Right! More accurately MaxMin ... maximize the minimum pairwise support. Unlike minimizing the max pairwise opposition it passes Plurality (if I remember correctly). Of course, they are the same in the complete rankings context, or under symmetric completion, or under margins. I think a simple description that totally avoids traditional nomenclature may have a psychologically better chance of winning-over adherents of other RCV factions. For example: Call a candidate that outranks any other candidate on more than half of the ballots a "Majority Matchup Winner" (MMW), or some other descriptive name with good fairness vibes. Remark that any ballot set beta can be converted into a ballot set that has an MMW by adding sufficiently many [perhaps zero] bullet ballots. [it is easy to see that this can be done without tripling the size of the ballot set] Elect the MMW of the smallest superset of beta that has an MMW. [End of proposed method description] Remarks for EM scientists only: Since MaxMinPairwiseSupport does not satisfy the Condorcet Criterion, when the ballot CW and the MaxMinPairwise Support candidates differ, it will take more bullet ballots to convert a ballot CW into a Majority Condorcet Winner than it will take to convert the MaxMinPairwiseSupport winner into a Majority Conndorcet Winner. Since lay voters don't care a fig about Condorcet, but hold sacred Majority Rule, it seems to me that we should stick with our majority heuristic for a public proposal. In light of Ted Stern's talk of top two runoff versions, here's one of great interest to me, but NOT for public proposal: In the rare event that there is a ballot CW that is not a ballot Majority CW, have a sincere runoff between the ballot CW and the ballot MaxMinPairwiseSupport candidate. "Sincere," of course, implies a separate ballot set reserved for exclusive use, or else a separate trip to the polls. It seems to me that the probability of such a rare event would be entirely negligible. How would a policy of preferring the ballot CW over the MaxMinPS winner affect Burial and Compromising incentives? -Forest P.S. Kevin ... very valid concerns in your previous reply! But imho, outweighed by proposal simplicity and other above mentioned considerations in the present context. El sáb., 28 de may. de 2022 1:50 p. m., Kristofer Munsterhjelm < km_elmet@t-online.de> escribió: > On 28.05.2022 20:59, Forest Simmons wrote: > > I am both a mathematician and a citizen. My main interest in the realm > > of election methods is to understand the theoretical limitations of > > practical election methods. Theory is supposed to be the servant of > > practice ... not the other way around. > > > > Election methods are tools of democracy. As such they have a > > psycho/politico aspect that we neglect at our own peril. > > > > What can we realistically expect from the voters? How do they want to > > express their preferences? How do they expect their preferences to be > > incorporated into a decision? > > > > For starters, most voters believe in some form of "majority rule." > > > > If there is a candidate A that is preferred by more than half of the > > voters over any other candidate A', then (all else being equal) A rather > > than A' should be elected. > > > > The problem is that sometimes there is no such ideal majority pairwise > > candidate IMPC. Who should be elected in that case? > > > > Answer: How about the candidate closest to being such an IMPC? > > > > How do you determine "closeness"? > > > > Why not by how few additional ballots would suffice to convert a > > candidate into an IMPC? > > > > Is this too hard for citizens of a democracy to accept? > > > > What objections might there be? > > > > How to overcome reservations and persuade the electorate? > > That's minmax, right? > > -km >

Minor Correction ... "In the rare event that there is a ballot CW that is not a ballot Majority CW, have a sincere runoff between the ballot CW and the ballot MaxMinPairwiseSupport candidate." ... should read ... In the rare event that there is a ballot CW that differs from the MaxMinPairwiseSupport candidate, have a sincere runoff between the ballot CW and the ballot MaxMinPairwiseSupport candidate. Also, since I have your attention, I would like to point out that this formulation of MaxMinPairwiseSupport is simpler than the related MinMax(margins) Condorcet method that has frequently been proposed in the past by Juho and many others. Thanks, guys, for persistent reminders of the potential possibilities of simplicity! The other inspiration, of course, was Kevin's MinMaxPairwiseOpposition, which satisfies the FBC but not the CC, and even more importantly, his MajorityDefeatDisqualification versions. In fact, you could reformulate MaxMinPairwiseSupport as what to do if all candidates are Majority Defeated or if there are several candidates that are not majority defeated ... just add the minimum number of bullet ballots that leaves precisely one candidate that is not majority defeated. -Forest El dom., 29 de may. de 2022 4:29 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > Right! > > More accurately MaxMin ... maximize the minimum pairwise support. Unlike > minimizing the max pairwise opposition it passes Plurality (if I remember > correctly). > > Of course, they are the same in the complete rankings context, or under > symmetric completion, or under margins. > > I think a simple description that totally avoids traditional nomenclature > may have a psychologically better chance of winning-over adherents of other > RCV factions. > > For example: > > Call a candidate that outranks any other candidate on more than half of > the ballots a "Majority Matchup Winner" (MMW), or some other descriptive > name with good fairness vibes. > > Remark that any ballot set beta can be converted into a ballot set that > has an MMW by adding sufficiently many [perhaps zero] bullet ballots. [it > is easy to see that this can be done without tripling the size of the > ballot set] > > Elect the MMW of the smallest superset of beta that has an MMW. > > [End of proposed method description] > > Remarks for EM scientists only: > > Since MaxMinPairwiseSupport does not satisfy the Condorcet Criterion, when > the ballot CW and the MaxMinPairwise Support candidates differ, it will > take more bullet ballots to convert a ballot CW into a Majority Condorcet > Winner than it will take to convert the MaxMinPairwiseSupport winner into a > Majority Conndorcet Winner. > > Since lay voters don't care a fig about Condorcet, but hold sacred > Majority Rule, it seems to me that we should stick with our majority > heuristic for a public proposal. > > In light of Ted Stern's talk of top two runoff versions, here's one of > great interest to me, but NOT for public proposal: > > In the rare event that there is a ballot CW that is not a ballot Majority > CW, have a sincere runoff between the ballot CW and the ballot > MaxMinPairwiseSupport candidate. > > "Sincere," of course, implies a separate ballot set reserved for exclusive > use, or else a separate trip to the polls. > > It seems to me that the probability of such a rare event would be > entirely negligible. > > How would a policy of preferring the ballot CW over the MaxMinPS winner > affect Burial and Compromising incentives? > > -Forest > > P.S. Kevin ... very valid concerns in your previous reply! But imho, > outweighed by proposal simplicity and other above mentioned considerations > in the present context. > > El sáb., 28 de may. de 2022 1:50 p. m., Kristofer Munsterhjelm < > km_elmet@t-online.de> escribió: > >> On 28.05.2022 20:59, Forest Simmons wrote: >> > I am both a mathematician and a citizen. My main interest in the realm >> > of election methods is to understand the theoretical limitations of >> > practical election methods. Theory is supposed to be the servant of >> > practice ... not the other way around. >> > >> > Election methods are tools of democracy. As such they have a >> > psycho/politico aspect that we neglect at our own peril. >> > >> > What can we realistically expect from the voters? How do they want to >> > express their preferences? How do they expect their preferences to be >> > incorporated into a decision? >> > >> > For starters, most voters believe in some form of "majority rule." >> > >> > If there is a candidate A that is preferred by more than half of the >> > voters over any other candidate A', then (all else being equal) A rather >> > than A' should be elected. >> > >> > The problem is that sometimes there is no such ideal majority pairwise >> > candidate IMPC. Who should be elected in that case? >> > >> > Answer: How about the candidate closest to being such an IMPC? >> > >> > How do you determine "closeness"? >> > >> > Why not by how few additional ballots would suffice to convert a >> > candidate into an IMPC? >> > >> > Is this too hard for citizens of a democracy to accept? >> > >> > What objections might there be? >> > >> > How to overcome reservations and persuade the electorate? >> >> That's minmax, right? >> >> -km >> >

In their March 2004 Scientific American articule "The Fairest Vote ..." P Gupta and E Maskin designate as "True Majority Winner" the candidato that outranks any other candidate on more ballots than not ... in other words the candidate most commonly referred to as the Condorcet Candidate. So they took the liberty of using "majorty" to mean "more than not" rather than "more than half." Maskin has since become a Nobel Laureate. Does that give the rest of us license to refer to the Condorcet Candidate as the "True Majority Winner" (TMW)? If so, then we can reformulate MinMax (for public proposal) in the form .... Given a set beta of ranked ballots, elect the TMW of the smallest superset of beta that has a True Majority Winner, i.e. a candidate that outranks any competing candidate on more ballots than not. [A superset of a set is a set containing the set.] Do you think Maskin's "cred" would carry the day? Would the OED or even Webster back up this usage? Would the voters buy it? It made it past the editors of Scientific American, and I haven't seen any objection to it, despite various other disagreements with the article. Another possibility would be to use the more modest phrase Relative Majority Winner instead of True Majority Winner. What do you think? -Forest El dom., 29 de may. de 2022 5:09 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > Minor Correction ... > > "In the rare event that there is a ballot CW that is not a ballot > Majority CW, have a sincere runoff between the ballot CW and the ballot > MaxMinPairwiseSupport candidate." > > ... should read ... > > In the rare event that there is a ballot CW that differs from the > MaxMinPairwiseSupport candidate, have a sincere runoff between the ballot > CW and the ballot MaxMinPairwiseSupport candidate. > > Also, since I have your attention, I would like to point out that this > formulation of MaxMinPairwiseSupport is simpler than the related > MinMax(margins) Condorcet method that has frequently been proposed in the > past by Juho and many others. > > Thanks, guys, for persistent reminders of the potential possibilities of > simplicity! The other inspiration, of course, was Kevin's > MinMaxPairwiseOpposition, which satisfies the FBC but not the CC, and even > more importantly, his MajorityDefeatDisqualification versions. > > In fact, you could reformulate MaxMinPairwiseSupport as what to do if all > candidates are Majority Defeated or if there are several candidates that > are not majority defeated ... just add the minimum number of bullet ballots > that leaves precisely one candidate that is not majority defeated. > > -Forest > > > El dom., 29 de may. de 2022 4:29 p. m., Forest Simmons < > forest.simmons21@gmail.com> escribió: > >> Right! >> >> More accurately MaxMin ... maximize the minimum pairwise support. Unlike >> minimizing the max pairwise opposition it passes Plurality (if I remember >> correctly). >> >> Of course, they are the same in the complete rankings context, or under >> symmetric completion, or under margins. >> >> I think a simple description that totally avoids traditional nomenclature >> may have a psychologically better chance of winning-over adherents of other >> RCV factions. >> >> For example: >> >> Call a candidate that outranks any other candidate on more than half of >> the ballots a "Majority Matchup Winner" (MMW), or some other descriptive >> name with good fairness vibes. >> >> Remark that any ballot set beta can be converted into a ballot set that >> has an MMW by adding sufficiently many [perhaps zero] bullet ballots. [it >> is easy to see that this can be done without tripling the size of the >> ballot set] >> >> Elect the MMW of the smallest superset of beta that has an MMW. >> >> [End of proposed method description] >> >> Remarks for EM scientists only: >> >> Since MaxMinPairwiseSupport does not satisfy the Condorcet Criterion, >> when the ballot CW and the MaxMinPairwise Support candidates differ, it >> will take more bullet ballots to convert a ballot CW into a Majority >> Condorcet Winner than it will take to convert the MaxMinPairwiseSupport >> winner into a Majority Conndorcet Winner. >> >> Since lay voters don't care a fig about Condorcet, but hold sacred >> Majority Rule, it seems to me that we should stick with our majority >> heuristic for a public proposal. >> >> In light of Ted Stern's talk of top two runoff versions, here's one of >> great interest to me, but NOT for public proposal: >> >> In the rare event that there is a ballot CW that is not a ballot Majority >> CW, have a sincere runoff between the ballot CW and the ballot >> MaxMinPairwiseSupport candidate. >> >> "Sincere," of course, implies a separate ballot set reserved for >> exclusive use, or else a separate trip to the polls. >> >> It seems to me that the probability of such a rare event would be >> entirely negligible. >> >> How would a policy of preferring the ballot CW over the MaxMinPS winner >> affect Burial and Compromising incentives? >> >> -Forest >> >> P.S. Kevin ... very valid concerns in your previous reply! But imho, >> outweighed by proposal simplicity and other above mentioned considerations >> in the present context. >> >> El sáb., 28 de may. de 2022 1:50 p. m., Kristofer Munsterhjelm < >> km_elmet@t-online.de> escribió: >> >>> On 28.05.2022 20:59, Forest Simmons wrote: >>> > I am both a mathematician and a citizen. My main interest in the realm >>> > of election methods is to understand the theoretical limitations of >>> > practical election methods. Theory is supposed to be the servant of >>> > practice ... not the other way around. >>> > >>> > Election methods are tools of democracy. As such they have a >>> > psycho/politico aspect that we neglect at our own peril. >>> > >>> > What can we realistically expect from the voters? How do they want to >>> > express their preferences? How do they expect their preferences to be >>> > incorporated into a decision? >>> > >>> > For starters, most voters believe in some form of "majority rule." >>> > >>> > If there is a candidate A that is preferred by more than half of the >>> > voters over any other candidate A', then (all else being equal) A >>> rather >>> > than A' should be elected. >>> > >>> > The problem is that sometimes there is no such ideal majority pairwise >>> > candidate IMPC. Who should be elected in that case? >>> > >>> > Answer: How about the candidate closest to being such an IMPC? >>> > >>> > How do you determine "closeness"? >>> > >>> > Why not by how few additional ballots would suffice to convert a >>> > candidate into an IMPC? >>> > >>> > Is this too hard for citizens of a democracy to accept? >>> > >>> > What objections might there be? >>> > >>> > How to overcome reservations and persuade the electorate? >>> >>> That's minmax, right? >>> >>> -km >>> >>