July 9th, 2024

Arrow's Impossibility Theorem [video]

The video discusses the importance of selecting a fair voting system for accurate representation in elections. It explores different systems, Arrow's theorem, and a scenario where one voter can dominate candidate rankings.

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The YouTube video delves into the significance of choosing an appropriate voting system to ensure fair representation in elections, illustrated through the analogy of selecting the best color based on voter preferences. Various voting systems are examined in terms of their influence on election outcomes, emphasizing the challenge of precisely capturing voter choices. The video introduces Arrow's impossibility theorem and delves into a specific voting system where a single voter holds the authority to dictate the ranking of candidates, effectively becoming a dictator within that system.

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3 comments

By @greyface- - 8 months

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.

By @a_cardboard_box - 8 months

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.

By @dang - 8 months

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)