> 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<p>The article alludes to one very important corollary, though IMHO it doesn't explain it very well: Arrow's theroem is like the CAP theorem - it seems to be a much stronger restriction than it is. In other words, if you're willing to make just a few very straightforward assumptions (ie, compromises), you <i>can</i> create a system that appears to "satisfy... rationality of their preferences".<p>Nobel laureate Amartya Sen[0] has demonstrated that if you assume that there are certain rankings of preferences that are rare enough to be ignored altogether, then instant-runoff voting[1] will in fact satisfy all the constraints of the Impossibility Theorem[2].<p>Let's use the 2000 US Presidential election as an example. There were three main candidates in Florida (Bush, Gore, Nader), for a total of 6 rankings. While Nader played a spoiler role, Nader and Gore shared more of a platform than Nader and Bush did. So it is very reasonable to assume that there are few people who would have voted for Nader over Bush, but Bush over Gore. This reasoning allows us to eliminate a number of those 6 rankings - and more importantly, enough rankings that the criteria of the Impossibility Theorem are likely to hold.<p>[0] <a href="https://en.wikipedia.org/wiki/Amartya_Sen" rel="nofollow">https://en.wikipedia.org/wiki/Amartya_Sen</a><p>[1] <a href="https://en.wikipedia.org/wiki/Instant-runoff_voting" rel="nofollow">https://en.wikipedia.org/wiki/Instant-runoff_voting</a><p>[2] The article does mention Sen, and alludes to this finding, but I don't think it explains it very clearly.