Arrow's Impossibility Theorem Explained Simply
Failure of IIA (Independence of Irrelevant Alternatives): Like a person changing their ice cream flavor preference when one flavor is out of stock. (e.g., from chocolate to vanilla because strawberry is unavailable), a group's decision can be influenced by irrelevant options.
Failure of Positive Association:: When a group rejects an option even when it's improved. Analogous to preferring vanilla over chocolate, even when chocolate comes with free sprinkles.
Failure of Transitivity: It’s possible for a group to choose inconsistently (e.g., preferring apples to bananas, bananas to coconuts, but coconuts to apples). This is comparable to how an individual might not always make consistent choices.
Implications:: Arrow's theorem shows that no decision-making mechanism can completely avoid these paradoxes. This can either create other paradoxes or necessitate non-democratic means. The theorem also demonstrates that group decision-making doesn't parallel individual decision-making.
Underlying Preferences: Unlike an individual whose choices indicate personal preferences; a group's choices do not reveal any collective preferences, according to Arrow. This is why group decisions may sometimes seem irrational.
Remember this theorem by thinking of group decisions as a person who changes ice-cream preferences when flavors are unavailable, switches preference when a flavor is improved, and doesn't make consistent choices between different options. Just like this quirky person, groups can behave in irrational ways because they don't have collective preferences.