Wei Dai is right to say:
I'm afraid that the Axiom of Independence cannot really be justified as a basic principle of rationality.
I urge the LW community to do more to explore the consequences of a weaker set of axioms.
Suppose that at 12:00PM I roll a hundred-sided die. If the die shows a number greater than 34, the game terminates. Otherwise, at 12:05PM I consult a switch with two settings, A and B. If the setting is A, I pay you $24,000. If the setting is B, I roll a 34-sided die and pay you $27,000 unless the die shows "34", in which case I pay you nothing.
Let's say you prefer 1A over 1B, and 2B over 2A, and you would pay a single penny to indulge each preference. The switch starts in state A. Before 12:00PM, you pay me a penny to throw the switch to B. The die comes up 12. After 12:00PM and before 12:05PM, you pay me a penny to throw the switch to A.
But you'd know that you'd switch back to A, so you'd never really get B. You'd keep B, as it's not a choice between A and B; it's a choice between A + 2 cents and A.
Today's post, The Allais Paradox was originally published on 19 January 2008. A summary (taken from the LW wiki):
Offered choices between gambles, people make decision-theoretically inconsistent decisions.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Trust in Math, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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