You seem to be comparing Arrow’s theorem to Lord Vetinari, implying that both are undisputed sovereigns? If so, I disagree. The part you left out about Arrow’s theorem — that it only applies to ranked voting methods (not “systems”) — means that its dominion is far more limited than that of the Gibbard-Satterthwaite theorem.
As for the RL-voting paper you cite: thanks, that’s interesting. Trying to automate voting strategy is hard; since most voters most of the time are not pivotal, the direct strategic signal for a learning agent is weak. In order to deal with this, you have to give the agents some ability, implicit or explicit, to reason about counterfactuals. Reasoning about counterfactuals requires make assumptions, or have information, about the generative model that they’re drawn from; and so, that model is super-important. And frankly, I think that the model used in the paper bears very little relationship to any political reality I know of. I’ve never seen a group of voters who believe “I would love it if any two of these three laws pass, but I would hate it if all three of them passed or none of them passed” for any set of laws that are seriously proposed and argued-for.
You seem to be comparing Arrow’s theorem to Lord Vetinari, implying that both are undisputed sovereigns?
It was a joke about how if you take Arrow’s theorem literally, the fairest ‘voting method’ (at least among ranked voting methods), the only rule which produces a definite transitive preference ranking and which meets the unanimity and independence conditions is ‘one man, one vote’, i.e. dictatorship.
And frankly, I think that the model used in the paper bears very little relationship to any political reality I know of. I’ve never seen a group of voters who believe “I would love it if any two of these three laws pass, but I would hate it if all three of them passed or none of them passed” for any set of laws that are seriously proposed and argued-for.
Such a situation doesn’t seem all that far-fetched to me—suppose there are three different stimulus bills on offer, and you want some stimulus spending but you also care about rising national debt. You might not care which bills pass, but you still want some stimulus money, but you also don’t want all of them to pass because you think the debt would rise too high, so maybe you decide that you just want any 2 out of 3 of them to pass. But I think the methods introduced in that paper might be most useful not to model the outcomes of voting systems, but for attempts to align an AI to multiple people’s preferences.
You seem to be comparing Arrow’s theorem to Lord Vetinari, implying that both are undisputed sovereigns? If so, I disagree. The part you left out about Arrow’s theorem — that it only applies to ranked voting methods (not “systems”) — means that its dominion is far more limited than that of the Gibbard-Satterthwaite theorem.
As for the RL-voting paper you cite: thanks, that’s interesting. Trying to automate voting strategy is hard; since most voters most of the time are not pivotal, the direct strategic signal for a learning agent is weak. In order to deal with this, you have to give the agents some ability, implicit or explicit, to reason about counterfactuals. Reasoning about counterfactuals requires make assumptions, or have information, about the generative model that they’re drawn from; and so, that model is super-important. And frankly, I think that the model used in the paper bears very little relationship to any political reality I know of. I’ve never seen a group of voters who believe “I would love it if any two of these three laws pass, but I would hate it if all three of them passed or none of them passed” for any set of laws that are seriously proposed and argued-for.
It was a joke about how if you take Arrow’s theorem literally, the fairest ‘voting method’ (at least among ranked voting methods), the only rule which produces a definite transitive preference ranking and which meets the unanimity and independence conditions is ‘one man, one vote’, i.e. dictatorship.
Such a situation doesn’t seem all that far-fetched to me—suppose there are three different stimulus bills on offer, and you want some stimulus spending but you also care about rising national debt. You might not care which bills pass, but you still want some stimulus money, but you also don’t want all of them to pass because you think the debt would rise too high, so maybe you decide that you just want any 2 out of 3 of them to pass. But I think the methods introduced in that paper might be most useful not to model the outcomes of voting systems, but for attempts to align an AI to multiple people’s preferences.