Hello, Here is the procedure for "Adjusted Condorcet Plurality": 1. From the submitted rankings, identify the first preference winner (FPW). 2. Edit all the ballots so that all preferences below the FPW are removed/truncated. 3. On the revised ballot set, check for a Condorcet winner. Elect them if there is one. 4. Else elect the FPW. What's interesting about this is that, like IRV, you can't hurt *or* help a candidate by adding additional lower preferences. But this is done without eliminating any candidates. The candidate with the fewest first preferences can win! 26 A 25 B>D 25 C>D 24 D D wins, no problem. Among other LNHarm methods, MMPO and "LNH Borda" will elect D as well, but neither of those satisfies the Plurality criterion. This "ACP" method does. In other cases IRV does do better: 25 A>B>D 20 B>C>D 20 C>D>A>B>E 18 D>C 17 E>D The CW is D, and IRV elects D. But the "adjusted" CW is C, and wins in ACP. Another: 25 A>E>B>C>D 21 B>D>C 20 C 19 D>C>A 15 E>C The CW is C, which IRV elects. But on the adjusted rankings C no longer beats D; there is no adjusted CW, and so ACP defaults to electing the FPW, A. With three candidates, ACP gives the same result as IRV. As the number of candidates increases, the Condorcet efficiency and compromise incentive seem to improve over IRV (i.e. in simulations), but it's very slight. I guess that if you generate ballots randomly, then no matter how many candidates there are, roughly the same percentage of preferences will get truncated in the adjustment. On the downside, ACP loses IRV's satisfaction of Condorcet Loser, mutual majority, and Mono-add-top. Mono-raise performance is also worse. I have added ACP to my LNHarm calculator, so if you like you can experiment and see how similar ACP is to IRV. You can click on the "Random scenario" button, so no need to type out any ballots: https://www.votingmethods.net/lnharm I found two ways to vary this to create a total of four methods, but I decided the others are more complicated while giving less interesting results. One thing you can do is find the top two instead of the FPW, runoff between them, and cut all preferences below *either* of those two. When there is no "adjusted CW" then elect the runoff winner. This method further distorts the "adjusted" form of the ballots since we now truncate under two candidates instead of one. The other thing you can do is produce a LNHarm method without LNHelp, by not simply truncating the preferences below the FPW. Instead, for example if your vote is FPW>X>Y, then your X>Y preference cannot help X beat Y when considering whether X is the adjusted CW, but *does* help X beat Y when considering whether Y is the adjusted CW. While it seems like it might (?) be desirable to allow voters to benefit somewhat from these lower preferences, all it can do is further help the FPW, which probably makes the method less interesting. Example: 40 A>C 35 B>C 25 C>B In the LNHarm-only version, the A>C voters are able to block B from beating C, and C can't defeat B, so A wins. Not great: FPP is probably the only other method that picks A here. (The normal version of ACP with both LNHs elects B.) Kevin votingmethods.net

On 1/22/23 17:55, Kevin Venzke wrote: > Hello, > > Here is the procedure for "Adjusted Condorcet Plurality": > > 1. From the submitted rankings, identify the first preference winner (FPW). > 2. Edit all the ballots so that all preferences below the FPW are removed/truncated. > 3. On the revised ballot set, check for a Condorcet winner. Elect them if there is one. > 4. Else elect the FPW. That's nice and indeed interesting! My method finder wouldn't have found this because (if I understand it right) it's not summable. Does your simulator have a strategy susceptibility calculator? If so, is it any good on that measure? > 40 A>C > 35 B>C > 25 C>B > > In the LNHarm-only version, the A>C voters are able to block B from beating C, and C can't > defeat B, so A wins. Not great: FPP is probably the only other method that picks A here. > (The normal version of ACP with both LNHs elects B.) That's even more Plurality-focused than IFPP. That does take some doing. -km

Hi Kristofer, > On 1/22/23 17:55, Kevin Venzke wrote: > > Hello, > >  > > Here is the procedure for "Adjusted Condorcet Plurality": > >  > > 1. From the submitted rankings, identify the first preference winner (FPW). > > 2. Edit all the ballots so that all preferences below the FPW are removed/truncated. > > 3. On the revised ballot set, check for a Condorcet winner. Elect them if there is one. > > 4. Else elect the FPW. >  > That's nice and indeed interesting! >  > My method finder wouldn't have found this because (if I understand it  > right) it's not summable. I have been assuming it isn't summable since at first glance you have to determine the FPW first, and then in a second pass get a pairwise matrix. But that's it. I'm not sure what the precise definition of summability is, but could it be allowed to do this in one pass? If there are n candidates then you need to track n + n( n(n-1) ) figures, counting in one pass. It's comparable to a single 3D matrix. My DNA framework technically can find this method, but realistically I wouldn't have found it this way, because it wouldn't have appeared to be definable in any terms I had thought of. > Does your simulator have a strategy susceptibility calculator? If so, is  > it any good on that measure? Not an overall susceptibility measure, just a collection of miscellaneous ones, two of which (truncation and burial) won't show anything for this method. The performance is very similar to IRV (which should make sense since with three candidates they are the same method). With four candidates and five blocs: Condorcet Loser: IRV satisfies, ACP does not Mono-add-top failures: IRV satisfies, ACP does not Mono-raise failures: ACP is 23% worse Condorcet efficiency: ACP .8% better CDTT efficiency: ACP .7% better Compromise incentive: ACP 2.6% better Winner has a majority against them: ACP 3.8% better Minimal defense failures: ACP 4.3% better SFC failures: ACP 4.4% better Maybe I should provide another pairing to show that these numbers are mostly pretty small. So here's a few numbers but comparing Bucklin and DSC to IRV. Condorcet efficiency: Bucklin 15% worse (than IRV); DSC 13.5% worse CDTT efficiency: Bucklin 4.6% better; DSC 7% worse Compromise incentive: Bucklin 49% better; DSC 7% worse Winner has a majority against them: Bucklin 19.7% better; DSC 31% worse Minimal defense failures: Bucklin satisfies this; DSC 67% worse SFC failures: Bucklin 6.2% better; DSC 41% worse Not sure if that helps but in short, it seems like ACP might show tiny gains in some areas, in exchange for worse monotonicity and clone independence, and also Condorcet Loser failures. Kevin votingmethods.net