I think most democratic countries use proportional representation, not FTPT. But talking about “most” is an FTPT error. Enough countries use proportional representation that you can study the effect of voting systems. And the results are shocking to me. The theoretical predictions are completely wrong. Duverger’s law is false in every FTPT country except America. On the flip side, while PR does lead to more parties, they still form 1-dimensional spectrum. For example, a Green Party is usually a far-left party with slightly different preferences, instead of a single issue party that is willing to form coalitions with the right.
If politics were two dimensional, why wouldn’t you expect Condorcet cycles? Why would population get rid of them? If you have two candidates, a tie between them is on a razor’s edge. The larger the population of voters, the less likely. But if you have three candidates and three roughly equally common preferences, the cyclic shifts of A > B > C, then this is a robust tie. You only get a Condorcet winner when one of the factions becomes as big as the other two combined. Of course I have assumed away the other three preferences, but this is robust to them being small, not merely nonexistent.
I don’t know what happens in the following model: there are three issues A,B,C. Everyone, both voter and candidate, is for all of them, but in a zero-sum way, represented a vector a,b,c, with a+b+c = 11, a,b,c>=0. Start with the voters as above, at (10,1,0), (0,10,1), (1,0,10). Then the candidates (11,0,0), (0,11,0), (0,0,11) form a Condorcet cycle. By symmetry there is no Condorcet winner over all possible candidates. Randomly shift the proportion of voters. Is there a candidate that beats the three given candidates? One that beats all possible candidates? I doubt it. Add noise to make the individual voters unique. Now, I don’t know.
I think most democratic countries use proportional representation, not FTPT. But talking about “most” is an FTPT error. Enough countries use proportional representation that you can study the effect of voting systems. And the results are shocking to me. The theoretical predictions are completely wrong. Duverger’s law is false in every FTPT country except America. On the flip side, while PR does lead to more parties, they still form 1-dimensional spectrum. For example, a Green Party is usually a far-left party with slightly different preferences, instead of a single issue party that is willing to form coalitions with the right.
If politics were two dimensional, why wouldn’t you expect Condorcet cycles? Why would population get rid of them? If you have two candidates, a tie between them is on a razor’s edge. The larger the population of voters, the less likely. But if you have three candidates and three roughly equally common preferences, the cyclic shifts of A > B > C, then this is a robust tie. You only get a Condorcet winner when one of the factions becomes as big as the other two combined. Of course I have assumed away the other three preferences, but this is robust to them being small, not merely nonexistent.
I don’t know what happens in the following model: there are three issues A,B,C. Everyone, both voter and candidate, is for all of them, but in a zero-sum way, represented a vector a,b,c, with a+b+c = 11, a,b,c>=0. Start with the voters as above, at (10,1,0), (0,10,1), (1,0,10). Then the candidates (11,0,0), (0,11,0), (0,0,11) form a Condorcet cycle. By symmetry there is no Condorcet winner over all possible candidates. Randomly shift the proportion of voters. Is there a candidate that beats the three given candidates? One that beats all possible candidates? I doubt it. Add noise to make the individual voters unique. Now, I don’t know.