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 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 can create a system that appears to "satisfy... rationality of their preferences".
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].
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.
This is probably just being pedantic, but the Nader->Bush->Gore ranking was commonly preferred by Nader supporters, not because they preferred Bush's policies to Gore's, but because they thought it would teach society the error of their ways in the long run or something. Also because they hated Nader being labeled a spoiler candidate, so it was probably something of a spiteful response.
accepting dictatorship in the former or non-availability in the later gives you consistency. Reminds about USSR - high consistency (at it least it was initially) with very limited availability of salami (all the way until the last day of USSR).
Comments
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 can create a system that appears to "satisfy... rationality of their preferences".
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].
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.
[0] https://en.wikipedia.org/wiki/Amartya_Sen
[1] https://en.wikipedia.org/wiki/Instant-runoff_voting
[2] The article does mention Sen, and alludes to this finding, but I don't think it explains it very clearly.
This is probably just being pedantic, but the Nader->Bush->Gore ranking was commonly preferred by Nader supporters, not because they preferred Bush's policies to Gore's, but because they thought it would teach society the error of their ways in the long run or something. Also because they hated Nader being labeled a spoiler candidate, so it was probably something of a spiteful response.
accepting dictatorship in the former or non-availability in the later gives you consistency. Reminds about USSR - high consistency (at it least it was initially) with very limited availability of salami (all the way until the last day of USSR).