[HN Gopher] Arrow's Impossibility Theorem [video]
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       Arrow's Impossibility Theorem [video]
        
       Author : FarhadG
       Score  : 14 points
       Date   : 2024-07-09 19:49 UTC (3 hours ago)
        
 (HTM) web link (www.youtube.com)
 (TXT) w3m dump (www.youtube.com)
        
       | a_cardboard_box wrote:
       | Independence of irrelevant alternatives doesn't seem like a
       | desirable property to me. It suggests that someone ranking a
       | candidate 2nd vs 100th does not tell you anything about how much
       | they prefer their 1st choice to that candidate.
       | 
       | Suppose 50% of people rank Alice first, Bob 100th, and the other
       | 50% rank Bob first, Alice 2nd. A voting system with independence
       | of irrelevant alternatives would have to rank Alice and Bob
       | equally (or at least it would have to rank them the same way as
       | it would if they were the only candidates, with 50% preferring
       | each one). But Alice is probably the better candidate - she's in
       | everyone's top 2. The extra candidates give you information about
       | Alice and Bob: they show that preferences for Bob are weak, and
       | preferences for Alice are strong.
        
         | Maxatar wrote:
         | I think I get the jist of your post and why IIA might seem
         | objectionable, but your example does not reflect IIA and the
         | claim that any voting system that satisfies IIA must rank Alice
         | and Bob equally is not true.
         | 
         | The score voting system satisfies IIA and can result in a
         | situation where 50% of votes assign their highest score to
         | Alice and lowest score to Bob, and 50% of voters assign their
         | highest score to Bob and their second highest score to Alice.
         | Alice would end up winning the election and there is no
         | opportunity for the introduction of a new candidate who could
         | act as a spoiler for Alice.
         | 
         | Arrow's impossibility theorem does not apply to score voting
         | since the theorem only applies to voting systems where you rank
         | your choices, it does not apply to systems where you rate your
         | choices.
         | 
         | https://en.wikipedia.org/wiki/Score_voting
        
       | dang wrote:
       | Related. Others?
       | 
       |  _Arrow 's Impossibility Theorem_ -
       | https://news.ycombinator.com/item?id=34842041 - Feb 2023 (7
       | comments)
       | 
       |  _Arrow and the Impossibility Theorem (2012) [pdf]_ -
       | https://news.ycombinator.com/item?id=28988491 - Oct 2021 (24
       | comments)
       | 
       |  _Show HN: A Visual Proof of Arrow 's Theorem_ -
       | https://news.ycombinator.com/item?id=24742502 - Oct 2020 (1
       | comment)
       | 
       |  _Arrow 's Theorem (2014)_ -
       | https://news.ycombinator.com/item?id=15673909 - Nov 2017 (69
       | comments)
       | 
       |  _Arrow 's impossibility theorem_ -
       | https://news.ycombinator.com/item?id=9655846 - June 2015 (84
       | comments)
       | 
       |  _Arrow 's Theorem_ -
       | https://news.ycombinator.com/item?id=8448553 - Oct 2014 (36
       | comments)
        
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