At each elimination step IPE eliminates the Condorcet Loser if there is one, otherwise it eliminates the loser of the pairwise contest with the most winning votes. We propose eliminating (at each elimination step among those not eliminated previously) the Condorcet Loser if there is one, else the pairwise loser between (1) the candidate whose maximum support for any of its pairwise wins is minimal, and (2) the loser from the pairwise contest with the fewest losing votes (i.e. the Gross Loser). In other words eliminate the CL when there is one, otherwise eliminate whichever is less preferred... the GL or the closest thing to a CL. Is this better than BRGL which simply eliminates the GL at each step? Yes and no. On the one hand it is more aggressive and thorough about getting rid of the least desireable remaining candidate as soon as possible. On the other hand it is probably a harder sell to a public lacking patience in these matters ... who tend to assume that the order of elimination of "losers" doesn't make much difference, if any. Sent from my MetroPCS 4G LTE Android Device

Simplified version: At each elimination step eliminate from among the remaining candidates the pairwise loser between (1) the candidate whose maximum margin of support is minimal, and (2) the loser in the pairwise contest with fewest losing votes. (1) is the Condorcet Loser if there is one, else (arguably) the candidate closest to that distinction in the sense that its max win margin is as close to zero as possible. [A candidate will have at least one positive margin of sjpport if and only if it is not the CL.] So let's call it the NCL, Nearest thing to Condorcet Loser. (2) is the Gross Loser from Benham's version of Reynaud, BRGL. So Improved Instant Pairwise Elimination eliminates (at each step) the pairwise loser between the NCL and the GL. If the NCL and the GL are different, then the eliminated candidate is beaten by the other one. If they are the same, then the eliminated candidate is the GL, which is never a Condorcet candidate. In neither case is a Condorcet candidate eliminated ... so the method meets the Condorcet Criterion. Note that the pairwise margins matrix is simply the pairwise support matrix minus its transpose, so the whole thing is efficiently precinct summable. My preferred version of the pairwise support matrix is this: the (i, j) entry is the number of ballots on which candidate i is ranked strictly ahead of j, plus the number of ballots on which both are ranked Top, plus half the number of ballots on which both are ranked together (i.e. equal to each other) strictly between Bottom and Top. This convention for equal rankings makes good sense, for example, when interpreting the diagonal elements of the matrix as implicit approvals, and in other similar contexts. Thanks for listening! Sent from my MetroPCS 4G LTE Android Device -------- Original message -------- From: Susan Simmons <suzerainsimmons@outlook.com> Date: 7/8/21 12:18 PM (GMT-08:00) To: election-methods@lists.electorama.com Subject: Improved Instant Pairwise Elimination At each elimination step IPE eliminates the Condorcet Loser if there is one, otherwise it eliminates the loser of the pairwise contest with the most winning votes. We propose eliminating (at each elimination step among those not eliminated previously) the Condorcet Loser if there is one, else the pairwise loser between (1) the candidate whose maximum support for any of its pairwise wins is minimal, and (2) the loser from the pairwise contest with the fewest losing votes (i.e. the Gross Loser). In other words eliminate the CL when there is one, otherwise eliminate whichever is less preferred... the GL or the closest thing to a CL. Is this better than BRGL which simply eliminates the GL at each step? Yes and no. On the one hand it is more aggressive and thorough about getting rid of the least desireable remaining candidate as soon as possible. On the other hand it is probably a harder sell to a public lacking patience in these matters ... who tend to assume that the order of elimination of "losers" doesn't make much difference, if any. Sent from my MetroPCS 4G LTE Android Device

On Thu, Jul 8, 2021 at 2:19 PM Susan Simmons <suzerainsimmons@outlook.com> wrote: > > At each elimination step IPE eliminates the Condorcet Loser if there is > one, otherwise it eliminates the loser of the pairwise contest with the > most winning votes. > > We propose eliminating (at each elimination step among those not > eliminated previously) the Condorcet Loser if there is one, else the > pairwise loser between (1) the candidate whose maximum support for any of > its pairwise wins is minimal, and (2) the loser from the pairwise contest > with the fewest losing votes (i.e. the Gross Loser). > > In other words eliminate the CL when there is one, otherwise eliminate > whichever is less preferred... the GL or the closest thing to a CL. > > Is this better than BRGL which simply eliminates the GL at each step? > > Yes and no. On the one hand it is more aggressive and thorough about > getting rid of the least desireable remaining candidate as soon as > possible. On the other hand it is probably a harder sell to a public > lacking patience in these matters ... who tend to assume that the order of > elimination of "losers" doesn't make much difference, if any. > I think this is a technically superior method that has zero chance of being adopted for a government election. If the goal is to get an ideal method, we already have them in the form of Ranked Pairs, followed by Schulze. But think of what it would actually take to present a proposal to (say) the city council of Burlington. Here is the text for the IRV proposal from 2019 (169 words): ----- All elections of mayor, city councilors and school commissioners shall be by ballot, using a system of ranked choice voting without a separate runoff election. The chief administrative officer shall implement a ranked choice voting protocol according to these guidelines: (1) The ballot shall give voters the option of ranking candidates in order of preference. (2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected. (3) If no candidate receives a majority of first preferences, an instant runoff re-tabulation shall be performed by the presiding election officer. The instant runoff re-tabulation shall be conducted in rounds. In each round, each voter’s ballot shall count as a single vote for whichever continuing candidate the voter has ranked highest. The candidate with the fewest votes after each round shall be eliminated until only two candidates remain, with the candidate then receiving the greatest number of votes being elected. (4) The city council may adopt additional regulations consistent with this subsection to implement these standards. ----- Here is my best attempt to write a similar proposal for BRGL (167 words): ----- All elections of mayor, city councilors and school commissioners shall be by ballot, using a system of ranked choice voting without a separate runoff election. The chief administrative officer shall implement a ranked choice voting protocol according to these guidelines: (1) The ballot shall give voters the option of ranking candidates in order of preference. (2) If a candidate receives a majority (over 50 percent) of first preferences, that candidate is elected. (3) If no candidate receives a majority of first preferences, the presiding officer shall conduct elimination rounds. For every pair of candidates "A" and "B", the presiding officer shall tally the number of votes that rank "A" higher than "B" and the number of voters that rank candidate "B" higher than "A". Then, the presiding officer shall successively remove the candidate with the fewest votes in any such pairwise tally until one candidate remains, who shall then be elected. (4) The city council may adopt additional regulations consistent with this subsection to implement these standards. ----- Now think of what it would take to write your modified BRGL in this language. Daniel.

I like Susan's suggestions (below). As a result of these suggestions and other recent developments, currently I'm writing software that implements the following method, which is an improvement over IPE (Instant Pairwise Elimination). The first two steps prevent misunderstandings about step 3. 1. When a voter does not rank a candidate, that candidate is ranked at the lowest preference level shown on the ballot. (This fairness compromise is designed to not alienate fans of write-in candidates.) 2. When a voter marks multiple ranking levels for the same candidate, the highest rank is used and the other marks for that candidate are ignored. 3. On each ballot each candidate receives the number of upvotes equal to the number of not-yet-eliminated candidates who are ranked lower than that candidate. 4. The upvotes are added across all the ballots to yield a "pairwise support count" for each candidate. 5. The two candidates who have the smallest pairwise support counts compete against each other in a bottom-two runoff. 6. During the bottom-two runoff each ballot indicates which of the two candidates is ranked at a lower level compared to the other candidate, and the candidate who is ranked lower on more ballots is eliminated. 7. Candidates are eliminated one at a time until a single candidate remains. 8. If this method is used in a US primary election for one of the two largest political parties (currently the Republican and Democratic parties), the last candidate to be eliminated also progresses to the general election as a second nominee. (This provision defeats the money-based tactics of blocking, concentration, and splitting.) I'm still working out details about how best to resolve ties. Currently I like Susan's idea of eliminating the candidate with the smallest single pairwise count (against any other candidate). On rare occasions this method can fail to elect the Condorcet winner. Under current conditions this is an advantage. That's because the FairVote organization has convinced large numbers of voters that Condorcet methods are bad. After writing the code for this method I'll measure its success rates for Clone independence and IIA (independence of irrelevant alternatives). Note that step 3 provides a fairer way to accomplish what STAR voting does with scores. In case it isn't obvious, this method allows two (or more) candidates to be marked at the same preference level, and the counts are precinct summable. These advantages overcome two of the biggest disadvantages of FairVote's version of IRV. Again, thank you Susan for your useful suggestions! Richard Fobes The VoteFair guy On 7/8/2021 6:04 PM, Susan Simmons wrote: > Simplified version: > > At each elimination step eliminate from among the remaining candidates > the pairwise loser between (1) the candidate whose maximum margin of > support is minimal, and (2) the loser in the pairwise contest with > fewest losing votes. > > (1) is the Condorcet Loser if there is one, else (arguably) the > candidate closest to that distinction in the sense that its max win > margin is as close to zero as possible. [A candidate will have at least > one positive margin of sjpport if and only if it is not the CL.] So > let's call it the NCL, Nearest thing to Condorcet Loser. > > (2) is the Gross Loser from Benham's version of Reynaud, BRGL. > > So Improved Instant Pairwise Elimination eliminates (at each step) the > pairwise loser between the NCL and the GL. > > If the NCL and the GL are different, then the eliminated candidate is > beaten by the other one. If they are the same, then the eliminated > candidate is the GL, which is never a Condorcet candidate. In neither > case is a Condorcet candidate eliminated ... so the method meets the > Condorcet Criterion. > > Note that the pairwise margins matrix is simply the pairwise support > matrix minus its transpose, so the whole thing is efficiently precinct > summable. > > My preferred version of the pairwise support matrix is this: the (i, j) > entry is the number of ballots on which candidate i is ranked strictly > ahead of j, plus the number of ballots on which both are ranked Top, > plus half the number of ballots on which both are ranked together (i.e. > equal to each other) strictly between Bottom and Top. > > This convention for equal rankings makes good sense, for example, when > interpreting the diagonal elements of the matrix as implicit approvals, > and in other similar contexts. > > Thanks for listening! > > > > Sent from my MetroPCS 4G LTE Android Device > > > -------- Original message -------- > From: Susan Simmons <suzerainsimmons@outlook.com> > Date: 7/8/21 12:18 PM (GMT-08:00) > To: election-methods@lists.electorama.com > Subject: Improved Instant Pairwise Elimination > > > At each elimination step IPE eliminates the Condorcet Loser if there is > one, otherwise it eliminates the loser of the pairwise contest with the > most winning votes. > > We propose eliminating (at each elimination step among those not > eliminated previously) the Condorcet Loser if there is one, else the > pairwise loser between (1) the candidate whose maximum support for any > of its pairwise wins is minimal, and (2) the loser from the pairwise > contest with the fewest losing votes (i.e. the Gross Loser). > > In other words eliminate the CL when there is one, otherwise eliminate > whichever is less preferred... the GL or the closest thing to a CL. > > Is this better than BRGL which simply eliminates the GL at each step? > > Yes and no. On the one hand it is more aggressive and thorough about > getting rid of the least desireable remaining candidate as soon as > possible. On the other hand it is probably a harder sell to a public > lacking patience in these matters ... who tend to assume that the order > of elimination of "losers" doesn't make much difference, if any. > > > > > Sent from my MetroPCS 4G LTE Android Device > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list info >

> On 07/12/2021 1:21 PM VoteFair <electionmethods@votefair.org> wrote: > ... > > On rare occasions this method can fail to elect the Condorcet winner. > Under current conditions this is an advantage. That's because the > FairVote organization has convinced large numbers of voters that > Condorcet methods are bad. > I don't think that's precisely true. I think FairVote's position is: a) that Hare RCV is exactly perfect and that it is the only method to tally ranked ballots. Don't question that. b) that Condorcet does not exist, so why worry about it? Remember: 1. Hare RCV "guarantees a majority winner". 2. Hare RCV "eliminates the spoiler effect". 3. Hare RCV allows voters to "Vote their hopes rather than their fears." Don't you ever forget or question that. Evidence from Vermont notwithstanding. -- r b-j . _ . _ . _ . _ rbj@audioimagination.com "Imagination is more important than knowledge." . . .