If you examine these supposed failures of Approval voting, you'll find that the bulk of them can be attributed to the divide between a "Majoritarian" or a "Consensus-driven" perspective. That is, many of the criteria suppose that the most-preferred candidate of the majority should win, but should that be the case? Imagine there are 3 candidates, one who is adored by the super-majority, a second who is very well-liked by that super-majority and a third who is hated. Meanwhile the minority hates the first and third candidates, but well-likes the second.

We can visualize this like so:

  #   Approval | Disapproval
  80 |-1--2----|--------------3-|
  20 |-2-------|-----------3--1-|

So while the first candidate is the favorite candidate of the super-majority, the second candidate has the unanimous approval of population. Which is preferable? I would say the second candidate.

So you see, the criteria themselves incorporate an ideological perspective - a majoritarian bias - rather than articulating some absolute objective truth.

Also I have to take issue with the basis for the "Especially Intolerable Failures" explanation - does it make sense to reject a system for being theoretically capable of producing a result, "regardless of the probability that these paradoxes may occur"? Given 2 systems, one which exhibits several flaws often, and another which rarely exhibits flaws but is theoretically capable of exhibiting a certain offensive flaw, does it make sense to reject the better-behaving system because of a theoretical result? I think not.

> Given 2 systems, one which exhibits several flaws often, and another which rarely exhibits flaws but is theoretically capable of exhibiting a certain offensive flaw, does it make sense to reject the better-behaving system because of a theoretical result? I think not

No, but if we want to go on the basis of how likely it is to produce those outcomes, Instant-runoff voting beats approval voting by a long shot. Amartya Sen has shown that, not only is IRV is highly unlikely to produce an outcome which violates transitivity and independence, but if ideologies are assumed to be relatively linear[1], then it never violates those conditions.

[1] Ie, very few people would rank Nader > Bush > Gore

IRV still has the problem that gaining a few percentage points can cause a candidate to lose. I'd prefer approval voting's potential paradoxes over that possibility any day.

I'd also consider a non-majority approval victory a highly desirable outcome, and the way politics goes right now, it'd be more like a 40% candidate with 85% approval beating a 51% candidate with 51% approval.

I'm not having any luck finding the Sen research you cite. And without it, I'm not sure what you mean by "IRV is highly unlikely to produce an outcome which violates transitivity and independence." Link?