I did talk about Arrow’s Theorem in my first post (again, can’t link right now, but it’s the “Voting Theory Primer for Rationalists”).
Also, I acknowledge in the last two pathologies here that they can’t all be solved. That is: if you actively punish CD defection so as to make cooperation a strong equilibrium, you allow center squeeze and so create pernicious 2-party equilibria. And no strong equilibrium can exist in case of a Condorcet cycle; that’s essentially the basis of Arrow’s theorem and thus also Gibbard and Satterthwaite’s.
But Arrow’s theorem only applies to ranked (ordinal) methods. Which is why I focus more on G-S. And you yourself acknowledge that when you mention cardinal voting.
The defects of cardinal voting are obvious: it becomes a pointless game of who can say the biggest number. If you limit the range of numbers allowed, it becomes score voting; which strategically reduces to approval voting; which I do discuss above.
Some acknowledgement of https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem seems appropriate in this series—some of these aren’t Moloch and misaligned incentives, but a fundamental impossibility in defining “correct” WRT aggregation of preferences.
Followed by an exploration of cardinal voting—if everyone just writes their utility function down, we just maximize U. Simple!
I did talk about Arrow’s Theorem in my first post (again, can’t link right now, but it’s the “Voting Theory Primer for Rationalists”).
Also, I acknowledge in the last two pathologies here that they can’t all be solved. That is: if you actively punish CD defection so as to make cooperation a strong equilibrium, you allow center squeeze and so create pernicious 2-party equilibria. And no strong equilibrium can exist in case of a Condorcet cycle; that’s essentially the basis of Arrow’s theorem and thus also Gibbard and Satterthwaite’s.
But Arrow’s theorem only applies to ranked (ordinal) methods. Which is why I focus more on G-S. And you yourself acknowledge that when you mention cardinal voting.
The defects of cardinal voting are obvious: it becomes a pointless game of who can say the biggest number. If you limit the range of numbers allowed, it becomes score voting; which strategically reduces to approval voting; which I do discuss above.
Arrow’s theorem was mentioned in the previous post in the series.