1. Let PL be the Pairwise Loser between the two candidates with the fewest transferred votes. 2. Eliminate every candidate that does not beat PL pairwise, including PL itself. 3. While more than one candidate remains,' repeat steps 1 and 2. Now Improved Coombs: 1. Let PL be the Pairwise Loser between the two candidates with the greatest Bottom counts among the remaining candidates. 2. Eliminate every candidate that does not beat PL pairwise, including PL itself. 3. While more than one candidate remains,' repeat steps 1 and 2. Improved Borda: 1. Let PL be the Pairwise Loser between the two candidates with the smallest Borda Counts among the remaining candidates. 2. Eliminate every candidate that does not beat PL pairwise, including PL itself. 3. While more than one candidate remains,' repeat steps 1 and 2. Improved Score 1. Let PL be the Pairwise Loser between the two candidates with the least scores among the remaining candidates. 2. Eliminate every candidate that does not beat PL pairwise, including PL itself. 3. While more than one candidate remains,' repeat steps 1 and 2. Improved Academic Washout Elimination 1. Let PL be the Pairwise Loser between the two candidates with the least GPA among the remaining candidates. 2. Eliminate every candidate that does not beat PL pairwise, including PL itself. 3. While more than one candidate remains,' repeat steps 1 and 2. Improved SPE 1. Let PL be the Pairwise Loser between the two candidates nearest the worst end of the Elimination Agenda among the remaining candidates. 2. Eliminate every candidate that does not beat PL pairwise, including PL itself. 3. While more than one candidate remains,' repeat steps 1 and 2. Of all these improved methods this one is the only one that preserves monotonicity ... which is why it is the one singled out for a progression proposal. But all of these methods are Banks efficient ... hence Landau efficient ... which prevents the embarrassment of electing winner that is covered by a loser. None of the extant methods have that guarantee... not Rannked Pairs, nor CSSD, nor Kemeny-Young , etc. -Forest

There's been a dramatically democratically improved IRV since about 1850, it's called the Hare system ("Andrae system", in Scandinava). There's been a decisively improved Borda method since 1880. It's called the Gregory method. It is why statisticians prefer weighting in arithmetic proportion (Gregory method) to weighting in arithmetic progression (Borda method). They only use the latter when they have to assume the magnitudes of intervals in their tabulations of data collection. Personally, I doubt whether pairwise contests are really suitable for more than single member contests (which are monopolistic not democratic enough, despite politicians contentions). My limited experience is that, in single member contests, weighted Condorcet and Borda methods are in agreement, as rational counts of quite marginal contests, compared to mere elimination methods, like Suppementary Vote, FPTP, IRV/AV, which are only ordinal scale measures (of more or less), not more accurate rational representations of data. Regards, Richard Lung. On 25/03/2023 07:17, Forest Simmons wrote: > 1. Let PL be the Pairwise Loser between the two candidates with the > fewest transferred  votes. > > 2. Eliminate every candidate that does not beat PL pairwise, including > PL itself. > > 3. While more than one candidate remains,' repeat steps 1 and 2. > > Now Improved Coombs: > > 1. Let PL be the Pairwise Loser between the two candidates with the > greatest Bottom  counts among the remaining candidates. > > 2. Eliminate every candidate that does not beat PL pairwise, including > PL itself. > > 3. While more than one candidate remains,' repeat steps 1 and 2. > > Improved Borda: > > 1. Let PL be the Pairwise Loser between the two candidates with the > smallest  Borda Counts  among the remaining candidates. > > 2. Eliminate every candidate that does not beat PL pairwise, including > PL itself. > > 3. While more than one candidate remains,' repeat steps 1 and 2. > > Improved Score > > 1. Let PL be the Pairwise Loser between the two candidates with the > least  scores among the remaining candidates. > > 2. Eliminate every candidate that does not beat PL pairwise, including > PL itself. > > 3. While more than one candidate remains,' repeat steps 1 and 2. > > Improved Academic Washout Elimination > 1. Let PL be the Pairwise Loser between the two candidates with the > least GPA among the remaining candidates. > > 2. Eliminate every candidate that does not beat PL pairwise, including > PL itself. > > 3. While more than one candidate remains,' repeat steps 1 and 2. > > Improved SPE > 1. Let PL be the Pairwise Loser between the two candidates nearest the > worst end of the Elimination Agenda among the remaining candidates. > > 2. Eliminate every candidate that does not beat PL pairwise, including > PL itself. > > 3. While more than one candidate remains,' repeat steps 1 and 2. > > Of all these improved methods this one is the only one that preserves > monotonicity ... which is why it is the one singled out for a > progression proposal. > > But all of these methods are Banks efficient ... hence Landau > efficient ... which prevents the embarrassment of electing winner that > is covered by a loser. > > None of the extant methods have that guarantee... not Rannked Pairs, > nor CSSD, nor Kemeny-Young , etc. > > -Forest > > > > > > > > > > ---- > Election-Methods mailing list - seehttps://electorama.com/em for list info