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35-probability&amp;decisions

# 35-probability&amp;decisions - HigherCogni onII...

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Higher Cogni+on II Probabilis+c Reasoning and Decision Making

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What is ra+onality? Claim: Man is a ra+onal animal How should we reason? Norma+ve theory How do we reason? Descrip+ve theory
How should we reason? Formal logic Logic deals with certainty We face considerable uncertainty Probability theory Probability theory deals with degrees of certainty But most of the reasoning we do is to inform our decisions

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From reasoning to decisions Expected value E = P ( x i ) U ( x i ) The expected gain from a decision Sum over all possible outcomes of decision Probability of each outcome Value (or u+lity) of that outcome
From reasoning to decisions Expected value E = P ( x i ) U ( x i ) Pay \$1 to play Roll one die Win \$4 for even Lose \$1 for odd E = 3/6 \$4 + ⋅ − \$4 = \$1.50 \$1.50 > \$1.00

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What is ra+onality? Claim: Man is a ra+onal animal How should we reason? Norma+ve theory How do we reason? Descrip+ve theory
What is ra+onality? Claim: Man is a ra+onal animal Norma+ve theory How do we reason? Descrip+ve theory Expected u+lity

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What is ra+onality? Claim: Man is a ra+onal animal Norma+ve theory Descrip+ve theory Expected u+lity Expected u+lity?
From reasoning to decisions Expected value E = P ( x i ) U ( x i )

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From reasoning to decisions Expected value E = P ( x i ) U ( x i ) = Probability × Value These two quan++es are enough to compute op#mal decisions! But how good are we at es+ma+ng them?
Monty Hall problem A B C There is a car behind one door and goats behind the other doors

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Monty Hall problem A B C You pick a door
Monty Hall problem A B You pick a door I open a door Do you switch to B or s+ck with A?

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Monty Hall problem A B 87% stay (Granberg & Brown, 1995) Best answer is to switch Do you switch to B or s+ck with A?
Monty Hall problem

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Monty Hall problem Switch or stay?
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• Spring '10
• theissen
• Probability, Probability theory, Descrip+vetheory Howdowereason, Probability × Value, Norma+vetheory Howshouldwereason, HigherCogni+onII Probabilis+cReasoningandDecision Making

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35-probability&amp;decisions - HigherCogni onII...

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