambling. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
[EM] That was MMT1. MMT2 is like MTAOC. Replacing the word "any" in the definitions.
MMT1: I'm not changing the definition of MMT that I posted last night. I'll call it "MMT1". It's even more demanding in its reciprocity requirements than was the original (one-paragraph-definition) MTAOC. It was that over-demandingness that led me to propose my pseudocode-defined MTAOC. MMT2: MMT2 is like the pseudocode-defined MTAOC, with all middle ratings conditional. Its definition differs from that of MMT1 only in a few words in its "mutual-majority candidate set". MMT2 definition: A "mutual majority" candidate set is a set of candidates who are each rated above bottom by each member of the same majority of the voters-- where that set includes at least one top-rated candidate on the ballot of every voter in that majority. If there are one or more mutual-majority candidate sets, then the winner is the most top-rated candidate who is in a mutual-majority candidate set. If there are no mutual-majority candidate sets, then the winner is the most top-rated candidate. [end of MMT2 definition] MMT3, likewise, differs only by a few words in its definition of a mutual-majority candidate set. MMT3 definition: A "mutual majority"candidate set is a set of candidates who are each rated above bottom by each member of the same majority of the voters-- where that set includes all of the top rated candidates of each ballot of the voters in that majority. If there are one or more mutual-majority candidate sets, then the winner is the most top-rated candidate who is in a mutual-majority candidate set. If there are no mutual-majority candidate sets, then the winner is the most top-rated candidate. [end of MMT3 definition] As I said, MMT2 is like the pseudocode-defined MTAOC, where all middle ratings are conditional. MMT3 is like my initial one-paragraph-definition MMT. It's too demanding in its reciprocity-requirement. MM1 is more demanding still. Henceforth, when I say "MMT", without a distinguishing number, I will be referring to MMT2. Likewise, when I say "MMPO", without a distinguishing number, I'll be referring to MMPO2. I'll refer to my initial, one-paragraph-definition, MTAOC as MTAOC1 I'll refer to my pseudocode-defined MTAOC as MTAOC2. When I say "MTAOC" without a distinguishing number, I'll be referring to MTAOC2. The advantage of MMT is its brevity of definition. The advantage of MTAOC is its flexibility, in allowing the option of giving, to any particular candidate, an unconditional middle rating. The word "any" is ambiguous: "I can beat _anyone_ at chess. Can you beat anyone at chess?" Therefore I replace "any" in my definition of MMT1 (which isn't my favorite MMT version, and isn't what I mean by "MMT"). For MMT1, here's how I define a mutual-majority candidate set: A "mutual-majority candidate set is a set of candidates who are each rated above bottom by each member of the same majority of the voters--where that set includes every candidate rated above bottom by one or more members of that majority of voters. I repeat, though, that I prefer MMT2, and MMT2 is what I mean when I say "MMT" without a distinguishing number. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Chris: MMT criterion compliances.
Chris: You wrote: I think this fails the FBC. [endquote] But you're specifically referring to what I now call "MMT1", which isn't my main MMT proposal now. Sorry that I've kept changing my MMT definitions--I know that's a nuisance--but now it's a matter of whether MMT2 meets FBC and Mono-Add-Plump. Of course, if MMT2 turned out to fail FBC, then of course I wouldn't propose it. And if it turned out to fail Mono-Add-Plump, that would eliminate its main advantage over MDDTR. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
[EM] How to vote in IRV
Chris: You wrote: Similar to the good Approval strategy "approve the candidate A you would vote for in FPP, plus all the candidates you like as much or better than A" as an IRV strategy guide is "vote in first place the candidate A you would vote for in FPP and in second place the candidate B that you would vote for in FPP if A wasn't on the ballot and in third place the candidate C you would vote for in FPP if neither A or B was on the ballot, and so on." [endquote] Yes, that's a reasonable approximation. You continued: So barring rare and risky Push-over strategy opportunities, I don't see how IRV voting strategy is qualitatively more difficult than FPP strategy. [endquote] But, strictly speaking, it _is_ more complicated, because, in Plurality it's just a matter of which acceptable candidate is most likely to be the best votergetter. The popularity-measure for ranking the acceptables in IRV will be more complicated. > When there are completely unacceptable candidates who might > win (I call that condition u/a, for “unacceptable/acceptable”) > > IRV, like many methods, has a relatively simple strategy: You replied: When the voter's over-riding priority is to prevent the election of an unacceptable candidate, the voter should rank the acceptable candidates in order of estimated pairwise strength versus the likely unacceptable finalist (i.e. the unacceptable candidate that isn't eliminated before the final virtual run-off). [endquote] But are you sure that it isn't more complicated than that. What about pairwise strength against the 2nd most likely unacceptable finalist. What about the ability to accumulate enough votes to even be a finalist? No, it's more complicated. You wrote: There is no reason at all to not rank the unacceptables sincerely. If your ranking among the unacceptables is ever counted it means that your strategy (aimed at preventing the election of an unacceptable candidate) has failed, and if any are even slightly less bad than the very worst you might as well help the lesser evil (unless you are concerned about your vote's symbolic gesture and want to deny any unacceptable winner "legitimacy"). [endquote] I agree with that. Strictly speaking, you gain some by ranking the unacceptables too. I merely meant that the matter of which unacceptable wins is far less important than the matter of whether the winner is an acceptable or an unacceptable. So the somewhat more complicated determination of unacceptable ranking order can reasonably be ignored. > What’s that you say? You might get lucky, even if you don’t > top-rank a compromise? You continued: I think it is at least as easy to argue that Approval is "a game of chance". [endquote] How so? Maybe you just mean that all strategy under uncertainty is a "game of chance". But I meant "game of chance" in a stronger sense. In Approval, if you choose to vote a certain candidate-set over all the other candidates, then it's certain that you're voting every candidate in that set over all the candidates outside of that set. So Approval is incomparably more responsive than IRV. And the matter of which candidate(s) you're giving your vote to has nothing to with chance. You, and only you, decide that and establish it explicitly on your ballot. It's in that sense that IRV is a game of chance, where Approval is not a game of chance. Vote your favorite in 1st place and your needed compromise in 2nd place? You can only guess and hope that you'll get to give vote to your compromise, who may very well need it, and not get it. A game of chance. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Dave Ketchum: IRV strategy
Dave: On Dec 6, 2011, at 4:19 PM, MIKE OSSIPOFF wrote: > > > How to vote in IRV: > > > > When there are completely unacceptable candidates who might > win (I call that condition u/a, for “unacceptable/acceptable”) You replied: You DO NOT rank such since, if you rank such a candidate, so might enough others for this one to win - you do not want to be part of causing such a win. [endquote] But your vote won't reach the candidates whom you consider unacceptable unless and until all of the acceptable candidates have been eliminated. So, by that time, it's no longer a question of _whether_ an unacceptable will win. It's only a question of _which_ unacceptable will win. But of course it's vastly more important to elect an acceptable vs determining which unacceptable wins. Still, if you have time, then you might as well rank the unacceptables too, so that, at least, the _worst_ ones won't win. > > > IRV, like many methods, has a relatively simple strategy: > > > > Rank the acceptable candidates in order of (some guessed or > complicatedly-calculated measure of) their popularity. Rank in the order of what YOU see as should be most popular first. [endquote] Yes--You must guess which acceptable is most likely to be helped to win by your top ranking. And then, which of the remaining acceptables is most likely to be helped to win by your 2nd-place ranking...etc. > Ideally, then rank the unacceptables in order of some > complicated combination of their disutility and > (some guessed or complicatedly-calculated measure of) their > popularity. > > > > Actually, ignore that last paragraph. In u/a, all the > unacceptables are just unacceptable. What matters is the election of > an > acceptable instead of an unacceptable. > > > > In u/a, IRV is just ranked Plurality. In Plurality you vote > for the acceptable candidate who is most popular (most likely to get > the most > votes). Read that carefully. You do not vote for unacceptable here [endquote] Quite so. You never vote for an unacceptable in Plurality ...unless you're a Democrat-voting progressive :-) But you shouldn't. Vote for the acceptable most likely to be helped to win by your vote. ...the acceptable most likely to be the best votegetter among the acceptables. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris: MMT criterion compliances.
2011/12/7 MIKE OSSIPOFF > > Chris: > > You wrote: > > I think this fails the FBC. > > [endquote] > > But you're specifically referring to what I now call "MMT1", which > isn't my main MMT proposal now. Sorry that I've kept changing my > MMT definitions--I know that's a nuisance--but now it's a matter of > whether MMT2 meets FBC and Mono-Add-Plump. > > Of course, if MMT2 turned out to fail FBC, then of course I > wouldn't propose it. > > And if it turned out to fail Mono-Add-Plump, that would eliminate > its main advantage over MDDTR. > But it does fail Mono-Add-Plump, using the same example Chris gave. Jameson > > Mike Ossipoff > > > > Election-Methods mailing list - see http://electorama.com/em for list info > Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Chris: MMT criterion compliances.
Mike, ...now it's a matter of whether MMT2 meets FBC and Mono-Add-Plump. MMT2 definition: A "mutual majority" candidate set is a set of candidates who are each rated above bottom by each member of the same majority of the voters-- where that set includes at least one top-rated candidate on the ballot of every voter in that majority. If there are one or more mutual-majority candidate sets, then the winner is the most top-rated candidate who is in a mutual-majority candidate set. If there are no mutual-majority candidate sets, then the winner is the most top-rated candidate. [end of MMT2 definition] As far as I can see the examples I gave apply equally well to "MMT2". I've pasted them in at the bottom. Chris Benham Mike Ossipoff wrote (7 Dec 2011): Chris: You wrote: I think this fails the FBC. [endquote] But you're specifically referring to what I now call "MMT1", which isn't my main MMT proposal now. Sorry that I've kept changing my MMT definitions--I know that's a nuisance--but now it's a matter of whether MMT2 meets FBC and Mono-Add-Plump. Of course, if MMT2 turned out to fail FBC, then of course I wouldn't propose it. And if it turned out to fail Mono-Add-Plump, that would eliminate its main advantage over MDDTR. Mike Ossipoff Mike, I think this fails the FBC. Say sincere is: 45: C 06: D>A 39: A>B 20: B>A There is no "mutual majority set" (by your latest definition) so C wins. That is also true if the 6 D>A voters change to D=A or D=A=B or D=A>B or anything else except A>B or A=B or B>A in which case the winner changes to A. It also fails Mono-add-Plump. 49: C 27: A>B 24: B>A Your latest version of MMT elects A, but if we add between 2 and 21 ballots that plump for A then there is no longer a "majority candidate set" and so the MMT winner changes from A to C. 49: C 21: A (new voters, whose ballots switch the MMT winner from A to C) 27: A>B 24: B>A (121 ballots, majority threshold = 61) I think all reasonable methods will elect A in both cases. Electing C in the second case will have voters wondering why they bothered switching from FPP, and is a very bad case of failing Condorcet and Mutual Dominant Third (DMT). A is voted above all other candidates on nearly 40% of the ballots, and pairwise A>C 72-49 and A>B 48-24. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
