[HN Gopher] Topological Problems in Voting
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       Topological Problems in Voting
        
       Author : rtolsma
       Score  : 28 points
       Date   : 2024-06-15 01:20 UTC (21 hours ago)
        
 (HTM) web link (www.ryantolsma.com)
 (TXT) w3m dump (www.ryantolsma.com)
        
       | johnkpaul wrote:
       | Hmm, is this author related to the Physics for the Birds YouTube
       | channel?
       | 
       | That channel just released a video on the same topic.
       | 
       | https://youtu.be/v5ev-RAg7Xs?si=X1LY6Qc_s-HDqI3S
        
       | unfamiliar wrote:
       | Am I missing something or does the article fail to explain the
       | point of Arrow's Theorem? Is it satisfied for the discrete case,
       | provably impossible, or what?
       | 
       | > While this applies to discrete rankings and voter preferences,
       | one might wonder if it's a unique property of its discrete nature
       | in how candidates are only ranked by ordering. Unfortunately, a
       | similarly flavored result holds even in the continuous setting!
       | It seems there's no getting around the fact that voting is pretty
       | hard to get right.
       | 
       | I don't follow any of this paragraph.
        
         | pxeger1 wrote:
         | I agree, it could do with a little more proofreading. Arrow's
         | theorem states that no voting state which ranks candidates can
         | satisfy the the given conditions.
        
       | contravariant wrote:
       | I'm not quite sure why one would use a sphere, unless you were
       | specifically trying to get a version of Arrow's theorem.
       | 
       | If anything it looks like it fails _precisely_ because the space
       | is not homologically trivial, but I 'm a bit unsure how to make
       | that precise. A similar set up with just [0,1]^n as preference
       | space works perfectly fine just by averaging all the scores for
       | each candidate.
       | 
       | I kind of sense that requiring a function X^k -> X to exist is
       | somehow hard if X is not 'simple', but I'm not yet sure what the
       | obstruction is.
        
       | lukifer wrote:
       | Arrow's Theorem is often invoked as a criticism of alternative
       | voting systems (RCV, etc). And not while not wrong exactly, it
       | seems textbook "perfect being the enemy of the good". (It's also
       | one reason I prefer Approval Voting, which in addition to its
       | benefit of simplicity, sidesteps Arrow by redefining the goal:
       | not perfectly capturing preferences, but maximizing Consent of
       | the Governed.)
        
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       (page generated 2024-06-15 23:00 UTC)