Is there any burial resistant Condorcet method simpler than this? The basic pre-requisite is to understand that whenever there is no Condorcet Winner there will be a pairwise cycle, called a "top-cycle" of candidates whose members are not defeated by any candidates outside of the cycle, just as a Condorcet Winner is a candidate undefeated by any other candidate. Here's the Q&D burial resistant method: Lacking a Condorcet Winner elect the candidate X having the greatest pairwise victory over the top-cycle member Y that has the smallest ratio of first to last place votes within the top cycle. Two examples illustrate the method: Example 1. 49 C 26 A>B 25 B (sincere B>A) The top cycle is ABCA Candidate A has the smallest ratio 26/74 of first to last place votes. Candidate C is the only candidate with a pairwise victory over it, so C wins. Notice how our rule does not reward B for insincerely lowering A to (equal) last? Example 2. 45 A>B (sincere A>C) 35 B>C 25 C>A Candidate C has the smallest ratio 25/45 of first to last. Candidate B wins as the only candidate with a pairwise victory over C. So A's burial of C backfires. Typically, the faction A that buries or truncates a Condorcet Winner C to create a top-cycle cannot by so doing become a pairwise victor over the buried Condorcet Winner ... but must (in order to create a cycle) help some other candidate B defeat C by insincerely voting B>C. Our Quick and Dirty method insures that if the sincere CW's rightful victory is subverted, it goes to B, not to A. Is this method quick enough and dirty enough for the FairVote IRV promoters? What objections/criticisms might they have? Do they have any counter proposal that rivals this one in any way? If so, let them educate us ... we'll gladly join them if they can show us a better way! If not, then they should join us to educate the politicians, public, and last but not least, the academics still stuck in the pre-EM era!

I apologize for the defiant tone at the end of the previous message ... I must have gotten carried away with the "Dirty Dozen"' theme. But isn't it frustrating to you when people use the 2nd law of thermodynamics (or Arrow and Gibbard-Satterthwaite in the EM context) to justify their stubborn resistance to any kind of engineering progress? In the previous message Q&D Burial Resistant Condorcet was formulate in the typical "stitched together" form ... "Elect the CW if there is one, Else ..." In this message I would like to formulate a seamless version: Let X be the Smith candidate who on the fewest ballots is ranked ahead of any other Smith candidate. On each ballot approve all candidates down to X, but include X only when no Smith candidate is ranked ahead of X. Elect the candidate approved on the most ballots. This method can be described as electing the approval winner when the approval cutoff is (at the rank of) the weakest of the Smith candidates, which itself is approved on (and only on) those ballots which do not approve any other Smith candidate. In other words, the approval cutoff is inclusive only when necessary to ensure approval of at least one member of Smith. Since a Smith member is approved on every ballot, the method satisfies the Condorcet Criterion, i.e. it elects the only Smith member when Smith is a singleton. How does that grab you? -FWS El dom., 2 de ene. de 2022 7:30 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > Is there any burial resistant Condorcet method simpler than this? > > The basic pre-requisite is to understand that whenever there is no > Condorcet Winner there will be a pairwise cycle, called a "top-cycle" of > candidates whose members are not defeated by any candidates outside of the > cycle, just as a Condorcet Winner is a candidate undefeated by any other > candidate. > > Here's the Q&D burial resistant method: > > Lacking a Condorcet Winner elect the candidate X having the greatest > pairwise victory over the top-cycle member Y that has the smallest ratio of > first to last place votes within the top cycle. > > Two examples illustrate the method: > > Example 1. > > 49 C > 26 A>B > 25 B (sincere B>A) > > The top cycle is ABCA > > Candidate A has the smallest ratio 26/74 of first to last place votes. > > Candidate C is the only candidate with a pairwise victory over it, so C > wins. > > Notice how our rule does not reward B for insincerely lowering A to > (equal) last? > > Example 2. > > 45 A>B (sincere A>C) > 35 B>C > 25 C>A > > Candidate C has the smallest ratio 25/45 of first to last. > > Candidate B wins as the only candidate with a pairwise victory over C. So > A's burial of C backfires. > > Typically, the faction A that buries or truncates a Condorcet Winner C to > create a top-cycle cannot by so doing become a pairwise victor over the > buried Condorcet Winner ... but must (in order to create a cycle) help some > other candidate B defeat C by insincerely voting B>C. > > Our Quick and Dirty method insures that if the sincere CW's rightful > victory is subverted, it goes to B, not to A. > > Is this method quick enough and dirty enough for the FairVote IRV > promoters? > > What objections/criticisms might they have? > > Do they have any counter proposal that rivals this one in any way? > > If so, let them educate us ... we'll gladly join them if they can show us > a better way! > > If not, then they should join us to educate the politicians, public, and > last but not least, the academics still stuck in the pre-EM era! >

Hi Forest, This sounds like an interesting method to me! However, I would change the winning criteria to "Elect the most approved member of the Smith Set". On Mon, Jan 3, 2022 at 11:06 AM Forest Simmons <forest.simmons21@gmail.com> wrote: > I apologize for the defiant tone at the end of the previous message ... I > must have gotten carried away with the "Dirty Dozen"' theme. > > But isn't it frustrating to you when people use the 2nd law of > thermodynamics (or Arrow and Gibbard-Satterthwaite in the EM context) to > justify their stubborn resistance to any kind of engineering progress? > > In the previous message Q&D Burial Resistant Condorcet was formulate in > the typical "stitched together" form ... "Elect the CW if there is one, > Else ..." > > In this message I would like to formulate a seamless version: > > Let X be the Smith candidate who on the fewest ballots is ranked ahead of > any other Smith candidate. On each ballot approve all candidates down to X, > but include X only when no Smith candidate is ranked ahead of X. > > Elect the candidate approved on the most ballots. > > This method can be described as electing the approval winner when the > approval cutoff is (at the rank of) the weakest of the Smith candidates, > which itself is approved on (and only on) those ballots which do not > approve any other Smith candidate. > > In other words, the approval cutoff is inclusive only when necessary to > ensure approval of at least one member of Smith. > > Since a Smith member is approved on every ballot, the method satisfies the > Condorcet Criterion, i.e. it elects the only Smith member when Smith is a > singleton. > > How does that grab you? > > -FWS > > El dom., 2 de ene. de 2022 7:30 p. m., Forest Simmons < > forest.simmons21@gmail.com> escribió: > >> Is there any burial resistant Condorcet method simpler than this? >> >> The basic pre-requisite is to understand that whenever there is no >> Condorcet Winner there will be a pairwise cycle, called a "top-cycle" of >> candidates whose members are not defeated by any candidates outside of the >> cycle, just as a Condorcet Winner is a candidate undefeated by any other >> candidate. >> >> Here's the Q&D burial resistant method: >> >> Lacking a Condorcet Winner elect the candidate X having the greatest >> pairwise victory over the top-cycle member Y that has the smallest ratio of >> first to last place votes within the top cycle. >> >> Two examples illustrate the method: >> >> Example 1. >> >> 49 C >> 26 A>B >> 25 B (sincere B>A) >> >> The top cycle is ABCA >> >> Candidate A has the smallest ratio 26/74 of first to last place votes. >> >> Candidate C is the only candidate with a pairwise victory over it, so C >> wins. >> >> Notice how our rule does not reward B for insincerely lowering A to >> (equal) last? >> >> Example 2. >> >> 45 A>B (sincere A>C) >> 35 B>C >> 25 C>A >> >> Candidate C has the smallest ratio 25/45 of first to last. >> >> Candidate B wins as the only candidate with a pairwise victory over C. So >> A's burial of C backfires. >> >> Typically, the faction A that buries or truncates a Condorcet Winner C to >> create a top-cycle cannot by so doing become a pairwise victor over the >> buried Condorcet Winner ... but must (in order to create a cycle) help some >> other candidate B defeat C by insincerely voting B>C. >> >> Our Quick and Dirty method insures that if the sincere CW's rightful >> victory is subverted, it goes to B, not to A. >> >> Is this method quick enough and dirty enough for the FairVote IRV >> promoters? >> >> What objections/criticisms might they have? >> >> Do they have any counter proposal that rivals this one in any way? >> >> If so, let them educate us ... we'll gladly join them if they can show us >> a better way! >> >> If not, then they should join us to educate the politicians, public, and >> last but not least, the academics still stuck in the pre-EM era! >> > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

Good idea! Although it seems to me that the highest approval candidate would have to pairwise beat or tie the approval cutoff candidate X pairwise (which would be impossible for a non-Smith candidate to do) ...I could be wrong ... and in any case redundancy reinforces communication and understanding. El lun., 3 de ene. de 2022 3:04 p. m., Ted Stern <dodecatheon@gmail.com> escribió: > Hi Forest, > > This sounds like an interesting method to me! > > However, I would change the winning criteria to "Elect the most approved > member of the Smith Set". > > On Mon, Jan 3, 2022 at 11:06 AM Forest Simmons <forest.simmons21@gmail.com> > wrote: > >> I apologize for the defiant tone at the end of the previous message ... I >> must have gotten carried away with the "Dirty Dozen"' theme. >> >> But isn't it frustrating to you when people use the 2nd law of >> thermodynamics (or Arrow and Gibbard-Satterthwaite in the EM context) to >> justify their stubborn resistance to any kind of engineering progress? >> >> In the previous message Q&D Burial Resistant Condorcet was formulate in >> the typical "stitched together" form ... "Elect the CW if there is one, >> Else ..." >> >> In this message I would like to formulate a seamless version: >> >> Let X be the Smith candidate who on the fewest ballots is ranked ahead of >> any other Smith candidate. On each ballot approve all candidates down to X, >> but include X only when no Smith candidate is ranked ahead of X. >> >> Elect the candidate approved on the most ballots. >> >> This method can be described as electing the approval winner when the >> approval cutoff is (at the rank of) the weakest of the Smith candidates, >> which itself is approved on (and only on) those ballots which do not >> approve any other Smith candidate. >> >> In other words, the approval cutoff is inclusive only when necessary to >> ensure approval of at least one member of Smith. >> >> Since a Smith member is approved on every ballot, the method satisfies >> the Condorcet Criterion, i.e. it elects the only Smith member when Smith is >> a singleton. >> >> How does that grab you? >> >> -FWS >> >> El dom., 2 de ene. de 2022 7:30 p. m., Forest Simmons < >> forest.simmons21@gmail.com> escribió: >> >>> Is there any burial resistant Condorcet method simpler than this? >>> >>> The basic pre-requisite is to understand that whenever there is no >>> Condorcet Winner there will be a pairwise cycle, called a "top-cycle" of >>> candidates whose members are not defeated by any candidates outside of the >>> cycle, just as a Condorcet Winner is a candidate undefeated by any other >>> candidate. >>> >>> Here's the Q&D burial resistant method: >>> >>> Lacking a Condorcet Winner elect the candidate X having the greatest >>> pairwise victory over the top-cycle member Y that has the smallest ratio of >>> first to last place votes within the top cycle. >>> >>> Two examples illustrate the method: >>> >>> Example 1. >>> >>> 49 C >>> 26 A>B >>> 25 B (sincere B>A) >>> >>> The top cycle is ABCA >>> >>> Candidate A has the smallest ratio 26/74 of first to last place votes. >>> >>> Candidate C is the only candidate with a pairwise victory over it, so C >>> wins. >>> >>> Notice how our rule does not reward B for insincerely lowering A to >>> (equal) last? >>> >>> Example 2. >>> >>> 45 A>B (sincere A>C) >>> 35 B>C >>> 25 C>A >>> >>> Candidate C has the smallest ratio 25/45 of first to last. >>> >>> Candidate B wins as the only candidate with a pairwise victory over C. >>> So A's burial of C backfires. >>> >>> Typically, the faction A that buries or truncates a Condorcet Winner C >>> to create a top-cycle cannot by so doing become a pairwise victor over the >>> buried Condorcet Winner ... but must (in order to create a cycle) help some >>> other candidate B defeat C by insincerely voting B>C. >>> >>> Our Quick and Dirty method insures that if the sincere CW's rightful >>> victory is subverted, it goes to B, not to A. >>> >>> Is this method quick enough and dirty enough for the FairVote IRV >>> promoters? >>> >>> What objections/criticisms might they have? >>> >>> Do they have any counter proposal that rivals this one in any way? >>> >>> If so, let them educate us ... we'll gladly join them if they can show >>> us a better way! >>> >>> If not, then they should join us to educate the politicians, public, and >>> last but not least, the academics still stuck in the pre-EM era! >>> >> ---- >> Election-Methods mailing list - see https://electorama.com/em for list >> info >> >