"Arrow's theorem says there are no such procedures whatsoever—none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences."
The trick there is the "apparently quite reasonable" part. Far too many people take it as a given that those assumptions are sacred, which leads to a form of worship about this theorem. The IIAC in particular is problematic, and if that is relaxed, it's not quite so certain anymore that a "perfect" vote-counting method is impossible.
If you have a Smith Set, you don't want to just arbitrarily remove one of its candidate to resolve the "tie".
Similarly, if an election has a Condorcet Winner, and adding a candidate creates a Smith Set (thus potentially violating IIA if a certain candidate is chosen in a "tiebreaker"), this is not necessarily a bad thing.
If that happens it means that people always legitimately had those views, and were not able to properly express their views by choosing among the more limited number of candidates.
Regarding your second sentence, who says that would be a bad thing? I'm a little confused about the situation you're describing. Most analysis of voting systems I've seen isn't concerned with the fact that valid candidates may be left off the ballot. That's obviously an important consideration in real elections, and if there are primary elections the choice of voting system there obviously matters, but in the final election it doesn't seem particularly relevant.
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"Arrow's theorem says there are no such procedures whatsoever—none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences."
The trick there is the "apparently quite reasonable" part. Far too many people take it as a given that those assumptions are sacred, which leads to a form of worship about this theorem. The IIAC in particular is problematic, and if that is relaxed, it's not quite so certain anymore that a "perfect" vote-counting method is impossible.
I'm curious which of the assumptions you think are unreasonable.
If you have a Smith Set, you don't want to just arbitrarily remove one of its candidate to resolve the "tie".
Similarly, if an election has a Condorcet Winner, and adding a candidate creates a Smith Set (thus potentially violating IIA if a certain candidate is chosen in a "tiebreaker"), this is not necessarily a bad thing.
If that happens it means that people always legitimately had those views, and were not able to properly express their views by choosing among the more limited number of candidates.
Regarding your second sentence, who says that would be a bad thing? I'm a little confused about the situation you're describing. Most analysis of voting systems I've seen isn't concerned with the fact that valid candidates may be left off the ballot. That's obviously an important consideration in real elections, and if there are primary elections the choice of voting system there obviously matters, but in the final election it doesn't seem particularly relevant.