> That sounds just like Arrow’s impossibility theorem, which shows that in every reasonable preferential voting system, there is a “dictator”, somebody whose preferences match the result. […]
> However, the word “dictator” is a misnomer; the “dictator” is not chosen ahead of time
There are three technical errors here:
(1) Arrow’s theorem doesn’t define a “dictator” as someone whose preferences match the result but as someone whose preferences determines the result with no input from the other voters preferences.
(2) Arrow’s theorem doesn’t say that every reasonable preference voting system has a dictator, it says that no preference voting system satisfies unanimity, pareto-efficiency (if everyone prefers X to Y, the result prefers X to Y), independence of irrelevant alternatives (the result preference between X and Y, depends only on pairwise preferences between X and Y and cannot be changed by changing ballots in a way which retains the same preferences between X and Y), and non-dictatorship.
(3) The dictator may not be preselected (e.g., the “random ballot” method), but the system providing and giving force to the election does force their preferences on everyone else.
Additionally:
Using “reasonable” to describe a voting system which satisfies pareto-efficiency and independence of irrelevant alternatives but not non-dictatorship is…odd. There is a reason that real-world preference voting systems prefer to compromise one or both of the other conditions rather than non-dictatorship in most cases.
> However, the word “dictator” is a misnomer; the “dictator” is not chosen ahead of time
There are three technical errors here:
(1) Arrow’s theorem doesn’t define a “dictator” as someone whose preferences match the result but as someone whose preferences determines the result with no input from the other voters preferences.
(2) Arrow’s theorem doesn’t say that every reasonable preference voting system has a dictator, it says that no preference voting system satisfies unanimity, pareto-efficiency (if everyone prefers X to Y, the result prefers X to Y), independence of irrelevant alternatives (the result preference between X and Y, depends only on pairwise preferences between X and Y and cannot be changed by changing ballots in a way which retains the same preferences between X and Y), and non-dictatorship.
(3) The dictator may not be preselected (e.g., the “random ballot” method), but the system providing and giving force to the election does force their preferences on everyone else.
Additionally:
Using “reasonable” to describe a voting system which satisfies pareto-efficiency and independence of irrelevant alternatives but not non-dictatorship is…odd. There is a reason that real-world preference voting systems prefer to compromise one or both of the other conditions rather than non-dictatorship in most cases.