Learning about Arrow’s Impossibility Theorem really kicked my edgy teenager phase into full gear. The theorem establishes (with mathematical certainty!) that “social utility” is an incoherent concept.
At some point, edgy teens who have learned about Arrow’s impossibility theorem should additionally learn that it does not apply to approval voting.
Approval voting intuitively represents the idea that the winner should be the candidate most broadly acceptable to the voters, rather than the candidate most strongly preferred over others.
Approval voting can be seen as encoding the principle of “government by the consent of the governed” rather than attempting to achieve “government by the will of the people” (i.e. coherent social utility). Arrow shows that there is no will of the people, so instead we can settle for what the most people are willing to go along with.
(Additionally, approval voting correctly records a lot of sentiments that can’t be expressed in plurality voting. It allows voters to express ideas like “I’m fine with anyone except that guy”. It allows single-issue voters to express their true preferences: “Any candidate who’s pro-skub is okay with me.”)
Plurality voting should really be taken as finding not the will of the people but rather the will of the largest one-shot coalition. In contrast, instant-runoff voting finds the will of the largest iterated coalition. Whereas approval voting aims at finding the largest near-consensus, these systems aim at finding several mutually-exclusive coalitions and putting the largest one in charge.
I wonder how this generalizes to decisions that aren’t just about electing candidates, but involve a combinatorial explosion of possible courses of action. E.g.: “We can have our conference on either Friday or Saturday. We can invite Professor Alice as a keynote speaker, or Senator Bob, but Senator Bob is only available on Saturday. If it’s Saturday we can invite both, but then we must choose another item to delete from the agenda. Or we could have a session on both Friday and Saturday, but then we must raise the ticket price by $X...”
In a typical Robert’s-Rules meeting the outcome will sometimes depend in a fairly arbitrary way upon the order in which the various alternatives were suggested. Approval voting wouldn’t have that problem, but may become inefficient if combinatorial decisions like this come up a lot.
At some point, edgy teens who have learned about Arrow’s impossibility theorem should additionally learn that it does not apply to approval voting.
Approval voting intuitively represents the idea that the winner should be the candidate most broadly acceptable to the voters, rather than the candidate most strongly preferred over others.
Approval voting can be seen as encoding the principle of “government by the consent of the governed” rather than attempting to achieve “government by the will of the people” (i.e. coherent social utility). Arrow shows that there is no will of the people, so instead we can settle for what the most people are willing to go along with.
(Additionally, approval voting correctly records a lot of sentiments that can’t be expressed in plurality voting. It allows voters to express ideas like “I’m fine with anyone except that guy”. It allows single-issue voters to express their true preferences: “Any candidate who’s pro-skub is okay with me.”)
Plurality voting should really be taken as finding not the will of the people but rather the will of the largest one-shot coalition. In contrast, instant-runoff voting finds the will of the largest iterated coalition. Whereas approval voting aims at finding the largest near-consensus, these systems aim at finding several mutually-exclusive coalitions and putting the largest one in charge.
arrow’s theorem is about social welfare functions not voting methods. once you have the correct social welfare function (https://www.rangevoting.org/UtilFoundns) you use it to perform voter satisfaction efficiency calculations on your voting method, and it doesn’t matter what properties it obeys. https://www.rangevoting.org/PropDiatribe
approval voting does perform quite well indeed.
https://www.rangevoting.org/BayRegsFig
I wonder how this generalizes to decisions that aren’t just about electing candidates, but involve a combinatorial explosion of possible courses of action. E.g.: “We can have our conference on either Friday or Saturday. We can invite Professor Alice as a keynote speaker, or Senator Bob, but Senator Bob is only available on Saturday. If it’s Saturday we can invite both, but then we must choose another item to delete from the agenda. Or we could have a session on both Friday and Saturday, but then we must raise the ticket price by $X...”
In a typical Robert’s-Rules meeting the outcome will sometimes depend in a fairly arbitrary way upon the order in which the various alternatives were suggested. Approval voting wouldn’t have that problem, but may become inefficient if combinatorial decisions like this come up a lot.
anscombe’s paradox.
https://www.rangevoting.org/XYvote