Only tangentially related, but I would say that if you study election theory, it's a pretty depressing field. Basically, either your voting system allows strategic voting (i.e individual voters...

Exemplary

Only tangentially related, but I would say that if you study election theory, it's a pretty depressing field. Basically, either your voting system allows strategic voting (i.e individual voters are not incentivized to vote for their truly optimal candidate), or in fair voting systems, because of Arrow's Impossibility Theorem, there will always be a dictator (dictator in this case being a single voter whose vote changes the entire result of the election).

Obviously FPTP is not optimal, and it promotes two party systems, but there apparently just aren't great voting systems possible.

Just giving it a quick glance, I don't think you do ranked choice voting justice: https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem My reading is that out of 4 desirable traits, you can...

However: I'm not convinced of the need not to have a dictator. If we do some form of ranked choice voting (i.e. some mode of determining the least worst option if everyone ranked the options from best to worst) - the dictator doesn't know he's the dictator. It might not even be a single person. Say we have three options and 1000 people casting ballots (ballots are important so no one knows at the time of voting what the tally is, so he doesn't know if he's the dictator). There can only be 6 different ballots (123, 132, 213, 231, 312, 321), so naturally most votes are there in multiples. All those voters (with the "dictating" ballot) would have to share their dictatorial mandate, meanwhile the other voters limit their dictatorial choices to the things they consider least bad. But the theorem says either we get a dictator (who doesn't know he's the dictator. In statistics this is also called a decision boundary and is just a fact of life, not some disaster.) or we get manipulable voting. The manipulable voting, I'm not too sure of either... Seems to me like you'd need some awfully good knowledge of the situation to make that happen.

Overall, the assumptions of the theorem sound like the homo oeconomicus to me, perfect knowledge and rational choices and all that. Except the homo oeconomicus tells us that business decisions are trivial and markets are perfect, while this one tells us that elections are shit. I don't buy either argument.

Dictators, unlike decision boundaries, aren't decided by the data. Regardless of what you vote, whoever the dictator's social preference choice is will be the one produced by the voting algorithm....

Dictators, unlike decision boundaries, aren't decided by the data. Regardless of what you vote, whoever the dictator's social preference choice is will be the one produced by the voting algorithm. That's the problem. Of course, in a voting system there will be people who are tie-breakers, the problem is that the dictator, like the name implies, will determine the system regardless of what everyone else votes.

The "good" part of Arrow's impossibility theorem is that one of the fairness criteria may not be something that's actually that important (independence of irrelevant rankings).

However, ranked choice voting unfortunately is squarely falls into the category of strategic voting. I'd have to dig through some textbooks to get an example, but it's optimal in many cases not to rank in your true preference ranking.

I don't see how your part about dictators can be independent of the data. I understood the wiki to mean that there has to be (at least) one voter whose choice will tilt a preference race among two...

I don't see how your part about dictators can be independent of the data. I understood the wiki to mean that there has to be (at least) one voter whose choice will tilt a preference race among two candidates, thus his preference decides the race. If suddenly everyone else decides to bail on A and vote for B, the dictator can't dictate no more and that title will move to someone else. I.e. I understood it to be very much given the data. Whoever the dictator is, if everyone else votes opposite to him, his will shall not be done. I'll keep looking for a good example of that being bad and/or data independent though.

[ETA: From wiki, definition of a dictator: "There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that for all (R1, …, RN) ∈ L(A)N, a ranked strictly higher than b by Ri implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b." - sounds to me as if it posits "there may not exist a voter i with ranking Ri whose ranking matches the outcome. Keep in mind that theoretically, these methods always output a full ranking over all options, and it seems to me that if someone voted the same as what ends up being the popular consensus, then that person is declared the dictator. The definition does not care whether this person "caused" the consensus, just that they exist. So in other words: The definition decides that the compromise must involve everyone compromising, even if one of them delivered a proposal that is a perfect compromise for the collective. "Because you want it, we can't have it, because that'd mean you wouldn't have to compromise!"]

I'm not sure strategic voting is a big problem either, given that it requires substantial knowledge of how the other people vote to pull off. Again, homo oeconomicus and so on. This is also strongly dependant on the manner of counting ballots. Ranked choice is a whole category of methods. The second wiki page gave an example, it assumed knowing other's ballots and a shitty counting algorithm. I'm completely convinced the example would break if it were counted using a reasonable algorithm.

That doesn’t happen though. People’s preferences are more-or-less fixed in the short term so the dictator always gets their way while everyone else is less happy.

If suddenly everyone else decides to bail on A and vote for B, the dictator can't dictate no more

That doesn’t happen though. People’s preferences are more-or-less fixed in the short term so the dictator always gets their way while everyone else is less happy.

A really thorough article on why the 2-party system is really bad for the US's constitutional democracy. Admittedly this is some pretty old news, but the reasoning and numbers are pretty modern.

A really thorough article on why the 2-party system is really bad for the US's constitutional democracy. Admittedly this is some pretty old news, but the reasoning and numbers are pretty modern.

Only tangentially related, but I would say that if you study election theory, it's a pretty depressing field. Basically, either your voting system allows strategic voting (i.e individual voters are not incentivized to vote for their truly optimal candidate), or in fair voting systems, because of Arrow's Impossibility Theorem, there will always be a dictator (dictator in this case being a single voter whose vote changes the entire result of the election).

Obviously FPTP is not optimal, and it promotes two party systems, but there apparently just aren't great voting systems possible.

Just giving it a quick glance, I don't think you do ranked choice voting justice: https://en.wikipedia.org/wiki/Arrow's_impossibility_theorem

My reading is that out of 4 desirable traits, you can only ever get 4. One of them is the lack of a dictator.

Or you're talking about

https://en.wikipedia.org/wiki/Gibbard%E2%80%93Satterthwaite_theorem

In which case your representation is fair.

However: I'm not convinced of the need not to have a dictator. If we do some form of ranked choice voting (i.e. some mode of determining the least worst option if everyone ranked the options from best to worst) - the dictator doesn't know he's the dictator. It might not even be a single person. Say we have three options and 1000 people casting ballots (ballots are important so no one knows at the time of voting what the tally is, so he doesn't know if he's the dictator). There can only be 6 different ballots (123, 132, 213, 231, 312, 321), so naturally most votes are there in multiples. All those voters (with the "dictating" ballot) would have to share their dictatorial mandate, meanwhile the other voters limit their dictatorial choices to the things they consider least bad. But the theorem says either we get a dictator (who doesn't know he's the dictator. In statistics this is also called a decision boundary and is just a fact of life, not some disaster.) or we get manipulable voting. The manipulable voting, I'm not too sure of either... Seems to me like you'd need some awfully good knowledge of the situation to make that happen.

Overall, the assumptions of the theorem sound like the homo oeconomicus to me, perfect knowledge and rational choices and all that. Except the homo oeconomicus tells us that business decisions are trivial and markets are perfect, while this one tells us that elections are shit. I don't buy either argument.

Dictators, unlike decision boundaries, aren't decided by the data. Regardless of what

youvote, whoever the dictator's social preference choice is will be the one produced by the voting algorithm. That's the problem. Of course, in a voting system there will be people who are tie-breakers, the problem is that the dictator, like the name implies, will determine the system regardless of what everyone else votes.The "good" part of Arrow's impossibility theorem is that one of the fairness criteria may not be something that's actually that important (independence of irrelevant rankings).

However, ranked choice voting unfortunately is squarely falls into the category of strategic voting. I'd have to dig through some textbooks to get an example, but it's optimal in many cases not to rank in your true preference ranking.

I don't see how your part about dictators can be independent of the data. I understood the wiki to mean that there has to be (at least) one voter whose choice will tilt a preference race among two candidates, thus his preference decides the race. If suddenly everyone else decides to bail on A and vote for B, the dictator can't dictate no more and that title will move to someone else. I.e. I understood it to be very much given the data. Whoever the dictator is, if everyone else votes opposite to him, his will shall not be done. I'll keep looking for a good example of that being bad and/or data independent though.

[ETA: From wiki, definition of a dictator: "There is no individual, i whose strict preferences always prevail. That is, there is no i ∈ {1, …, N} such that for all (R1, …, RN) ∈ L(A)N, a ranked strictly higher than b by Ri implies a ranked strictly higher than b by F(R1, R2, …, RN), for all a and b." - sounds to me as if it posits "there may not exist a voter i with ranking Ri whose ranking matches the outcome. Keep in mind that theoretically, these methods always output a full ranking over all options, and it seems to me that if someone voted the same as what ends up being the popular consensus, then that person is declared the dictator. The definition does not care whether this person "caused" the consensus, just that they exist. So in other words: The definition decides that the compromise must involve everyone compromising, even if one of them delivered a proposal that is a perfect compromise for the collective. "Because you want it, we can't have it, because that'd mean you wouldn't have to compromise!"]

I'm not sure strategic voting is a big problem either, given that it requires substantial knowledge of how the other people vote to pull off. Again, homo oeconomicus and so on. This is also strongly dependant on the manner of counting ballots. Ranked choice is a whole category of methods. The second wiki page gave an example, it assumed knowing other's ballots and a shitty counting algorithm. I'm completely convinced the example would break if it were counted using a reasonable algorithm.

That doesn’t happen though. People’s preferences are more-or-less fixed in the short term so the dictator always gets their way while everyone else is less happy.

A really thorough article on why the 2-party system is really bad for the US's constitutional democracy. Admittedly this is some pretty old news, but the reasoning and numbers are pretty modern.