Hi everyone, I've just invented a new voting rule. It seems to me that it has very good axiomatic properties (it satisfies e.g., Smith, ISDA, cloneproofness, monotonicity, reversal symmetry) but I haven't found anything similar in the voting literature. I'm curious about your thoughts. The algorithm proceeds in rounds. Each round is structured as follows: * we process pairwise matchups from strongest to weakest, * in each processed matchup, the winner qualifies for the next round, and any further matchups involving them in the current round are skipped, * this continues until only one candidate remains unqualified, who is then eliminated from the election, * then the next round begins with all candidates who qualified from the previous round. The process repeats until only one candidate remains (which happens after m-1 rounds), who is declared the winner. Equivalently, we can stop when there is a Condorcet winner in the election. This method is significantly different from Schulze or Ranked Pairs --- for example, in an election with 3 candidates in a cycle, it elects the candidate with the strongest victory, not the one with the weakest defeat. Do you see any other strengths/weaknesses of this method? Best, Grzegorz Pierczyński

On 3/11/25 5:49 AM, Grzegorz Pierczyński wrote: > I've just invented a new voting rule. It seems to me that it has very good > axiomatic properties (it satisfies e.g., Smith, ISDA, cloneproofness, > monotonicity, reversal symmetry) but I haven't found anything similar in > the voting literature. I'm curious about your thoughts. Interesting. However, if I'm understanding the algorithm correctly, it's not monotonic. In the step-throughs below, an uppercase pair XY means that X qualifies based on that pairwise matchup; a lowercase pair xy means that at least one of X and Y was already qualified at that step so nothing happens. First election: 0 ABCD 2 ADBC 3 ADCB 2 BACD 7 BADC 5 CADB 8 DCBA Margin of row over column: A B C D A 0 -7 1 11 B 7 0 -5 -9 C -1 5 0 -13 D -11 9 13 0 Algorithm step-through: D B A (DC ad db BA cb AC) A D (AD DB) A (AD) Second election (same as before except the BACD voters switch to ABCD): 2 ABCD 2 ADBC 3 ADCB 0 BACD 7 BADC 5 CADB 8 DCBA Margin of row over column: A B C D A 0 -3 1 11 B 3 0 -5 -9 C -1 5 0 -13 D -11 9 13 0 Algorithm step-through: D C B (DC ad db CB BA) D C (DC db CB) D (DC) A goes from the winner to the first candidate eliminated!

In addition, I believe the method fails Burial, Chicken Dilemma (defection), and forced cycle. On Mon, Mar 17, 2025, 04:19 Joshua Boehme <joshua.p.boehme@gmail.com> wrote: > > > On 3/11/25 5:49 AM, Grzegorz Pierczyński wrote: > > > I've just invented a new voting rule. It seems to me that it has very > good > > axiomatic properties (it satisfies e.g., Smith, ISDA, cloneproofness, > > monotonicity, reversal symmetry) but I haven't found anything similar in > > the voting literature. I'm curious about your thoughts. > > Interesting. > > However, if I'm understanding the algorithm correctly, it's not monotonic. > > In the step-throughs below, an uppercase pair XY means that X qualifies > based on that pairwise matchup; a lowercase pair xy means that at least > one > of X and Y was already qualified at that step so nothing happens. > > > First election: > 0 ABCD > 2 ADBC > 3 ADCB > 2 BACD > 7 BADC > 5 CADB > 8 DCBA > > Margin of row over column: > A B C D > A 0 -7 1 11 > B 7 0 -5 -9 > C -1 5 0 -13 > D -11 9 13 0 > > Algorithm step-through: > D B A (DC ad db BA cb AC) > A D (AD DB) > A (AD) > > > Second election (same as before except the BACD voters switch to ABCD): > 2 ABCD > 2 ADBC > 3 ADCB > 0 BACD > 7 BADC > 5 CADB > 8 DCBA > > Margin of row over column: > A B C D > A 0 -3 1 11 > B 3 0 -5 -9 > C -1 5 0 -13 > D -11 9 13 0 > > Algorithm step-through: > D C B (DC ad db CB BA) > D C (DC db CB) > D (DC) > > > > A goes from the winner to the first candidate eliminated! > ---- > Election-Methods mailing list - see https://electorama.com/em for list > info >

On 2025-03-19 23:35, Ted Stern wrote: > In addition, I believe the method fails Burial, Chicken Dilemma > (defection), and forced cycle. What do you mean by failing Burial and forced cycle? -km