by infinity on 10/13/14, 1:13 PM with 36 comments
by YokoZar on 10/13/14, 5:49 PM
I'm not being hyperbolic here. Number 1 and 2 are how people quickly use vague citations to Arrow's Theorem to shut down talk about voting reform even when the status quo consists of provably terrible systems like plurality voting.
Number 3 is the true result that if you relax the rather overly-strongly defined IIA criteria with a much more-reasonable criteria -- that the winner must remain among the top rock-paper-scissors loop of the voters -- then Arrow's theorem simply doesn't apply. This is well known: that "top loop" is the Smith Set and every Condorcet method of voting satisfies it.
There's also another interesting result: if voters have merely "single-peaked preferences", such as opinions about where to set a volume knob, then Arrow's theorem also doesn't apply since there will be no rock-paper-scissors set of equally fair options.
by chimeracoder on 10/13/14, 5:07 PM
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.
by tunesmith on 10/13/14, 4:39 PM
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.
by Kryptor on 10/13/14, 6:06 PM
by theschwa on 10/13/14, 10:34 PM
[1] http://en.wikipedia.org/wiki/Condorcet_method#Pairwise_count... [2] http://en.wikipedia.org/wiki/Borda_count#Voting_and_counting
by aaron-lebo on 10/13/14, 3:52 PM
by yomritoyj on 10/14/14, 2:16 PM
by jordanpg on 10/13/14, 4:36 PM
Given some objective, like "stay informed" or "make the best possible choice when I vote", and given certain problems like "news is corrupted by advertising" or "news is dumbed down", is it at all plausible to achieve any of those goals in 1 hour of news consumption each day?
A naive application of this theorem suggests not... "none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences."
In other words, might it be the case that there is little intrinsic value in consuming the news piecemeal, in the way that most of us do?
by Symmetry on 10/13/14, 5:52 PM