Hello everyone, here I am with another musing on an uncommon type of mixed system, which is basically the mixed (two tier) equivalent of STV with group voting ticket only: Voters vote for individual candidates in their local districts, and their votes get transferred to their party if it is not "used up". There are two main variants, one is with only the losing candidates votes getting used as list votes (imagine STV with no surplus vote transfer, only transfer from elimination), the other one is the plurality surplus version: instead of using a quota, the few countries which used or use this system define surplus votes as (votes of plurality candidate) - ((votes of second candidate) + 1 ). Since there are usually not enough list seats to make this kind of system even close to proportional, it's not hard to see that the second version is probably quite bad. But it is also intuitive for anyone familiar with STV that some sort of surplus vote system should be used in general. I have grappled with this topic and have before suggested a quota system, but even then proportionality cannot be achieved unless the right number of seats is used and districts/turnout are equal enough, and there are some problems arising from plurality. I might write about this but it is generally very impractical with (seat linkage) MMP being a thing. And as the response of Markus Schulze on my last email shows, the proper and efficient solution for the problems of MMP (if the number of seats is not fixed) is already found, but not widely known and sadly, not implemented (which lead to failures of two vote MMP in multiple countries). Nevertheless, while I would say these vote transfer systems are better left as a curiosity, I think the research of Daniel Bochsler (2015 paper on "bending the rules") and Johannes Raabe on this subject does raise a few points in its favour. Even single vote MMP is not perfect, it can be manipulated, but the same strategies don't work in the standard versions of these vote transfer systems. No party wins by running winning candidates and losing candidates on different lists, unless there is vote subtraction involved (this was the case in Italy). There are two other tactics, which are less likely to lead to actual abuse of the system, so maybe under some specific conditions, vote transfer systems can be more robust against manipulation than MMP, while being almost as proportional (or more, if it depends on the manipulation) One is when there are two many list seats, but this is usually very unlikely and in practice there are always too few. But if there were too many, the value of transfer votes would be worth more than votes for plurality winners. Imagine an STV system where the first candidate got elected with a quota of 33% but the next candidates may all start from a quota of 25%. The second tactic is when the surplus votes are not taken into account at all. In this case the parties will kind of try to get those surplus votes by running a clone list candidate in safe seats (stronghold-split tactic). This tactic has been theorized, but not really observed, but this problem is not there at all if the winning candidates receive a surplus counted from the second place candidate anyway. So you could say that the same way, the worst a two-vote MMP can do (and maybe under extreme presumptions, a one vote MMP) is become parallel voting (MMM), the worst a vote transfer system without full plurality-second surplus votes can become is the system with this surplus formula. While this will effect any quota-based system too, it actually seems not too bad, since it's still just surplus winners votes, so it's better than completely manipulated MMP, even if very inefficient (lots of list seats, few district seats). But I have thought of a concerning hypothetical regarding this system, that might indicate that it can be WORSE than parallel voting, even with perfectly "fair" single-winner districts. Let me show two examples. Both rely on defining how many district and list seats are is not important, since adding list seats will not make the result converge to (and never reach) proportionality (like parallel voting) or cross the point of proportionality (like vote transfer systems are usually treated/excepted to do in theory). Example 1: The district result is coincidentally the same as the proportional result, so parallel voting (in any ratio) is proportional, but the "losers + plurality surplus" model of vote transfer (which again is a theorized equilibrium of the stronghold-split strategy) would actually make it more disproportional, no matter how many list seats there are. Parallel voting Losers + plurality surplus District(s) Party A Party B Party A Party B Party A Party B 1 60% 40% 60% 40% 20% 40% 2 30% 70% 30% 70% 30% 40% 3 10% 90% 10% 90% 10% 80% wins 1 2 sum 100% 200% 60% 160% % 33% *67%* % 33% *67%* 27% *73%* Example 2: The districts give a disproportional result, and even though adding the transfer votes with list seats would slightly mitigate it, it would not mitigate it as much as parallel voting would. So again, parallel voting would with more seats converge to proportional, but the vote transfer compensation will not even converge, let alone fully compensate. The interesting thing is that this is with only two parties! With more parties, maybe exact proportionality would never be reached, but for two parties usually the transfer votes would give some percentage on the other side of the parallel voting ones, meaning that with the right weights of the two, you could get proportional. It seems that is not always the case. Parallel voting Losers + plurality surplus District(s) Party C Party D Party C Party D Party C Party D 1 60% 40% 60% 40% 20% 40% 2 25% 75% 25% 75% 25% 50% 3 25% 75% 25% 75% 25% 50% 4 10% 90% 10% 90% 10% 80% wins 1 3 sum 120% 280% 80% 220% % 25% *75%* % 30% *70%* 27% *73%* Example 3: I wanted to have one example for a two-party setup, where the majority party gets less seats on both sides of the system. I suspect this is impossible. The plurality vote transfer rule seems inherently to work in the opposite direction as gerrymandering would in this case. I think because it's mathematically linear, you cannot "gerrymander both ways": You can gerrymander the districts for the minority party, but then the transfer votes will always serve the majority party. Because you have to pack the voters of the majority into fewer, therefore on average higher margin districts, they will always receive enough surplus votes to have the majority of transfer votes. I don't think there is a strategy where you have parts of the minority party in small margin seats, and some of it in very high margin seats because of the linearity. In the example, the ratio of transfer votes will not change if you remove the second district, which is the average of the first two. Parallel voting Losers + plurality surplus District(s) Party E Party F Party E Party F Party E Party F 1 52% 48% 52% 48% 4% 48% *2* *71%* *29%* *71%* *29%* *42%* *29%* 3 90% 10% 90% 10% 80% 10% wins 3 0 sum 213% 87% 126% 87% % 100,0% 0,0% % 71,0% 29,0% 59,2% 40,8% Example 4: Just to illustrate the already intuitive effect that more than 2 parties can have even if all the districts are won by a clear 51% majority, here the strongest performing party (list) may receive less seats from both the districts and the compensatory tier than they would be entitled to in PR, so again, there is no combination ratio that would make it proportional for this party. Parallel voting Losers + plurality surplus District(s) Party G Party H Party I Party J Party G Party H Party I Party J Party G Party H Party I Party J 1 51% 0% 0% 49% 51% 0% 0% 49% 2% 0% 0% 49% 2 51% 0% 0% 49% 51% 0% 0% 49% 2% 0% 0% 49% 3 26% 51% 12% 11% 26% 51% 12% 11% 26% 25% 12% 11% 4 26% 51% 12% 11% 26% 51% 12% 11% 26% 25% 12% 11% 5 26% 51% 12% 11% 26% 51% 12% 11% 26% 25% 12% 11% 6 26% 0% 51% 23% 26% 0% 51% 23% 26% 0% 25% 23% 7 26% 0% 51% 23% 26% 0% 51% 23% 26% 0% 25% 23% wins 2 3 2 0 sum 232% 153% 138% 177% 134% 75% 86% 177% % *28,6%* 42,9% 28,6% 0,0% % *33,1%* 21,9% 19,7% 25,3% *28,4%* 15,9% 18,2% 37,5% To me these were not intuitive maybe exactly because I've been thinking of such systems for too long, although maybe for some of you it is obvious, still wanted to share. My (admittedly very impractical) approach at the moment for the ideal vote transfer mixed system would be to not use any district-based (%) quota, but to take the district winner with the lowest amount of votes and say they have 0 surplus votes, and every other winners surplus votes would be above this benchmark. This would of course need a flexible amount of seats, and probably a lot since this system would almost be perfectly proportional (the error would come from any list-PR apportionment being applied to a modified vote total, where the rankings of parties may be different than originally) therefore there will be a lot of low-vote plurality winners. The "perfect" solution in my mind which would totally counteract even the stronghold split strategy would be to take the district second with the lowest amount of votes, but in my opinion, this is unnecessary if everyone knows there will be as many extra seats as it takes for almost perfect proportionality under the lowest winner-model. Unless there are any objections, I think I would post this model in more detail here, but if someone sees a critical flaw, please let me know. Best, Abel

On 2024-09-11 19:52, Abel Stan wrote: > Hello everyone, > > here I am with another musing on an uncommon type of mixed system, which > is basically the mixed (two tier) equivalent of STV with group voting > ticket only: Voters vote for individual candidates in their local > districts, and their votes get transferred to their party if it is not > "used up". I'll have to look at this later, but I was just wondering if making a method that supports biproportional apportionment would solve the problems of MMP. For simplicity (since the math is easier), consider a cardinal optimization method where parties and districts are given weights, and one vote (approval or full rating) is multiplied by the district weight times the party weight. Then perhaps we could run something like Pukelsheim's method with the upper apportionment being the result for the country as a whole. If possible, such a method would allow voters to vote for candidates belonging to some party, but without having closed list, since the base method would be a candidate-centered method. It would just be one that weights votes to get the right upper apportionment. The question is whether it could be done, though, or if the interaction effects would make it impossible (e.g. lowering one's rating of A turns the council from {A,X} to {B,Y}, which means that the number of X party seats changes based on the weight given to party A). (I would prefer the method to be ordinal, but cardinal is easier to deal with mathematically; it's better to start on easy mode when trying to figure out if the thing is at all possible :-) -km