Very good point, Richard, these loser-elimination methods are just stop-gap methods that might be a stepping stone to something better ... we shall see. Note that Teams is not an elimination method ... losing teams are not eliminated but absorbed into the team whose member-champion captured their captain, where they, in turn, through valiant future action may contribute to the absorption of other teams. Do you recognize "Teams" as a reformulation of "River"? Sent from my MetroPCS 4G LTE Android Device -------- Original message -------- From: Richard Lung <voting@ukscientists.com> Date: 7/9/21 10:10 AM (GMT-08:00) To: Susan Simmons <suzerainsimmons@outlook.com> Subject: Re: [EM] Improved Instant Pairwise Elimination To all, By eliminating candidates, you are losing voter information. No candidate should be excluded until the count is complete. Regards Richard. Lung. On 9 Jul 2021, at 2:04 am, Susan Simmons <suzerainsimmons@outlook.com<mailto:suzerainsimmons@outlook.com>> 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<mailto:suzerainsimmons@outlook.com>> Date: 7/8/21 12:18 PM (GMT-08:00) To: election-methods@lists.electorama.com<mailto: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 09.07.2021 23:02, Susan Simmons wrote: > > Very good point, Richard, these loser-elimination methods are just > stop-gap methods that might be a stepping stone to something better ... > we shall see. Sometimes it's the only way we know how to get certain properties (like Condorcet and DMTBR), but I suspect that just means that the theory is lacking. The manipulability integer programs suggest that a monotone strategy-resistant method exists. But I have no idea how to actually construct one, because the strong monotonicity requirements for something like Benham are way too strong - as are the DMTBR ones. -km

Dear All, As there is only one truth, a valid voting method must have the same count for an election as an exclusion/elimination (symmetrical count requirement) otherwise one of the counts must be false (more or less). (The basic dysfunction of MMP is that it has votes for two contradictory election counts, so one of them must be wrong -- indeed both are!) Generally, voting methods have one election count and a buttress of an elimination count, to keep the election count going to completion. The elimination generally is not even considered as an equal count, in its own right, to the election count. Elections are generally just that, (uninomial) election counts. Symmetrical election and exclusion counts are a binomial count. It took me a life-time to arrive at that (when over 50). It took another 14 years to fully develop FAB STV. (Afterwards, I worked out how to do a 2-D voting system with a complex number count. I consider myself retired.) FAB STV Is monotonic. Shifting about the preferences won't give perverse results. And so it is not manipulable by strategic voting. Regards, Richard Lung. On 9 Jul 2021, at 10:18 pm, Kristofer Munsterhjelm <km_elmet@t-online.de> wrote: > On 09.07.2021 23:02, Susan Simmons wrote: > > Very good point, Richard, these loser-elimination methods are just > stop-gap methods that might be a stepping stone to something better ... > we shall see. Sometimes it's the only way we know how to get certain properties (like Condorcet and DMTBR), but I suspect that just means that the theory is lacking. The manipulability integer programs suggest that a monotone strategy-resistant method exists. But I have no idea how to actually construct one, because the strong monotonicity requirements for something like Benham are way too strong - as are the DMTBR ones. -km