Let's call it Q&CBRS. Pre-requisite background: Candidate X pairwise defeats candidate Y iff candidate X is ranked above/before/ahead of candidate Y on more ballots than not. A defeat chain is a sequence of candidates in which each candidate pairwise defeats the subsequent member of the chain. Using a "bubble sort" procedure to sort a list of candidates into pairwise order produces a defeat chain of the listed candidates. In this way we can easily find a defeat chain that includes all of the candidates. The first candidate in such a chain is an example of a Smith candidate. More generally, any candidate who has a defeat chain to any other candidate is a member of the Smith Set. Q&CBRS: First, find the "basic score" for each candidate defined as the number of ballots on which it is ranked above one or more candidates. Then let X be the Smith candidate with the smallest basic score. Finally, among the candidates not defeated by X, elect the one with the greatest basic score. That's it! Quick & Clean! Note that if there is only one Smith candidate X, then X will be the only candidate not defeated by X, and therefore the one elected . In general a candidate not defeated by X will defeat X, and thereby find itself at the head of a defeat chain to every other candidate, i.e. it will be a Smith candidate. When there is only one Smith candidate, that candidate will not be pairwise defeated by any other candidate. I repeat the entire method procedure here: First, find the "basic score" for each candidate defined as the number of ballots on which it is ranked above one or more candidates. Then let X be the Smith candidate with the smallest basic score. Finally, among the candidates not defeated by X, elect the one with the greatest basic score. Where else can you find such a simple, quick, and clean election method? El lun., 3 de ene. de 2022 4:19 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > 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 >>> >>