My Cat Violates Arrow's Axiom of Independence of Irrelevant Alternatives

Arrow's Axiom of Independence of Irrelevant Alternatives says that if you prefer apple pie to peach pie, the appearance on the table of a slice of cherry pie inside an unbreakable glass box won't change your preference for an available slice of apple over an available slice of peach. This seemingly intuitive axiom is one of the assumptions for Arrow's famous impossibility theorem, that there is no democratic choice system (i.e., voting method) that satisfies this and several other equally "obviously true" principles.

Our cat Fluffy (aka Fluffy the Finicky) routinely violates this axiom. She prefers dry food to no food. She prefers no food to wet food - she will almost never eat it unless she's very hungry. However, often when presented with dry food she turns up her nose, even if she's hungry. The trick to get her to eat (so that the other cats don't eat her food first) is to put down another bowl containing a tiny amount of wet food. As soon as sniffs the wet food bowl, she heads back over to the dry food bowl and starts eating.

So her preferences at these times start out as No Food > Dry Food. Presented with some wet food, an irrelevant alternative since she almost never prefers it to either, her preferences switch to Dry Food > No Food.

This is probably why cats have never developed advanced democratic societies.