Kevin – I'm not sure if you're right about IRV. If someone votes A=B>C, I'd attribute half a first-place preference to each of A and B. I don't know what other people would do.    Colin On 24/09/2023 18:41, Kevin Venzke wrote: > Hi Colin, > > Le dimanche 24 septembre 2023 à 07:41:45 UTC−5, Colin Champion <colin.champion@routemaster.app> a écrit : >> Kevin – thanks for this helpful reply. I'm inclined to favour viewing a tie as two >> half-voters with opposed preferences. I admit that this can only be a rule of thumb, >> but I find it quite persuasive. After all, the whole point of ranked voting is that >> voters start out, I assume, with nebulous cardinal judgements in their heads, and >> that turning these judgements into rankings puts them onto a common basis (albeit >> with loss of information) which allows them to be meaningfully combined. The WV rule >> could easily undermine the premise of this procedure. > I understand this as an abstract ideal. Something jarring to me is that the practical > consequence of converting equal preferences into half-votes would vary a lot based > on what the base method is. Under IRV it wouldn't do anything. (But maybe you don't > find that IRV conforms to "the whole point of ranked voting.") > >> I believe that asymmetric treatment of ties in the Borda count leads quite directly >> to errors of the sort I described, but I don't know if this is widely accepted. > Isn't it pretty clear that symmetric treatment of ties under Borda results in a > practically unusable method? In terms of strategic dilemmas it's like margins on > steroids. > > I wonder if the errors you mean are defined precisely enough to say. > >> It's true that Darlington models ties as genuine expressions of indifference. In >> practice ties can mean almost anything; indifference, laziness, ignorance... Quite >> possibly voting methods which work well for one sort of tie will work less well for >> another. The result I produced myself is probably genuine, and indicates that WV is >> more accurate than margins for mandatory truncation; but I was wrong to suppose that >> it could be interpreted more generally since it omits the effect which is most >> likely to work against WV. >> >> As for the positive arguments you put forward, well they might justify a rule of >> thumb but I wouldn't find them compelling. > Yes, I offered a rule of thumb that leads to a heuristic called WV. There can be > other rules of thumb and other heuristics, and if they test in simulations as having > low strategic incentives (especially low compromise incentive) then I will advocate > those methods, too. > > I left out talk of my own simulations, but compromise incentive is a focus of mine. > >> I don't find the Condorcet principle >> persuasive on its own merits (and do not believe it generally sound), but I accept >> it as a working principle because I don't know any other way of obtaining simple >> accurate voting methods under a spatial model. > I would agree that Condorcet itself shouldn't be taken as a first principle. > > It sounds like you would advocate Condorcet as the best heuristic available to > identify the best outcome when voters are sincere under a spatial model. > > I would advocate Condorcet because it makes the ballot a more effective agent to > represent the voter's interests. > > Kevin > votingmethods.net > > > > On 23/09/2023 02:47, Kevin Venzke wrote: >>   Hi Colin, >> >> Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion <colin.champion@routemaster.app> a écrit : >> >>>   A possible explanation for the discrepancy between my result and Darlington's is that >>> in my evaluation every ballot had the same number of ties and in Darlington's the >>> numbers differed. >>> On the face of it, WV doesn't treat voters equally. If we defined "winning votes" as >>> "the number of voters who prefer A to B plus half the number who rank them equally", >>> then every voter would contribute m(m-1)/2 winning votes and WV would be equivalent >>> (I think) to Margins. But instead we define winning votes asymmetrically so that WV >>> is *not* equivalent to margins but voters contribute different numbers of winning >>> votes depending on the number of ties in their ballots. I can imagine this leading to >>> artefacts which Darlington's evaluation would pick up and mine would miss. If this is >>> what happened, then even Darlington's evaluation must be too lenient to WV since he >>> doesn't include effects which would in fact arise, such as voters truncating >>> differentially according to their political viewpoint. >>> Maybe these things have been taken into account; I have no idea, having never seen the >>> thinking behind WV. >>> >> I am not sure what to make of Darlington's defeat strength comparison. It sounds like >> it was basically a simulation of sincere voters who vote equality because they actually >> consider the candidates equal. That premise is fine but somewhat far removed from how >> this topic is usually discussed, i.e. with some consideration of comparative strategy. >> >> I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a >> Condorcet method. I wonder whether he implemented it as one to get his numbers on that. >> >> In any case: >> >> To find the motivation for WV I would start with first principles. How should we design >> a Condorcet completion method to minimize strategic incentives? A motivation behind >> Condorcet itself is that voters should not vote sincerely only to find that they >> should've voted another way. >> >> What could this mean here? Well, a full majority can always get what they want by >> changing their votes. Therefore if a majority votes A>B yet B is elected, we have >> *probably* done something wrong, because the majority certainly did have the power to >> make A win instead. The election of B gives the A>B voters an incentive to vote >> differently to change the outcome. The voters obtain a "complaint," I will call it. >> Since majorities will most predictably obtain such complaints when we override their >> preference, we should prioritize locking majorities. >> >> With WV, there is no special heed paid to majorities, it just goes down the list of >> contests starting with the largest winning blocs. But this achieves the goal. It >> applies its principle to sub-majority contests as well, and maybe this is good bad or >> neutral, but maybe we can believe that if it was helpful (for our end goal) to favor >> majorities over sub-majorities then it could also be helpful to favor larger >> sub-majorities over smaller sub-majorities. It certainly stands to reason that the more >> voters you have sharing some stance, the more likely it is that a vote change on their >> part could change the outcome. >> >> (On my website I describe a different approach focused on compromise incentive, and >> measuring the potential for this more directly, and one can take that as me suggesting >> that WV actually leaves some room for improvement.) >> >> You notice that adding half-votes to equal rankings under WV will turn it into margins. >> This would give every contest a full majority on the winning side, and seemingly we can >> trivialize this requirement of mine to prioritize majorities. >> >> But I think it's clear, in the context of this analysis, that adding half-votes for >> equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of >> opposing "half-complaints," where one of the complaints has the potential to be voiced >> when *either* of A or B is elected. The A=B voter has no possible complaint either way, >> as neither result can incentivize them to change their vote. >> >> Additionally, I think that voters expect and want it to be the case that abstaining >> from a pairwise contest does not mean the same thing as saying they rate both >> candidates equal. I touched on this in my previous post. >> >> Consider this election: >> >> 7 A>B >> 5 B >> 8 C >> >> Margins elects A, which is very unusual across election methods, and I think most >> people would find this result surprising due to a sense of what truncation ought to >> mean. >> >> (Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone >> here.) >> >> Perhaps with enough education people can *understand* that the method takes seriously >> the apparent equality of the truncated preferences. But I don't think voters will find >> it comfortable to vote under those circumstances. I think voters want to be able to >> identify the set of candidates that they believe they are trying to defeat, leave them >> out of their ranking, and not have to think any further about it. >> >> Kevin >> votingmethods.net

On 9/24/2023 1:31 PM, Colin Champion wrote: > Kevin – I'm not sure if you're right about IRV. If someone votes A=B>C, > I'd attribute half a first-place preference to each of A and B. I don't > know what other people would do. > Colin Under IRV another counting option is to pair this same-rank ballot (A=B>C) with another ballot that also reaches the counting round where the same two candidates (A and B) are top ranked (after ignoring any higher-ranked candidates who have been eliminated). Then one of the two ballots goes to one of the two candidates and the other ballot goes to the other candidate. Of course mathematically this is equivalent to splitting each ballot into 0.5 votes for candidate A and 0.5 votes for candidate B. However this decimal interpretation violates what many non-math-savvy voters would regard as a violation of "one person one vote." So academic testing software can use the easier-to-code decimal numbers. But for real certifiable election software the non-ballot-splitting method would be easier to understand as fair. Detail: When a ballot can't be paired with a pattern-matching ballot, that ballot is ignored. This is equivalent to the decimal option with rounding non-integer numbers down to the nearest integer. Of course the pairing concept can be extended to any number of candidates -- 3, 4, etc. -- being ranked at the same choice level. However, beyond about 5 or 6 this approach consumes too much memory because every possible "pairing" must be tracked. To avoid this issue I think it's reasonable to have a rule that says the ballot is set aside until the number of currently same-ranked candidates is 5 or less. This "pairing" option is what I coded here: https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/rcipe_stv.cpp It calculates these methods: * RCIPE * RCIPE STV. * IRV (for comparison purposes only) * STV Richard Fobes

I have some preliminary results for "approval truncation" in which a voter truncates at the largest gap between cardinal rankings. Minimax (margins) does slightly better than minimax (WV). Voting is sincere; there are 8 candidates and 10001 voters (a ballot is truncated on average to 4.6 entries). Full figures follow (which won't be very readable in a variable-width font). It's noticeable that the results are worse than for fixed truncation, even though the average ballot length is slightly greater.             random    fptp     dblv seq    conting   nauru    borda     sbc2   bucklin sinkhorn    mj       av     coombs            12.5820  35.9910     -     45.8790     - 53.6880  80.5090     -     67.5170     -        - 55.7040  69.1810             clower  knockout   spe     benham  btr-irv baldwin   nanson  minimax minimaxwv minisum     rp river   schulze    asm     cupper            75.1840  75.8440  76.2830  76.0300  75.8900 75.8700  75.9440  75.9660  75.9580  75.9680  75.8200 -     75.7640  75.9200  77.3430 condorcet+  random    fptp     dblv   conting   borda av            75.4610  75.5690  75.6860  75.8110  76.4530 75.8300     llull+ randomr   fptpf    fptpr    dblvf   contingr bordaf   bordar    avf      avr    minimaxf minimaxr            75.8750  75.8660  76.2610  75.8330  76.2600 76.3780  76.2620  75.9250  76.2590  75.9530  76.2620     smith+ randomr   fptpf    fptpr    dblvf   contingr bordaf   bordar    avf      avr    minimaxf minimaxr tideman            75.7640  75.7470  76.2310  75.7630  76.2400 76.4530  76.2530  75.8650  76.2420  75.9680  76.2470 76.0700 I will try a couple of other truncation models and then look at strategic voting.     CJC On 24/09/2023 13:41, Colin Champion wrote: > Kevin – thanks for this helpful reply. I'm inclined to favour viewing > a tie as two half-voters with opposed preferences. I admit that this > can only be a rule of thumb, but I find it quite persuasive. After > all, the whole point of ranked voting is that voters start out, I > assume, with nebulous cardinal judgements in their heads, and that > turning these judgements into rankings puts them onto a common basis > (albeit with loss of information) which allows them to be meaningfully > combined. The WV rule could easily undermine the premise of this > procedure. >    I believe that asymmetric treatment of ties in the Borda count > leads quite directly to errors of the sort I described, but I don't > know if this is widely accepted. >    It's true that Darlington models ties as genuine expressions of > indifference. In practice ties can mean almost anything; indifference, > laziness, ignorance... Quite possibly voting methods which work well > for one sort of tie will work less well for another. The result I > produced myself is probably genuine, and indicates that WV is more > accurate than margins for mandatory truncation; but I was wrong to > suppose that it could be interpreted more generally since it omits the > effect which is most likely to work against WV. >    As for the positive arguments you put forward, well they might > justify a rule of thumb but I wouldn't find them compelling. I don't > find the Condorcet principle persuasive on its own merits (and do not > believe it generally sound), but I accept it as a working principle > because I don't know any other way of obtaining simple accurate voting > methods under a spatial model. >    I will try to extend my own evaluation software to allow a less > restrictive model of truncation. >       Colin > > On 23/09/2023 02:47, Kevin Venzke wrote: >> Hi Colin, >> >> Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion<colin.champion@routemaster.app> a écrit : >>> A possible explanation for the discrepancy between my result and Darlington's is that >>> in my evaluation every ballot had the same number of ties and in Darlington's the >>> numbers differed. >>> On the face of it, WV doesn't treat voters equally. If we defined "winning votes" as >>> "the number of voters who prefer A to B plus half the number who rank them equally", >>> then every voter would contribute m(m-1)/2 winning votes and WV would be equivalent >>> (I think) to Margins. But instead we define winning votes asymmetrically so that WV >>> is *not* equivalent to margins but voters contribute different numbers of winning >>> votes depending on the number of ties in their ballots. I can imagine this leading to >>> artefacts which Darlington's evaluation would pick up and mine would miss. If this is >>> what happened, then even Darlington's evaluation must be too lenient to WV since he >>> doesn't include effects which would in fact arise, such as voters truncating >>> differentially according to their political viewpoint. >>> Maybe these things have been taken into account; I have no idea, having never seen the >>> thinking behind WV. >> I am not sure what to make of Darlington's defeat strength comparison. It sounds like >> it was basically a simulation of sincere voters who vote equality because they actually >> consider the candidates equal. That premise is fine but somewhat far removed from how >> this topic is usually discussed, i.e. with some consideration of comparative strategy. >> >> I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a >> Condorcet method. I wonder whether he implemented it as one to get his numbers on that. >> >> In any case: >> >> To find the motivation for WV I would start with first principles. How should we design >> a Condorcet completion method to minimize strategic incentives? A motivation behind >> Condorcet itself is that voters should not vote sincerely only to find that they >> should've voted another way. >> >> What could this mean here? Well, a full majority can always get what they want by >> changing their votes. Therefore if a majority votes A>B yet B is elected, we have >> *probably* done something wrong, because the majority certainly did have the power to >> make A win instead. The election of B gives the A>B voters an incentive to vote >> differently to change the outcome. The voters obtain a "complaint," I will call it. >> Since majorities will most predictably obtain such complaints when we override their >> preference, we should prioritize locking majorities. >> >> With WV, there is no special heed paid to majorities, it just goes down the list of >> contests starting with the largest winning blocs. But this achieves the goal. It >> applies its principle to sub-majority contests as well, and maybe this is good bad or >> neutral, but maybe we can believe that if it was helpful (for our end goal) to favor >> majorities over sub-majorities then it could also be helpful to favor larger >> sub-majorities over smaller sub-majorities. It certainly stands to reason that the more >> voters you have sharing some stance, the more likely it is that a vote change on their >> part could change the outcome. >> >> (On my website I describe a different approach focused on compromise incentive, and >> measuring the potential for this more directly, and one can take that as me suggesting >> that WV actually leaves some room for improvement.) >> >> You notice that adding half-votes to equal rankings under WV will turn it into margins. >> This would give every contest a full majority on the winning side, and seemingly we can >> trivialize this requirement of mine to prioritize majorities. >> >> But I think it's clear, in the context of this analysis, that adding half-votes for >> equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of >> opposing "half-complaints," where one of the complaints has the potential to be voiced >> when *either* of A or B is elected. The A=B voter has no possible complaint either way, >> as neither result can incentivize them to change their vote. >> >> Additionally, I think that voters expect and want it to be the case that abstaining >> from a pairwise contest does not mean the same thing as saying they rate both >> candidates equal. I touched on this in my previous post. >> >> Consider this election: >> >> 7 A>B >> 5 B >> 8 C >> >> Margins elects A, which is very unusual across election methods, and I think most >> people would find this result surprising due to a sense of what truncation ought to >> mean. >> >> (Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone >> here.) >> >> Perhaps with enough education people can *understand* that the method takes seriously >> the apparent equality of the truncated preferences. But I don't think voters will find >> it comfortable to vote under those circumstances. I think voters want to be able to >> identify the set of candidates that they believe they are trying to defeat, leave them >> out of their ranking, and not have to think any further about it. >> >> Kevin >> votingmethods.net > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list info

I tried two other forms of truncation. Under "candidate-specific truncation" the m candidates have associated truncation levels which are a random permutation of the numbers 1...m. A ballot is truncated to the level corresponding to its first candidate. I expected this to be a hard case for WV, but in fact it does appreciably better than margins.             random    fptp     dblv seq    conting   nauru    borda     sbc2   bucklin  sinkhorn mj       av     coombs            12.6630  35.6490  50.7000  44.9140  51.6650  54.5890 73.6530     -     66.3850     -        -     53.3880  68.9630             clower  knockout   spe     benham  btr-irv  baldwin nanson  minimax minimaxwv minisum     rp     river   schulze asm     cupper            70.0190  71.5400  71.7760  71.2680  70.9510  71.4700 71.8440  72.0970  72.9090  72.1000  71.5630  71.9420  71.3330 72.2980  75.2630 condorcet+  random    fptp     dblv   conting   borda      av            70.6780  70.6580  70.9080  71.0760  72.2750  70.9920     llull+ randomr   fptpf    fptpr    dblvf   contingr  bordaf bordar    avf      avr    minimaxf minimaxr            71.6220  71.2570  71.9820  71.2600  71.9970  72.2020 72.0080  71.3300  72.0120  72.0510  72.0070     smith+ randomr   fptpf    fptpr    dblvf   contingr  bordaf bordar    avf      avr    minimaxf minimaxr tideman            71.3330  70.8970  71.5080  70.9620  71.5820  72.2730 71.6550  71.0270  71.6240  72.0990  71.6490  71.1760 The other form I tried was 'ignorance truncation'. Each candidate has a prominence - i.e. probability of being recognised by an arbitrary voter - drawn (separately for each election) from a Beta(r,s) distribution. Voters rank the candidates they recognise in order of proximity, truncating after the last candidate they recognise. I used r=2, s=1, giving a recognition probability of 2/3. This was essentially a tie between the two minimax variants. Borda, which looked good against other forms of truncation, did badly this time. Evidently ignorance truncation is more damaging than the other sorts.            random    fptp     dblv seq    conting   nauru    borda     sbc2   bucklin  sinkhorn mj       av     coombs            12.5510  37.4290  43.1720  36.6340  41.2690  40.7330 34.6170     -     41.5260     -        -     40.9330  42.4740             clower  knockout   spe     benham  btr-irv  baldwin nanson  minimax minimaxwv minisum     rp     river   schulze asm     cupper            43.1770  43.8040  44.4050  43.5870  44.0050  44.0480 43.9970  43.9990  43.9330  44.0170  43.8610  44.0040  43.7660 43.6000  46.7470 condorcet+  random    fptp     dblv   conting   borda      av            43.6260  44.0730  44.1880  43.9420  43.2570  43.5720     llull+ randomr   fptpf    fptpr    dblvf   contingr  bordaf bordar    avf      avr    minimaxf minimaxr            43.7980  43.9980  43.4990  44.0330  43.4980  43.3220 43.4960  43.6550  43.4950  43.9890  43.4980     smith+ randomr   fptpf    fptpr    dblvf   contingr  bordaf bordar    avf      avr    minimaxf minimaxr tideman            43.7660  44.1030  43.4060  44.1810  43.4080  43.2570 43.4000  43.5750  43.4000  44.0000  43.4100  43.5840 At risk of repetition... correctness of software is not guaranteed.    CJC On 27/09/2023 12:45, Colin Champion wrote: > I have some preliminary results for "approval truncation" in which a > voter truncates at the largest gap between cardinal rankings. Minimax > (margins) does slightly better than minimax (WV). Voting is sincere; > there are 8 candidates and 10001 voters (a ballot is truncated on > average to 4.6 entries). Full figures follow (which won't be very > readable in a variable-width font). It's noticeable that the results > are worse than for fixed truncation, even though the average ballot > length is slightly greater. >             random    fptp     dblv seq    conting   nauru    > borda     sbc2   bucklin sinkhorn    mj       av     coombs >            12.5820  35.9910     -     45.8790     - 53.6880  > 80.5090     -     67.5170     -        - 55.7040  69.1810 >             clower  knockout   spe     benham  btr-irv baldwin   > nanson  minimax minimaxwv minisum     rp river   schulze    asm     > cupper >            75.1840  75.8440  76.2830  76.0300  75.8900 75.8700  > 75.9440  75.9660  75.9580  75.9680  75.8200 -     75.7640  75.9200  > 77.3430 > condorcet+  random    fptp     dblv   conting   borda av >            75.4610  75.5690  75.6860  75.8110  76.4530 75.8300 >     llull+ randomr   fptpf    fptpr    dblvf   contingr bordaf   > bordar    avf      avr    minimaxf minimaxr >            75.8750  75.8660  76.2610  75.8330  76.2600 76.3780  > 76.2620  75.9250  76.2590  75.9530  76.2620 >     smith+ randomr   fptpf    fptpr    dblvf   contingr bordaf   > bordar    avf      avr    minimaxf minimaxr tideman >            75.7640  75.7470  76.2310  75.7630  76.2400 76.4530  > 76.2530  75.8650  76.2420  75.9680  76.2470 76.0700 > I will try a couple of other truncation models and then look at > strategic voting. >     CJC > > On 24/09/2023 13:41, Colin Champion wrote: >> Kevin – thanks for this helpful reply. I'm inclined to favour viewing >> a tie as two half-voters with opposed preferences. I admit that this >> can only be a rule of thumb, but I find it quite persuasive. After >> all, the whole point of ranked voting is that voters start out, I >> assume, with nebulous cardinal judgements in their heads, and that >> turning these judgements into rankings puts them onto a common basis >> (albeit with loss of information) which allows them to be >> meaningfully combined. The WV rule could easily undermine the premise >> of this procedure. >>    I believe that asymmetric treatment of ties in the Borda count >> leads quite directly to errors of the sort I described, but I don't >> know if this is widely accepted. >>    It's true that Darlington models ties as genuine expressions of >> indifference. In practice ties can mean almost anything; >> indifference, laziness, ignorance... Quite possibly voting methods >> which work well for one sort of tie will work less well for another. >> The result I produced myself is probably genuine, and indicates that >> WV is more accurate than margins for mandatory truncation; but I was >> wrong to suppose that it could be interpreted more generally since it >> omits the effect which is most likely to work against WV. >>    As for the positive arguments you put forward, well they might >> justify a rule of thumb but I wouldn't find them compelling. I don't >> find the Condorcet principle persuasive on its own merits (and do not >> believe it generally sound), but I accept it as a working principle >> because I don't know any other way of obtaining simple accurate >> voting methods under a spatial model. >>    I will try to extend my own evaluation software to allow a less >> restrictive model of truncation. >>       Colin >> >> On 23/09/2023 02:47, Kevin Venzke wrote: >>> Hi Colin, >>> >>> Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion<colin.champion@routemaster.app> a écrit : >>>> A possible explanation for the discrepancy between my result and Darlington's is that >>>> in my evaluation every ballot had the same number of ties and in Darlington's the >>>> numbers differed. >>>> On the face of it, WV doesn't treat voters equally. If we defined "winning votes" as >>>> "the number of voters who prefer A to B plus half the number who rank them equally", >>>> then every voter would contribute m(m-1)/2 winning votes and WV would be equivalent >>>> (I think) to Margins. But instead we define winning votes asymmetrically so that WV >>>> is *not* equivalent to margins but voters contribute different numbers of winning >>>> votes depending on the number of ties in their ballots. I can imagine this leading to >>>> artefacts which Darlington's evaluation would pick up and mine would miss. If this is >>>> what happened, then even Darlington's evaluation must be too lenient to WV since he >>>> doesn't include effects which would in fact arise, such as voters truncating >>>> differentially according to their political viewpoint. >>>> Maybe these things have been taken into account; I have no idea, having never seen the >>>> thinking behind WV. >>> I am not sure what to make of Darlington's defeat strength comparison. It sounds like >>> it was basically a simulation of sincere voters who vote equality because they actually >>> consider the candidates equal. That premise is fine but somewhat far removed from how >>> this topic is usually discussed, i.e. with some consideration of comparative strategy. >>> >>> I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a >>> Condorcet method. I wonder whether he implemented it as one to get his numbers on that. >>> >>> In any case: >>> >>> To find the motivation for WV I would start with first principles. How should we design >>> a Condorcet completion method to minimize strategic incentives? A motivation behind >>> Condorcet itself is that voters should not vote sincerely only to find that they >>> should've voted another way. >>> >>> What could this mean here? Well, a full majority can always get what they want by >>> changing their votes. Therefore if a majority votes A>B yet B is elected, we have >>> *probably* done something wrong, because the majority certainly did have the power to >>> make A win instead. The election of B gives the A>B voters an incentive to vote >>> differently to change the outcome. The voters obtain a "complaint," I will call it. >>> Since majorities will most predictably obtain such complaints when we override their >>> preference, we should prioritize locking majorities. >>> >>> With WV, there is no special heed paid to majorities, it just goes down the list of >>> contests starting with the largest winning blocs. But this achieves the goal. It >>> applies its principle to sub-majority contests as well, and maybe this is good bad or >>> neutral, but maybe we can believe that if it was helpful (for our end goal) to favor >>> majorities over sub-majorities then it could also be helpful to favor larger >>> sub-majorities over smaller sub-majorities. It certainly stands to reason that the more >>> voters you have sharing some stance, the more likely it is that a vote change on their >>> part could change the outcome. >>> >>> (On my website I describe a different approach focused on compromise incentive, and >>> measuring the potential for this more directly, and one can take that as me suggesting >>> that WV actually leaves some room for improvement.) >>> >>> You notice that adding half-votes to equal rankings under WV will turn it into margins. >>> This would give every contest a full majority on the winning side, and seemingly we can >>> trivialize this requirement of mine to prioritize majorities. >>> >>> But I think it's clear, in the context of this analysis, that adding half-votes for >>> equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of >>> opposing "half-complaints," where one of the complaints has the potential to be voiced >>> when *either* of A or B is elected. The A=B voter has no possible complaint either way, >>> as neither result can incentivize them to change their vote. >>> >>> Additionally, I think that voters expect and want it to be the case that abstaining >>> from a pairwise contest does not mean the same thing as saying they rate both >>> candidates equal. I touched on this in my previous post. >>> >>> Consider this election: >>> >>> 7 A>B >>> 5 B >>> 8 C >>> >>> Margins elects A, which is very unusual across election methods, and I think most >>> people would find this result surprising due to a sense of what truncation ought to >>> mean. >>> >>> (Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone >>> here.) >>> >>> Perhaps with enough education people can *understand* that the method takes seriously >>> the apparent equality of the truncated preferences. But I don't think voters will find >>> it comfortable to vote under those circumstances. I think voters want to be able to >>> identify the set of candidates that they believe they are trying to defeat, leave them >>> out of their ranking, and not have to think any further about it. >>> >>> Kevin >>> votingmethods.net >> >> >> ---- >> Election-Methods mailing list - seehttps://electorama.com/em for list info >

And here, as promised, are some results for strategic voting. * Constant truncation: WV beats margins for sincere voting, and also for compromising and false cycles, but margins beats WV by quite a long way (2.7%) for burial. * Approval truncation: margins beats WV for sincere voting. The two methods almost tie under compromising; margins wins by a long way under false cycles (5.5%) and under burial. * Candidate-specific truncation: WV beats margins for sincere voting; it also wins (slightly more convincingly) under compromising; it loses under false cycles and burial. * Ignorance truncation: this was essentially a tie under sincere voting and remains one under compromising; margins wins slightly under false cycles and burial. Approval truncation takes place before a voter's strategic reordering of candidates; other forms of truncation take place after it. In each case I measure the accuracy of a voting method in the presence of strategic voting, not the vulnerability of the method to manipulation.    CJC On 28/09/2023 13:00, Colin Champion wrote: > I tried two other forms of truncation. Under "candidate-specific > truncation" the m candidates have associated truncation levels which > are a random permutation of the numbers 1...m. A ballot is truncated > to the level corresponding to its first candidate. I expected this to > be a hard case for WV, but in fact it does appreciably better than > margins. >             random    fptp     dblv seq    conting   nauru    > borda     sbc2   bucklin  sinkhorn mj       av     coombs >            12.6630  35.6490  50.7000  44.9140  51.6650  54.5890 > 73.6530     -     66.3850     -        -     53.3880  68.9630 >             clower  knockout   spe     benham  btr-irv baldwin   > nanson  minimax minimaxwv minisum     rp     river schulze    asm     > cupper >            70.0190  71.5400  71.7760  71.2680  70.9510  71.4700 > 71.8440  72.0970  72.9090  72.1000  71.5630  71.9420  71.3330 72.2980  > 75.2630 > condorcet+  random    fptp     dblv   conting   borda      av >            70.6780  70.6580  70.9080  71.0760  72.2750  70.9920 >     llull+ randomr   fptpf    fptpr    dblvf   contingr bordaf   > bordar    avf      avr    minimaxf minimaxr >            71.6220  71.2570  71.9820  71.2600  71.9970  72.2020 > 72.0080  71.3300  72.0120  72.0510  72.0070 >     smith+ randomr   fptpf    fptpr    dblvf   contingr bordaf   > bordar    avf      avr    minimaxf minimaxr tideman >            71.3330  70.8970  71.5080  70.9620  71.5820  72.2730 > 71.6550  71.0270  71.6240  72.0990  71.6490  71.1760 > > The other form I tried was 'ignorance truncation'. Each candidate has > a prominence - i.e. probability of being recognised by an arbitrary > voter - drawn (separately for each election) from a Beta(r,s) > distribution. Voters rank the candidates they recognise in order of > proximity, truncating after the last candidate they recognise. I used > r=2, s=1, giving a recognition probability of 2/3. This was > essentially a tie between the two minimax variants. Borda, which > looked good against other forms of truncation, did badly this time. > Evidently ignorance truncation is more damaging than the other sorts. >            random    fptp     dblv seq    conting   nauru    borda     > sbc2   bucklin  sinkhorn mj       av     coombs >            12.5510  37.4290  43.1720  36.6340  41.2690  40.7330 > 34.6170     -     41.5260     -        -     40.9330  42.4740 >             clower  knockout   spe     benham  btr-irv baldwin   > nanson  minimax minimaxwv minisum     rp     river schulze    asm     > cupper >            43.1770  43.8040  44.4050  43.5870  44.0050  44.0480 > 43.9970  43.9990  43.9330  44.0170  43.8610  44.0040  43.7660 43.6000  > 46.7470 > condorcet+  random    fptp     dblv   conting   borda      av >            43.6260  44.0730  44.1880  43.9420  43.2570  43.5720 >     llull+ randomr   fptpf    fptpr    dblvf   contingr bordaf   > bordar    avf      avr    minimaxf minimaxr >            43.7980  43.9980  43.4990  44.0330  43.4980  43.3220 > 43.4960  43.6550  43.4950  43.9890  43.4980 >     smith+ randomr   fptpf    fptpr    dblvf   contingr bordaf   > bordar    avf      avr    minimaxf minimaxr tideman >            43.7660  44.1030  43.4060  44.1810  43.4080  43.2570 > 43.4000  43.5750  43.4000  44.0000  43.4100  43.5840 > At risk of repetition... correctness of software is not guaranteed. >    CJC > > On 27/09/2023 12:45, Colin Champion wrote: >> I have some preliminary results for "approval truncation" in which a >> voter truncates at the largest gap between cardinal rankings. Minimax >> (margins) does slightly better than minimax (WV). Voting is sincere; >> there are 8 candidates and 10001 voters (a ballot is truncated on >> average to 4.6 entries). Full figures follow (which won't be very >> readable in a variable-width font). It's noticeable that the results >> are worse than for fixed truncation, even though the average ballot >> length is slightly greater. >>             random fptp     dblv     seq    conting   nauru    borda >> sbc2   bucklin  sinkhorn    mj       av     coombs >>            12.5820  35.9910     -     45.8790     - 53.6880  >> 80.5090     -     67.5170     -        - 55.7040  69.1810 >>             clower  knockout   spe     benham  btr-irv baldwin   >> nanson  minimax minimaxwv minisum     rp river   schulze    asm     >> cupper >>            75.1840  75.8440  76.2830  76.0300  75.8900 75.8700  >> 75.9440  75.9660  75.9580  75.9680  75.8200 -     75.7640  75.9200  >> 77.3430 >> condorcet+  random    fptp     dblv   conting borda      av >>            75.4610  75.5690  75.6860  75.8110  76.4530 75.8300 >>     llull+ randomr   fptpf    fptpr    dblvf   contingr bordaf   >> bordar    avf      avr    minimaxf minimaxr >>            75.8750  75.8660  76.2610  75.8330  76.2600 76.3780  >> 76.2620  75.9250  76.2590  75.9530  76.2620 >>     smith+ randomr   fptpf    fptpr    dblvf   contingr bordaf   >> bordar    avf      avr    minimaxf minimaxr tideman >>            75.7640  75.7470  76.2310  75.7630  76.2400 76.4530  >> 76.2530  75.8650  76.2420  75.9680  76.2470 76.0700 >> I will try a couple of other truncation models and then look at >> strategic voting. >>     CJC >> >> On 24/09/2023 13:41, Colin Champion wrote: >>> Kevin – thanks for this helpful reply. I'm inclined to favour >>> viewing a tie as two half-voters with opposed preferences. I admit >>> that this can only be a rule of thumb, but I find it quite >>> persuasive. After all, the whole point of ranked voting is that >>> voters start out, I assume, with nebulous cardinal judgements in >>> their heads, and that turning these judgements into rankings puts >>> them onto a common basis (albeit with loss of information) which >>> allows them to be meaningfully combined. The WV rule could easily >>> undermine the premise of this procedure. >>>    I believe that asymmetric treatment of ties in the Borda count >>> leads quite directly to errors of the sort I described, but I don't >>> know if this is widely accepted. >>>    It's true that Darlington models ties as genuine expressions of >>> indifference. In practice ties can mean almost anything; >>> indifference, laziness, ignorance... Quite possibly voting methods >>> which work well for one sort of tie will work less well for another. >>> The result I produced myself is probably genuine, and indicates that >>> WV is more accurate than margins for mandatory truncation; but I was >>> wrong to suppose that it could be interpreted more generally since >>> it omits the effect which is most likely to work against WV. >>>    As for the positive arguments you put forward, well they might >>> justify a rule of thumb but I wouldn't find them compelling. I don't >>> find the Condorcet principle persuasive on its own merits (and do >>> not believe it generally sound), but I accept it as a working >>> principle because I don't know any other way of obtaining simple >>> accurate voting methods under a spatial model. >>>    I will try to extend my own evaluation software to allow a less >>> restrictive model of truncation. >>>       Colin >>> >>> On 23/09/2023 02:47, Kevin Venzke wrote: >>>> Hi Colin, >>>> >>>> Le vendredi 22 septembre 2023 à 02:57:42 UTC−5, Colin Champion<colin.champion@routemaster.app> a écrit : >>>>> A possible explanation for the discrepancy between my result and Darlington's is that >>>>> in my evaluation every ballot had the same number of ties and in Darlington's the >>>>> numbers differed. >>>>> On the face of it, WV doesn't treat voters equally. If we defined "winning votes" as >>>>> "the number of voters who prefer A to B plus half the number who rank them equally", >>>>> then every voter would contribute m(m-1)/2 winning votes and WV would be equivalent >>>>> (I think) to Margins. But instead we define winning votes asymmetrically so that WV >>>>> is *not* equivalent to margins but voters contribute different numbers of winning >>>>> votes depending on the number of ties in their ballots. I can imagine this leading to >>>>> artefacts which Darlington's evaluation would pick up and mine would miss. If this is >>>>> what happened, then even Darlington's evaluation must be too lenient to WV since he >>>>> doesn't include effects which would in fact arise, such as voters truncating >>>>> differentially according to their political viewpoint. >>>>> Maybe these things have been taken into account; I have no idea, having never seen the >>>>> thinking behind WV. >>>> I am not sure what to make of Darlington's defeat strength comparison. It sounds like >>>> it was basically a simulation of sincere voters who vote equality because they actually >>>> consider the candidates equal. That premise is fine but somewhat far removed from how >>>> this topic is usually discussed, i.e. with some consideration of comparative strategy. >>>> >>>> I notice incidentally that Darlington says incorrectly on page 22 that MinMax(PO) is a >>>> Condorcet method. I wonder whether he implemented it as one to get his numbers on that. >>>> >>>> In any case: >>>> >>>> To find the motivation for WV I would start with first principles. How should we design >>>> a Condorcet completion method to minimize strategic incentives? A motivation behind >>>> Condorcet itself is that voters should not vote sincerely only to find that they >>>> should've voted another way. >>>> >>>> What could this mean here? Well, a full majority can always get what they want by >>>> changing their votes. Therefore if a majority votes A>B yet B is elected, we have >>>> *probably* done something wrong, because the majority certainly did have the power to >>>> make A win instead. The election of B gives the A>B voters an incentive to vote >>>> differently to change the outcome. The voters obtain a "complaint," I will call it. >>>> Since majorities will most predictably obtain such complaints when we override their >>>> preference, we should prioritize locking majorities. >>>> >>>> With WV, there is no special heed paid to majorities, it just goes down the list of >>>> contests starting with the largest winning blocs. But this achieves the goal. It >>>> applies its principle to sub-majority contests as well, and maybe this is good bad or >>>> neutral, but maybe we can believe that if it was helpful (for our end goal) to favor >>>> majorities over sub-majorities then it could also be helpful to favor larger >>>> sub-majorities over smaller sub-majorities. It certainly stands to reason that the more >>>> voters you have sharing some stance, the more likely it is that a vote change on their >>>> part could change the outcome. >>>> >>>> (On my website I describe a different approach focused on compromise incentive, and >>>> measuring the potential for this more directly, and one can take that as me suggesting >>>> that WV actually leaves some room for improvement.) >>>> >>>> You notice that adding half-votes to equal rankings under WV will turn it into margins. >>>> This would give every contest a full majority on the winning side, and seemingly we can >>>> trivialize this requirement of mine to prioritize majorities. >>>> >>>> But I think it's clear, in the context of this analysis, that adding half-votes for >>>> equal rankings doesn't make sense. The voter who says A=B doesn't turn into a pair of >>>> opposing "half-complaints," where one of the complaints has the potential to be voiced >>>> when *either* of A or B is elected. The A=B voter has no possible complaint either way, >>>> as neither result can incentivize them to change their vote. >>>> >>>> Additionally, I think that voters expect and want it to be the case that abstaining >>>> from a pairwise contest does not mean the same thing as saying they rate both >>>> candidates equal. I touched on this in my previous post. >>>> >>>> Consider this election: >>>> >>>> 7 A>B >>>> 5 B >>>> 8 C >>>> >>>> Margins elects A, which is very unusual across election methods, and I think most >>>> people would find this result surprising due to a sense of what truncation ought to >>>> mean. >>>> >>>> (Consider copying it into votingmethods.net/calc to see margins and MMPO stand alone >>>> here.) >>>> >>>> Perhaps with enough education people can *understand* that the method takes seriously >>>> the apparent equality of the truncated preferences. But I don't think voters will find >>>> it comfortable to vote under those circumstances. I think voters want to be able to >>>> identify the set of candidates that they believe they are trying to defeat, leave them >>>> out of their ranking, and not have to think any further about it. >>>> >>>> Kevin >>>> votingmethods.net >>> >>> >>> ---- >>> Election-Methods mailing list - seehttps://electorama.com/em for list info >> > > > ---- > Election-Methods mailing list - see https://electorama.com/em for list info