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vi21maobk9vp comments on Stupid Questions Open Thread Round 4 - Less Wrong Discussion
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I can see how the money pump argument demonstrates the irrationality of an agent with cyclic preferences. Is there a more general argument that demonstrates the irrationality of an agent with intransitive preferences of any kind (not merely one with cyclic preferences)?
Just in case - synchronising the definitions.
I usually consider something transitive if "X≥Y, Y≥Z then X≥Z" holds for all X,Y,Z.
If this holds, preferences are transitive. Otherwise, there are some X,Y,Z: X≥Y, Y≥Z, Z>X. I would call that cyclical.