3 ms·

> There's also the inescapable incentive conflict of 2 wolves and a sheep voting on what to have for dinner. That problem isn't entirely inescapable, though. T

by c7b 4y ago

> There's also the inescapable incentive conflict of 2 wolves and a sheep voting on what to have for dinner. That problem isn't entirely inescapable, though. There's a whole mathematical discipline on voting systems (social choice theory) - unfortunately the important results are mostly negative (google eg Arrow's impossibility theorem, Condorcet paradox,...), but the specific problem of the "dictatorship of the majority" has a solution in principle, namely quadratic voting. But yeah, we won't really ever get a perfect voting system.

GoblinSlayer 4y ago
>efficiently selects the outcome for which the population has the highest willingness to pay Majority rule does the same, no?
- c7b 4y ago
  only if there are only two options, for more options any rank-ordering system will be plagued by Arrow's and other impossibility theorems. quadratic voting uses cardinal preferences, which avoids some of those issues, and QV specifically has linear marginal cost of votes, which can be shown to be optimal in a very simplified mathematical model of voter preferences. but I don't want to evangelize QV too much here, it has enough proponents already and I'm not fully convinced that's is resilient to problems like collusion
  - GoblinSlayer 4y ago
    You don't need collusion when quadratic voting works only in hypothetical cases.
hackerlight 4y ago
It's something I haven't studied before. Why does quadratic voting solve the dictatorship of the majority problem? Do you mean to say that it attenuates the worst effects even if it doesn't solve it completely?
- c7b 4y ago
  oh wow, I really got drawn into a discussion here. now I'm not an expert on QV, but my recollection is this: cardinal voting allows people to express the strength of their preferences rather than just the order. so if there's an issue that a minority cares about a lot while the majority is just indifferent, then the minority can concentrate their votes on that issue and move it higher up the ballot (more so than in an ordinal voting system). so in your example, if the wolves have a 2/3 preference for sheep for dinner and 1/3 for apples, and the sheep has a 100% preference for apples, then with linear voting the group decision would be 5/3 vs 4/3 in favour of apples. with quadratic voting, the vote weights would be sqrt(1)+2sqrt(1/3) for apples and 2sqrt(2/3) for sheep, and apples would still win. so in this example, the sheep can push the group decision because its preference is stronger than the wolves', something it couldn't express by just ranking the options (if the wolves had a 100% for sheep, that would still win) so as we just saw, there are different ways to implement cardinal preferences, and QV is one of them that has been shown to be optimal under some standard (but still debatable) utility assumptions. that being said, if we were going to seriously consider implementing QV, I'd still have a lot of questions - I mentioned collusion, but also about manipulation resistance: what if the wolves anticipate this outcome and strategically misrepresent the relative strength of their preferences to make sure that their absolutely preferred option wins? they could still do that even without collusion. it's another common problem in voting mechanisms, I don't know how strong that problem is in QV (maybe the manipulation would be exponentially hard to compute, or very easy, Idk rn)

by c7b 4y ago

GoblinSlayer 4y ago

>efficiently selects the outcome for which the population has the highest willingness to pay Majority rule does the same, no?

c7b 4y ago
only if there are only two options, for more options any rank-ordering system will be plagued by Arrow's and other impossibility theorems. quadratic voting uses cardinal preferences, which avoids some of those issues, and QV specifically has linear marginal cost of votes, which can be shown to be optimal in a very simplified mathematical model of voter preferences. but I don't want to evangelize QV too much here, it has enough proponents already and I'm not fully convinced that's is resilient to problems like collusion
- GoblinSlayer 4y ago
  You don't need collusion when quadratic voting works only in hypothetical cases.

hackerlight 4y ago

It's something I haven't studied before. Why does quadratic voting solve the dictatorship of the majority problem? Do you mean to say that it attenuates the worst effects even if it doesn't solve it completely?

c7b 4y ago
oh wow, I really got drawn into a discussion here. now I'm not an expert on QV, but my recollection is this: cardinal voting allows people to express the strength of their preferences rather than just the order. so if there's an issue that a minority cares about a lot while the majority is just indifferent, then the minority can concentrate their votes on that issue and move it higher up the ballot (more so than in an ordinal voting system). so in your example, if the wolves have a 2/3 preference for sheep for dinner and 1/3 for apples, and the sheep has a 100% preference for apples, then with linear voting the group decision would be 5/3 vs 4/3 in favour of apples. with quadratic voting, the vote weights would be sqrt(1)+2sqrt(1/3) for apples and 2sqrt(2/3) for sheep, and apples would still win. so in this example, the sheep can push the group decision because its preference is stronger than the wolves', something it couldn't express by just ranking the options (if the wolves had a 100% for sheep, that would still win) so as we just saw, there are different ways to implement cardinal preferences, and QV is one of them that has been shown to be optimal under some standard (but still debatable) utility assumptions. that being said, if we were going to seriously consider implementing QV, I'd still have a lot of questions - I mentioned collusion, but also about manipulation resistance: what if the wolves anticipate this outcome and strategically misrepresent the relative strength of their preferences to make sure that their absolutely preferred option wins? they could still do that even without collusion. it's another common problem in voting mechanisms, I don't know how strong that problem is in QV (maybe the manipulation would be exponentially hard to compute, or very easy, Idk rn)