The entire point of Arrow's theorem, as I see it, is that criteria which apply to an individual's preferences do not apply to an aggregate of many individual's preferences. Since aggregating the preferences of many individuals is ostensibly the point of any election, it's extremely relevant to point out this rather unfortunate and counterintuitive fact.
IIA is an extremely reasonable quality of an individual's preferences. Although you could probably construct pathological cases where it might sort of make sense for an individual to swap his preference of X and Y when Z is introduced, I contend that it would be exceedingly rare. Showing that IIA is impossible to guarantee (at the same time as other criteria) in an aggregate of preferences is a pretty big deal.
Arrow's theorem does not say or logically imply that, if there is a cyclical Smith set, the voting system shouldn't acknowledge that and pick someone within that loop.
Comments
The entire point of Arrow's theorem, as I see it, is that criteria which apply to an individual's preferences do not apply to an aggregate of many individual's preferences. Since aggregating the preferences of many individuals is ostensibly the point of any election, it's extremely relevant to point out this rather unfortunate and counterintuitive fact.
IIA is an extremely reasonable quality of an individual's preferences. Although you could probably construct pathological cases where it might sort of make sense for an individual to swap his preference of X and Y when Z is introduced, I contend that it would be exceedingly rare. Showing that IIA is impossible to guarantee (at the same time as other criteria) in an aggregate of preferences is a pretty big deal.
Arrow's theorem does not say or logically imply that, if there is a cyclical Smith set, the voting system shouldn't acknowledge that and pick someone within that loop.