Okay, I just read it and as I expected, it just proves my point. Some excerpts:
IIA conflicts with the majority-rule criterion whenever there is a Condorcet paradox with three candidates.
Yes! This is how we know the majority rule criterion is false! He made the right initial observation about two criteria being mutually exclusive, but picked the wrong one when trying to determine which one was incorrect.
IoIA is logically necessary from the definition of “social choice”. We are asking, given what each individual thinks about X vs. Y, what does the group think about X vs. Y. That does not require knowing anything about what any individual thinks about Z, by definition. Whereas there is no logical principle undergirding the majority criterion.
And because some people insisted that IoIA was the criterion that would have to be rejected instead, I formulated a more robust proof that does not rely on IoIA. We see that it is possible for a group to simultaneously prefer X to pass, and Y to pass, but prefer that neither passes rather than both passing. And these contradictory majorities all exist simultaneously. So there is no shell game for you to play.
Therefore, if those two stay in the race and the other candidate drops out, the system would violate majority rule if it stayed with the same winner as required by IIA.
Again, correct. Therefore majority rule is wrong.
the data involving C seems highly relevant in betting on the forthcoming game.
This is a classic rookie mistake that doesn’t make sense in the context of social choice. In this example, he’s saying that watching C compete against A or B tells you something about A or B that you didn’t already know. It changes your estimation of A and B. IoIA in social choice is completely different. We’re saying even if absolutely nothing changes about voters’ preferences between A and B, the presence or absence of C can still change the outcome if your social welfare function violates IoIA.
To really drive this point home, imagine you remove C as an option, changing the winner from A to B. Then imagine you add C right back in, changing the winner back from B to A. You can repeat that process as many times as you like. There is no rational justification for why the outcome should toggle between A and B, given that the voters aren’t getting any additional information about A or B each time C is added or removed.
Similarly, suppose that in a 10-candidate race, A beats B by 1 vote, but B beats all the other 8 candidates by much broader margins than A beats them. It’s not obvious that the latter fact should be ignored as IIA requires.
Yeah, this is a severe case of the same fallacy. He’s using an example where relative performances change voter information. IoIA is about removing or adding C without any change in preference/knowledge for A or B. Not understanding that point is a simply egregious failure of comprehension.
Indeed, a computer simulation study in Section 3.2 found that an electoral system conforming to IIA was, on the average, less good at picking the best winners than an alternative system which violates IIA.
This is a fallacy, because he’s changing multiple variables. If you in theory take any system violating IoIA and change it only satisfy IoIA, it would be better. (Mind you this is only possible in theory, so I’m using this merely as a rhetorical thought experiment.)
IIA’s conflict with majority rule means that nearly all electoral systems violate IIA, since they reduce to majority rule in two-candidate elections.
Technically that’s not true. Score Voting and Approval Voting satisfy IoIA in the sense that you can take a stack of cast ballots and remove any non-winning candidate, and the winner won’t change. Of course if voters strategically re-normalize, that’s another story. But the point is, ranked voting methods don’t satisfy IoIA even in the case where voters keep all other rankings exactly the same after Z is removed.
3.3. All this suggests that IIA can be dismissed.
Absolutely false. His reasoning is just a stack of common fallacies.