That "rock-paper-scissors" cycle among the top preferences is the Smith set, and every sensible voting "violates" Arrows theorem by saying that sometimes it's o

That "rock-paper-scissors" cycle among the top preferences is the Smith set, and every sensible voting "violates" Arrows theorem by saying that sometimes it's ok to acknowledge that cycle. One of Arrows assumptions, "Irrelevance of Independent Alternatives", is far too strong. If you relax it to "Local Independence of Irrelevant Alternatives", then Arrows theorem no longer applies. It's just not a relevant theorem. Claiming that allowing a voting system to recognize a rock-paper-scissors cycle among the top candidates is the same as allowing dictators is obvious rubbish. But if you interpret Arrow's theorem naively, you might be tempted to make such a claim.