Kristofer suggested introducing a sequence of methods m0, m1, m2, ... forming a path of small steps gradually progressing from some simple method m0 towards some ideal end method m_infinity. Any ideas? Here's a related question: how did butterflies evolve? Forest

On 3/9/23 23:14, Forest Simmons wrote: > Kristofer suggested introducing a sequence of methods m0,  m1, m2, ... > forming a path of small steps gradually progressing from some simple > method m0 towards some ideal end method m_infinity. > > Any ideas? Here are some: BTR-IRV to Benham (if the voters don't care about monotonicity or summability); first preference Copeland to Benham (if they care about strategy resistance but not monotonicity); Minmax to Schulze, Ranked Pairs or River (if failing Condorcet loser is not too tough a sell); possibly to some uncovered RP variant after this? STAR to Smith,Range or Smith|Range (for cardinal ballots; X|Y is just notation I made up now for renormalizing after excluding everybody in the X set as I couldn't find a better designation for it) These are all finite sequences. /Perhaps/ Approval -> STAR -> Smith,Range would work, but it would require a ballot format change. On a related subject, as I understand it, FairVote likes to point out that their preferred single-winner method is a stepping stone to multiwinner. The IRV-likes above easily generalize to STV by adding the surplus election and redistribution steps, e.g. STV-ME (BTR-IV). I once devised a multiwinner Ranked Pairs method with a polynomial runtime (in the number of voters and candidates), but in practice the polynomial is too large for large elections; it requires solving large linear programs. There's also CPO-STV and Schulze STV, but they're very complex. Range has PRV, so possibly something like PRV -> Sequential Monroe -> Monroe (or PRV -> Sequential Ebert -> Ebert). For Majority Judgement or Bucklin there's BTV/EAR and my MCAB (though the latter is also pretty complex). Condorcet methods in general? STV-CLE, but it feels kind of like cheating; the step from Condorcet to bolting it onto STV may feel a bit too artificial. -km

Perhaps VPR... vote for a published ranking or ballot at some early stage of a method or sequence of methods... especially if there is some way to keep political parties from hijacking the VPR process the way they have hijacked the primaries, the debates, etc. Versions of Asset Voting for single winner to multi winner ... with proportional weighted votes in assemblies ... as steps towards more sophisticated methods of proxy hierarchies. Even proportional approval voting based on Vote For a Published Ballot Approval Voting. It could just be regular Approval ... it's so easy to copy a published ballot ... just put check marks next to the names of the recommended candidates (except the ones you disagree with) on your official ballot Keep those ideas coming ... then after we get past the pure brainstorming we can flesh out some of the ones that.seem most promising. On Fri, Mar 10, 2023, 9:45 AM Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 3/9/23 23:14, Forest Simmons wrote: > > Kristofer suggested introducing a sequence of methods m0, m1, m2, ... > > forming a path of small steps gradually progressing from some simple > > method m0 towards some ideal end method m_infinity. > > > > Any ideas? > > Here are some: > > BTR-IRV to Benham (if the voters don't care about monotonicity or > summability); > first preference Copeland to Benham (if they care about strategy > resistance but not monotonicity); > Minmax to Schulze, Ranked Pairs or River (if failing Condorcet loser is > not too tough a sell); possibly to some uncovered RP variant after this? > STAR to Smith,Range or Smith|Range (for cardinal ballots; X|Y is just > notation I made up now for renormalizing after excluding everybody in > the X set as I couldn't find a better designation for it) > > These are all finite sequences. /Perhaps/ Approval -> STAR -> > Smith,Range would work, but it would require a ballot format change. > > On a related subject, as I understand it, FairVote likes to point out > that their preferred single-winner method is a stepping stone to > multiwinner. The IRV-likes above easily generalize to STV by adding the > surplus election and redistribution steps, e.g. STV-ME (BTR-IV). > > I once devised a multiwinner Ranked Pairs method with a polynomial > runtime (in the number of voters and candidates), but in practice the > polynomial is too large for large elections; it requires solving large > linear programs. There's also CPO-STV and Schulze STV, but they're very > complex. > > Range has PRV, so possibly something like PRV -> Sequential Monroe -> > Monroe (or PRV -> Sequential Ebert -> Ebert). For Majority Judgement or > Bucklin there's BTV/EAR and my MCAB (though the latter is also pretty > complex). > > Condorcet methods in general? STV-CLE, but it feels kind of like > cheating; the step from Condorcet to bolting it onto STV may feel a bit > too artificial. > > -km >

Here's a path with baby steps starting from IRV: Step 0 ... IRV itself; Until only one candidate remains ... Eliminate MinTop EndUntil Step 1 ... An efficiently summable pairwise version: Until just one candidate remains ... eliminate minminPS EndUntil Step2 ... a Banks efficient version: Until just one candidate remains ... eliminate Friends(minminPS) EndUntil Step3 ... a burial resistant Banks version: Until just one candidate remains ... eliminate Friends(PL(mmPO,MMPO)) EndUntil If the transition to pairwise was too sudden ... intercalate into the sequence ... Step O.5 Until just one candidate remains ... eliminate PL(minTop, MaxBot) EndUntil Step 0.9 ...Until just one candidate remains ... eliminate Friends PL(MaxTop, MaxBot) EndUntil This version 0.9 is burial resistant, Banks efficient, etc...but not efficiently summable. However, it takes only two or three passes through the ballots at most ... unlike IRV, which takes up to n-1 passes. >From here go to step 3 ... same perks as 0.9 but only one pass needed. -Forest On Fri, Mar 10, 2023, 12:34 PM Forest Simmons <forest.simmons21@gmail.com> wrote: > Perhaps VPR... vote for a published ranking or ballot at some early stage > of a method or sequence of methods... especially if there is some way to > keep political parties from hijacking the VPR process the way they have > hijacked the primaries, the debates, etc. > > Versions of Asset Voting for single winner to multi winner ... with > proportional weighted votes in assemblies ... as steps towards more > sophisticated methods of proxy hierarchies. > > Even proportional approval voting based on Vote For a Published Ballot > Approval Voting. > > It could just be regular Approval ... it's so easy to copy a published > ballot ... just put check marks next to the names of the recommended > candidates (except the ones you disagree with) on your official ballot > > Keep those ideas coming ... then after we get past the pure brainstorming > we can flesh out some of the ones that.seem most promising. > > On Fri, Mar 10, 2023, 9:45 AM Kristofer Munsterhjelm <km_elmet@t-online.de> > wrote: > >> On 3/9/23 23:14, Forest Simmons wrote: >> > Kristofer suggested introducing a sequence of methods m0, m1, m2, ... >> > forming a path of small steps gradually progressing from some simple >> > method m0 towards some ideal end method m_infinity. >> > >> > Any ideas? >> >> Here are some: >> >> BTR-IRV to Benham (if the voters don't care about monotonicity or >> summability); >> first preference Copeland to Benham (if they care about strategy >> resistance but not monotonicity); >> Minmax to Schulze, Ranked Pairs or River (if failing Condorcet loser is >> not too tough a sell); possibly to some uncovered RP variant after this? >> STAR to Smith,Range or Smith|Range (for cardinal ballots; X|Y is just >> notation I made up now for renormalizing after excluding everybody in >> the X set as I couldn't find a better designation for it) >> >> These are all finite sequences. /Perhaps/ Approval -> STAR -> >> Smith,Range would work, but it would require a ballot format change. >> >> On a related subject, as I understand it, FairVote likes to point out >> that their preferred single-winner method is a stepping stone to >> multiwinner. The IRV-likes above easily generalize to STV by adding the >> surplus election and redistribution steps, e.g. STV-ME (BTR-IV). >> >> I once devised a multiwinner Ranked Pairs method with a polynomial >> runtime (in the number of voters and candidates), but in practice the >> polynomial is too large for large elections; it requires solving large >> linear programs. There's also CPO-STV and Schulze STV, but they're very >> complex. >> >> Range has PRV, so possibly something like PRV -> Sequential Monroe -> >> Monroe (or PRV -> Sequential Ebert -> Ebert). For Majority Judgement or >> Bucklin there's BTV/EAR and my MCAB (though the latter is also pretty >> complex). >> >> Condorcet methods in general? STV-CLE, but it feels kind of like >> cheating; the step from Condorcet to bolting it onto STV may feel a bit >> too artificial. >> >> -km >> >