Slides in PDF - of Marcus Hutter
Slides in PDF - of Marcus Hutter
Slides in PDF - of Marcus Hutter
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<strong>Marcus</strong> <strong>Hutter</strong> - 28 - Universal Induction & Intelligence<br />
Exercise: Envelope Paradox<br />
• I <strong>of</strong>fer you two closed envelopes, one <strong>of</strong> them conta<strong>in</strong>s twice the<br />
amount <strong>of</strong> money than the other. You are allowed to pick one and<br />
open it. Now you have two options. Keep the money or decide for<br />
the other envelope (which could double or half your ga<strong>in</strong>).<br />
• Symmetry argument: It doesn’t matter whether you switch, the<br />
expected ga<strong>in</strong> is the same.<br />
• Refutation: With probability p = 1/2, the other envelope conta<strong>in</strong>s<br />
twice/half the amount, i.e. if you switch your expected ga<strong>in</strong><br />
<strong>in</strong>creases by a factor 1.25=(1/2)*2+(1/2)*(1/2).<br />
• Present a Bayesian solution.
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