- good governance is difficult
what is arrow’s theorem with respect to governance
Arrow’s Theorem, named after Nobel laureate Kenneth Arrow, is a fundamental result in social choice theory, which deals with methods of aggregating individual preferences into a single collective preference or decision. In the context of governance or voting, the theorem presents a challenge to the design of a perfect voting system.
Arrow’s Impossibility Theorem states that no rank-order voting system can meet all of the following criteria for three or more distinct alternatives:
- **Unrestricted Domain (Universality): **For any set of individual voter preferences, the system should produce a clear collective ranking.
- **Non-Dictatorship: **No single voter possesses the power to determine the collective ranking irrespective of other voters’ preferences.
- **Pareto Efficiency: **If every voter prefers one option to another, then the collective ranking should do the same.
- **Independence of Irrelevant Alternatives (IIA): **If an option is removed or added, it shouldn’t change the relative ranking of the other options. In other words, rankings should depend only on individual preferences between pairs of alternatives and not on the presence or absence of other options.
Arrow’s Theorem proves that no voting system can satisfy all these criteria simultaneously. This has profound implications for the design of electoral systems, suggesting that trade-offs are inevitable when trying to find a method that fairly represents collective preferences.
explain simply
Imagine you and your friends are trying to decide on a movie to watch: action, comedy, or drama. Everyone ranks their choices. Arrow’s Theorem says there’s no perfect way to pick the “best” movie based on everyone’s lists without running into some problems. No method is perfect when you have three or more movie genres to choose from.
Alright! Let’s use the movie example:
**Unrestricted Domain: **No matter how you and your friends rank the movies, there should be a way to get a group favorite.
**Non-Dictatorship: **The group’s favorite movie isn’t just chosen by one bossy friend. Everyone’s opinion matters.
**Pareto Efficiency: **If ALL your friends like action more than comedy, then action should be the group’s top choice over comedy.
**Independence of Irrelevant Alternatives: **If you remove a genre, like drama, it shouldn’t mess up the group’s choice between action and comedy. The choice between those two should stay the same.
Arrow’s Theorem says no method can meet all these rules perfectly when picking the group’s favorite movie.
so it’s just saying that some people will be unhappy no matter how things get decided?
Exactly! In more complex terms, Arrow’s Theorem says there’s no perfect voting system that meets all the ideal criteria. But in simpler terms, yes, it’s saying that when making a group decision with three or more choices, some compromises or imperfections are inevitable, and not everyone will be fully satisfied with the outcome.