Kenneth Arrow, proved that the problem that Condorcet (and Llull) had seen was in fact a fundamental issue with any ranked voting method. He posed 3 basic “fairness criteria” and showed that no ranked method can meet all of them:
Ranked unanimity, Independence of irrelevant alternatives, Non-dictatorial
I’ve been reading up on voting theory recently and Arrow’s result—that the only voting system which produces a definite transitive preference ranking, that will pick the unanimous answer if one exists, and doesn’t change depending on irrelevant alternatives—is ‘one man, one vote’.
“Ankh-Morpork had dallied with many forms of government and had ended up with that form of democracy known as One Man, One Vote. The Patrician was the Man; he had the Vote.”
In my opinion, aside from the utilitarian perspective offered by VSE, the key to evaluating voting methods is an understanding of strategic voting; this is what I’d call the “mechanism design” perspective. I’d say that there are 5 common “anti-patterns” that voting methods can fall into; either where voting strategy can lead to pathological results, or vice versa.
One recent extension to these statistical approaches is to use RL agents in iterated voting and examine their convergence behaviour. The idea is that we embrace the inevitable impossibility results (such as Arrow and GS theorems) and consider agents’ ability to vote strategically as an opportunity to reach stable outcomes. This paperuses very simple Q-learning agents with a few different policies—epsilon-greedy, greedy and upper confidence bound, in an iterated voting game, and gets behaviour that seems sensible. Many thousands of rounds of iterated voting isn’t practical for real-world elections, but for preference elicitation in other contexts (such as value learning) it might be useful as a way to try and estimate people’s underlying utilities as accurately as possible.
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.
I’ve been reading up on voting theory recently and Arrow’s result—that the only voting system which produces a definite transitive preference ranking, that will pick the unanimous answer if one exists, and doesn’t change depending on irrelevant alternatives—is ‘one man, one vote’.
One recent extension to these statistical approaches is to use RL agents in iterated voting and examine their convergence behaviour. The idea is that we embrace the inevitable impossibility results (such as Arrow and GS theorems) and consider agents’ ability to vote strategically as an opportunity to reach stable outcomes. This paperuses very simple Q-learning agents with a few different policies—epsilon-greedy, greedy and upper confidence bound, in an iterated voting game, and gets behaviour that seems sensible. Many thousands of rounds of iterated voting isn’t practical for real-world elections, but for preference elicitation in other contexts (such as value learning) it might be useful as a way to try and estimate people’s underlying utilities as accurately as possible.
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.