Arrow's impossibility theorem has always seemed a little fishy to me: I think the axioms are too strong (if you pressed me on this, I'd wonder if the 'independence of irrelevant alternatives' axiom is problematic).
The fact that it holds when there are three or more options but not for two options just doesn't sit right with me.
It turns out that there is very little scope to relax the axioms: for almost any voting scheme, there are circumstances where you do better by not voting your true preferences.
See the Gibbard-Satterthwaite theorem.
Pretty much the only scheme that avoids this is "choose a voter at random and elect the candidate they like best".
>for almost any voting scheme, there are circumstances where you do better by not voting your true preferences.
Which isn't a very important consideration compared to other attributes of election methods. Usually, coordination and signalling problems make tactical voting inadvisable. But even when tactical voting does work, it's not necessarily a problem.
The source of all of Arrow's nonsense is treating an election as a very large opinion poll on a single candidate. Of course pollsters hate liars, so everyone who takes Arrow seriously tries to eliminate tactical voting.
However, that's the completely wrong model. An election is an opportunity for a citizen to use their equal political weight to try to steer the polity. If some citizens managed to be smart and use their political weight smartly good for them. So what if their vote wasn't their true preference?
Tactical voting is only a problem when the election method allows a minority to win frequently - because political weight isn't really equal in that case - but one can imagine methods where tactical voting can happen yet the winning candidate always ends up with a majority (e.g. France's 2-stage Presidential elections). In those cases, tactical voting is not a problem to be eliminated.
The fact that it holds when there are three or more options but not for two options just doesn't sit right with me.