Arrow's Impossibility Theorem [video]

https://www.youtube.com/watch?v=AhVR7gFMKNg

by FarhadG • 2 years ago

24 6 2 years ago

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.

Maxatar2• 2 years ago

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• 2 years ago

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)

greyface-2• 2 years ago

Why, then, does approval voting continue to be so unpopular? It's much simpler than ranked choice or score voting, doesn't suffer from the failure modes described here, and elects candidates that satisfy a larger subset of voters than either FPTP or RCV - maximizing the consent of the governed.

Maxatar2• 2 years ago

Because the type of voting system to use ends up being subject to the same problem as the voting system it's trying to replace.

I live in Ontario, Canada, where there was a referendum on switching our voting system from first past the post. What ended up happening is that everyone starts to bicker over which specific voting system to switch to, proportional representation, run-off, this system, that system... so how do you vote for which alternative voting system to use?

While most people agree first past the post is a terrible system, not enough people are willing to unite to pick an alternative to replace it.

So approval voting probably is a fine system, but if you open the door to approval voting then you open the door to a host of other systems which act as spoilers and you're left with the status quo.

greyface-2• 2 years ago

Something similar happened in Seattle recently, too: https://ballotpedia.org/Seattle,_Washington,_Proposition_1A_...

It started with a referendum to switch several races from FPTP to approval. The (FPTP-elected) city council flipped out about this and proposed a RCV alternative, which triggered a vote between the two, and approval voting lost, thanks to a successful campaign that decried it as a "tech bro" "centrist" voting system that somehow produced worse outcomes than FPTP. It was baffling to watch these arguments succeed.

Arrow's Impossibility Theorem [video]

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