I disagree with a lot of that. Most people's criticism of a particular voting system takes the form of "your system sucks because it doesn't fulfill desirable criteria A." It's very appropriate to point out that no voting system can fulfill all desirable criteria. Obviously, it doesn't mean that certain voting systems aren't "better" than others, at least if we've agreed on what our goals are (and thus what constitutes "better").
For example, you confidently dismiss plurality voting, but you can't really do that unless you establish what the goals of your voting system are. These goals need to be clearly defined, you can't just say your goal is "making sure everyone has a voice" or "making sure the best candidate wins." That's really all Arrow's theorem says: there are several criteria that most of us agree are desirable, but you cannot have all of them.
Once you actually explain them to people, it's hard to argue that Arrow's theorem still lists desirable criteria. Some are surely reasonable sounding (eg non-dictatorship), but the "independence of irrelevant alternatives" is very deceptively-named: it requires that when voters preferences form a rock-paper-scissors relationship among a set of candidates, the system should never reflect that by having rock win once scissors enters the race.
Arrow calls scissors an "irrelevant alternative" to the race between paper and rock (since scissors doesn't win but makes paper lose). This is just unreasonable -- if there exists a rock-paper-scissors loop among the top preferences of voters, then the voting system should at least acknowledge that reality and make sure it picks someone within that loop (the particular winner is somewhat arbitrary).
And, indeed, if you instead use a more reasonable criteria that requires just that -- that the winner must come from the smith set -- then all of the "reasonable" criteria are satisfiable. Hence the overhyping of Arrow's theorem.
You are right, though, that basing analysis of voting systems on rigid criteria can lead you into trouble. Over-reliance on Arrow's theorem is just an example of that.
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.
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I disagree with a lot of that. Most people's criticism of a particular voting system takes the form of "your system sucks because it doesn't fulfill desirable criteria A." It's very appropriate to point out that no voting system can fulfill all desirable criteria. Obviously, it doesn't mean that certain voting systems aren't "better" than others, at least if we've agreed on what our goals are (and thus what constitutes "better").
For example, you confidently dismiss plurality voting, but you can't really do that unless you establish what the goals of your voting system are. These goals need to be clearly defined, you can't just say your goal is "making sure everyone has a voice" or "making sure the best candidate wins." That's really all Arrow's theorem says: there are several criteria that most of us agree are desirable, but you cannot have all of them.
Once you actually explain them to people, it's hard to argue that Arrow's theorem still lists desirable criteria. Some are surely reasonable sounding (eg non-dictatorship), but the "independence of irrelevant alternatives" is very deceptively-named: it requires that when voters preferences form a rock-paper-scissors relationship among a set of candidates, the system should never reflect that by having rock win once scissors enters the race.
Arrow calls scissors an "irrelevant alternative" to the race between paper and rock (since scissors doesn't win but makes paper lose). This is just unreasonable -- if there exists a rock-paper-scissors loop among the top preferences of voters, then the voting system should at least acknowledge that reality and make sure it picks someone within that loop (the particular winner is somewhat arbitrary).
And, indeed, if you instead use a more reasonable criteria that requires just that -- that the winner must come from the smith set -- then all of the "reasonable" criteria are satisfiable. Hence the overhyping of Arrow's theorem.
You are right, though, that basing analysis of voting systems on rigid criteria can lead you into trouble. Over-reliance on Arrow's theorem is just an example of that.
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.