Schulze, RP(wv), MinMax(wv) & Smith//MinMax(wv) are all very strongly probabilistically-autodeterent. I applied them to a typical example with a complete exhaustive set of 18 cases. The test: Factions& candidates: The example is with 3 factions, respectively favoring 3 candidates: CW, BF, & Bus. CW stands for sincere Condorcet winner (who is buried in the example’s 18 cases. BF stands for Buriers’ Favorite. Bus refers to the candidate under whom the buriers have buried the CW. Basic example & its variables: The 3 factions all differer in size, because in actuality they usually do. But their sizes as nearly equal as nearly equal as possible, & their size difference is uniform. …because that’s the center state of affairs about which the actual instances will vary…the most typical state of affairs (& probably most frequent state-of affairs, among all possible states of affairs). Both the BF faction & the Bus faction prefer CW to eachother’s candidate. The Bus faction ranks CW 2nd, because the examples are about ONE faction, the BF faction, attempting strategy. The BF faction (insincerely) ranks Bus 2nd. The CW faction, in the various cases, rank a 2nd choice of BF, Bus, or no one. The 18 cases are for all 6 size-orderings for the 3 factions, & for all 3 ways for the CW faction to rank a 2nd choice (including no 2nd choice). There are 99 voters. e.g. the 1st case is: 32: CW>BF 34: BF>Bus 33: Bus>CW The other cases cover all the combinations of the variations of the size-ordering variable & the CW faction’s2nd-choice variable. The faction sizes of 34, 33, & 32 are used in all of the cases, in which the factions’ size ordering changes. The measure of autodeterence is the ratio of the probability of electing Bus to the probability of electing BF. …measured by the number of instances of the election of Bus, among the 18 cases, divided by the number of instances of the election of BF among those 18 cases. So the measure of autodeterence in this test is: Bus/BF…referring to the ratio of their numbers of wins among the 18 cases. Results for Schulze, RP(wv), MinMax(wv), & Smith//MinMax(wv): Bus/BF = 7. Bus/BF when CW faction is smallest = 5. Bus/BF when CW faction is middle = 5. Bus/BF when BF faction is largest & CW faction is smallest = 2. Bus/BF when BF faction is largest & Bus faction is smallest = 2. Bus/BF when CW faction is largest is infinite (or undefined, because division by zero is undefined). Offensive truncation wasn’t tested, because, for the above-named methods, it’s been well-known here for 35 years that offensive truncation doesn’t work when only one faction truncates, & the CW is supported by the other faction. But, for any other method, of course the test would have to include an additional 18 cases of offensive truncation. When I introduced Condorcet(wv), & told its properties, 35 years ago, they included compliance with what is now called the Minimal-Defense Criterion. Because of the possibility of defensive truncation being used, that criterion-compliance conferred burial-deterrence. But, even if defensive truncation isn’t used by enough voters, burial is nonetheless strongly deterred by those methods’ probabilistic autodeterence, described above. Those methods are the only ones that have been determined to be probabilistically autodeterrent by exhaustive testing. Given that Schulze & RP are widely popular & widely recognized as the kings of criteria-compliance, & given the extreme brevity possible for RP, RP(wv) is the obvious natural best proposal for a Condorcet-Criterion rang-method. RP(wv): If no voted CW (due to a top-cycle): Drop the weakest defeat in every cycle. Elect the resulting unbeaten candidate. (Defeat-strength measured by number of ballots ranking defeater over defeated.)

Hi Mike, Interesting work: Feb 24 2024 à 16:39:27 UTC−6, Michael Ossipoff <email9648742@gmail.com> a écrit : > Schulze, RP(wv), MinMax(wv) & Smith//MinMax(wv) are all very strongly > probabilistically-autodeterent. >  > I applied them to a typical example with a complete exhaustive set of 18 cases. [...] > When I introduced Condorcet(wv), & told its properties, 35 years ago, they > included compliance with what is now called the Minimal-Defense Criterion. >  > Because of the possibility of defensive truncation being used, that > criterion-compliance conferred burial-deterrence. [...] > Those methods are the only ones that have been determined to be > probabilistically autodeterrent by exhaustive testing. >  > Given that Schulze & RP are widely popular & widely recognized as the kings of > criteria-compliance, & given the extreme brevity possible for RP, RP(wv) is the > obvious natural best proposal for a Condorcet-Criterion rang-method. >  > RP(wv): > If no voted CW (due to a top-cycle): > Drop the weakest defeat in every cycle. > Elect the resulting unbeaten candidate. > (Defeat-strength measured by number of ballots ranking defeater over defeated.) Putting aside popularity or name recognition I tend to think that River dominates RP due to ease of calculation, whether one performs it manually or has to write an algorithm. I guess maybe you didn't check River, but I think it would evaluate the same. I like your conception of RP here, which looks pretty easy, but I wonder if it leads to ties. For example, if there is a cycle A>B>C>A where B>C is the weakest among these, and also a cycle A>B>D>A where A>B is the weakest, do we drop B>C and A>B simultaneously? If we do, it starts to look like we won't know how to order B relative to C in the final ranking. Kevin votingmethods.net votingmethods.net/cond (relevant Condorcet calculator)

Oops! Thanks for pointing that out. It convincingly seemed to me that dropping the weakest defeat in every cycle would do exactly the same as the Ranked-Pairs procedure, where you make a list starting with the stronger defeats, skipping any defeat that cycles with listed defeats. Evidently not so. The definition that I gave results, as you said, in a tie—even if all the defeats are different magnitudes, & there are no pair-ties. So that tie with B & C unbeaten would happen even in any big public election. Again, thanks for telling me about that. As you can tell, I was so sure that I didn’t even try a multi-cycle example. So much for my briefer RP definition-wording. But RP still seems easier to define & explain than Beatpath/CSSD. Also, Steve said that the RP winner usually pairbeats the Beatpath winner. Is River as easy to define &. explain as RP?. Fortunately, all Condorcet(wv) methods are the same with 3 candidates. So, in my 18 cases with only 3 candidates, my wrong definition didn’t make any difference, with just that one cycle. But in a larger election, the buriers might bury CW under 2 Buses, making 2 parallel cycles both involving CW & BF, but each cycle with a different Bus. I hope that doesn’t affect RP’s autodeterence when the right definition is used. I should try that with MinMax too. BTW, I added 6 more cases, with the CW faction half ranking BF 2nd, & half ranking Bus 2nd…summing to 4 ways for the CW voters to 2nd-rank: CW>BF CW>Bus CW Half each of CW>BF & CW>Bus. It just seemed to more realistically cover how toCW voters could vote. That brought it to 24 cases. It raised the Bus/BF ratio from 7 up to 10. There was a journal paper with the words “Split-Cycle” in its title. The author defined Split-Cycle the same way as my incorrect brief RP mis-definition. He said it was different from RP. Ain’t that the truth ! He used margins instead of wv, & claimed all sorts of fantastic criterion-compliances for it…presumably in natural sincere circular ties. I didn’t know what he was talking about. Well, with luck, the autodeterence will still work , with the right RP definition in multi-Bus examples. Thanks again for pointing that out to me. On Wed, Feb 28, 2024 at 22:41 Kevin Venzke <stepjak@yahoo.fr> wrote: > Hi Mike, > > Interesting work: > > Feb 24 2024 à 16:39:27 UTC−6, Michael Ossipoff <email9648742@gmail.com> a > écrit : > > Schulze, RP(wv), MinMax(wv) & Smith//MinMax(wv) are all very strongly > > probabilistically-autodeterent. > > > > I applied them to a typical example with a complete exhaustive set of 18 > cases. > [...] > > When I introduced Condorcet(wv), & told its properties, 35 years ago, > they > > included compliance with what is now called the Minimal-Defense > Criterion. > > > > Because of the possibility of defensive truncation being used, that > > criterion-compliance conferred burial-deterrence. > [...] > > Those methods are the only ones that have been determined to be > > probabilistically autodeterrent by exhaustive testing. > > > > Given that Schulze & RP are widely popular & widely recognized as the > kings of > > criteria-compliance, & given the extreme brevity possible for RP, RP(wv) > is the > > obvious natural best proposal for a Condorcet-Criterion rang-method. > > > > RP(wv): > > If no voted CW (due to a top-cycle): > > Drop the weakest defeat in every cycle. > > Elect the resulting unbeaten candidate. > > (Defeat-strength measured by number of ballots ranking defeater over > defeated.) > > Putting aside popularity or name recognition I tend to think that River > dominates RP due to ease of calculation, whether one performs it manually > or > has to write an algorithm. I guess maybe you didn't check River, but I > think > it would evaluate the same. > > I like your conception of RP here, which looks pretty easy, but I wonder > if it > leads to ties. > > For example, if there is a cycle A>B>C>A where B>C is the weakest among > these, > and also a cycle A>B>D>A where A>B is the weakest, do we drop B>C and A>B > simultaneously? If we do, it starts to look like we won't know how to > order B > relative to C in the final ranking. > > Kevin > votingmethods.net > votingmethods.net/cond (relevant Condorcet calculator) >