Arrow’s Impossibility Theorem does an excellent job keeping us from chasing a perfect method that doesn’t exist, at least among ordinal methods. Though the Gibbard–Satterthwaite theorem put the lid on the idea of a tactical-proof method, whether it be ordinal or cardinal.
I don’t think Arrow would claim that we can’t improve over plurality though, and I think he’d agree that that’s not what his theorem gets at. His theorem just looks at a set of criteria and says no (ordinal) method will pass all those criteria all the time. It says nothing, however, about the degree nor the frequency that any particular voting method would fail any one criterion.
Arrow appropriately points out plurality because it fails Independence of Irrelevant Alternatives (IIA). And it doesn’t just fail it in a convoluted scenario. Plurality fails IIA regularly and with terrible consequence.
To say that plurality is bad because it allows tactical voting isn’t really getting at the picture. As the Gibbard–Satterthwaite theorem indicates, all voting methods succumb to tactical voting. Plurality is bad because it fails the favorite betrayal criterion. And it fails it hideously. If we can’t at least indicate whom we like the most, then of course we will get terrible results — because we never gave the information we needed to begin with.
One particular method, approval voting, really does let you vote your honest favorite — under any possible scenario. Vote for as many as you want. Most votes wins. The Gibbard–Satterthwaite theorem holds true in that approval voting is not tactical proof. But it encourages voters to not only choose their honest favorites but also to compromise with additional votes to hedge their bets against candidates they don’t want. This encourages a more consensus winner, which at the center of a normal distribution for political ideology, appeals to the widest breadth of voters.
And it’s important that we decide on something. Because what we’re using now — plurality voting — is the worst voting method there is, other than a lottery.
As a reward for reading through the end of this long response, here are some animated fruit:
