5 ms·

It took me a while to find the statement of the theorem. For other readers like me, starting at page 5 might help. It's about how it is impossible for democrac

It took me a while to find the statement of the theorem. For other readers like me, starting at page 5 might help. It's about how it is impossible for democracies to simultaneously satisfy certain desirable traits.

mdp2021 5y ago
More precisely: suppose that all voters provide an ordered list of preferences, each complete and transitive (option A preferred to B, both preferred to C - no other options available): there does not exist a function that returns a "collective" preference so that ("non-dictatorship") there is no individual list that will always predominate irregardless of the other lists, and ("unanimity") if all voters declare the same highest preference the collective preference will reflect that, and ("non-irrelevance") the collective preference between two alternatives will only depend on the preferences voters claim about those two alternatives. The page member rfreytag indicates, https://mises.org/wire/arrows-impossibility-theorem-exposes-big-problem-democracy https://mises.org/wire/arrows-impossibility-theorem-exposes-... , has a very good explanation. Edit: I realize there could be another (suggestive) way to express it: at least in the (theoretically possible) cases where preferences show a cyclic pattern (when similar numbers of voters claim A>B>C, C>A>B, B>C>A), there is no """optimal""" way to determine a collective preference. Edit: there is again another nice way to express it - member ajennings shows it at the end of his video (see nearby) with a simulation: if when all voters express preference for an option the outcome reflects that ("unanimity"), and we take a decision in the controversial scenarios, and we demand that the collective preference between two alternatives will be a function of the preferences individual voters claim about those two alternatives ("relevance"), then one ordered list of preferences will make the others uninfluent ("dictatorship").
- YokoZar 5y ago
  The "theoretically possible" case of voters having cyclic preferences is actually quite reasonable! A rock-paper-scissors situation among the top 3 candidates doesn't require irrational voters or anything of the sort: all you need is for there to be at least 2 issues. This is the rational response to Arrow's theorem - not to cynically conclude all voting systems are "bad", or that "dictatorship" makes some sort of sense, but rather just to say that if there's a rock-paper-scissors situation among the top candidates, one of them should win.

mdp2021 5y ago

More precisely: suppose that all voters provide an ordered list of preferences, each complete and transitive (option A preferred to B, both preferred to C - no other options available): there does not exist a function that returns a "collective" preference so that ("non-dictatorship") there is no individual list that will always predominate irregardless of the other lists, and ("unanimity") if all voters declare the same highest preference the collective preference will reflect that, and ("non-irrelevance") the collective preference between two alternatives will only depend on the preferences voters claim about those two alternatives. The page member rfreytag indicates, https://mises.org/wire/arrows-impossibility-theorem-exposes-big-problem-democracy https://mises.org/wire/arrows-impossibility-theorem-exposes-... , has a very good explanation. Edit: I realize there could be another (suggestive) way to express it: at least in the (theoretically possible) cases where preferences show a cyclic pattern (when similar numbers of voters claim A>B>C, C>A>B, B>C>A), there is no """optimal""" way to determine a collective preference. Edit: there is again another nice way to express it - member ajennings shows it at the end of his video (see nearby) with a simulation: if when all voters express preference for an option the outcome reflects that ("unanimity"), and we take a decision in the controversial scenarios, and we demand that the collective preference between two alternatives will be a function of the preferences individual voters claim about those two alternatives ("relevance"), then one ordered list of preferences will make the others uninfluent ("dictatorship").

YokoZar 5y ago
The "theoretically possible" case of voters having cyclic preferences is actually quite reasonable! A rock-paper-scissors situation among the top 3 candidates doesn't require irrational voters or anything of the sort: all you need is for there to be at least 2 issues. This is the rational response to Arrow's theorem - not to cynically conclude all voting systems are "bad", or that "dictatorship" makes some sort of sense, but rather just to say that if there's a rock-paper-scissors situation among the top candidates, one of them should win.