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Monte Hall Paradox. Famous game show from the 70's Problem: Three doors One prize (car), 2 goats You chose 1 door Monte Hall (host) opens a door with a goat Asks if you want to switch Should you switch?. Monty Hall Problem. 1 Car, 2 goats Choose door. 1. 2. 3. Monty Hall Problem.

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Monte Hall Paradox

  • Famous game show from the 70's

  • Problem:

    • Three doors

    • One prize (car), 2 goats

  • You chose 1 door

  • Monte Hall (host) opens a door with a goat

  • Asks if you want to switch

  • Should you switch?


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Monty Hall Problem

  • 1 Car, 2 goats

  • Choose door

1

2

3


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Monty Hall Problem

  • Monty Hall reveals goat

  • Asks if you want to switch

  • What do you do?

1

2

3


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Monty Hall Links

  • http://www.stat.sc.edu/~west/applets/LetsMakeaDeal.html

  • http://math.ucsd.edu/~anistat/chi-an/MonteHallParadox.html


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Monty Hall Problem

1

2

3

2/3

1/3


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Easier Monty Hall

  • 1000 Doors, 1 car

  • You chose 1

  • Monty opens 998 goats

  • Should you switch?


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Monte Hall Paradox

  • Famous game show from the 70's

  • Problem:

    • Three doors

    • One prize (car), 2 goats

  • You chose 1 door

  • Monte Hall (host) opens a door with a goat

  • Asks if you want to switch

  • Should you switch?


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Monte Hall

1

3

2

Your Choice


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Monte Hall

Goat!!

1

3

2

Your Choice

Should you switch?


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Monte HallProbabilities

1

1/3

3

1/3

2

1/3

Your Choice


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Monte HallProbabilities

1

3

1/3

2

2/3

Your Choice

Should you switch?

Yes


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Two Final (difficult) Topics

  • Time

  • Chaos/complexity


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Time

  • Horizon

    • Days, weeks, months, years

  • Decisions

    • How effected by new information


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Complexity/connections

  • Interconnection between different variables difficult to predict, control, or understand

  • System failures

  • May impact the correctness of our risk model

  • Model risk


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Behavioral Features

  • Simple rules

  • Probability/ambiguity

  • Gambler’s fallacy

  • Regret/loss aversion

  • Overconfidence

  • Choice (information) overload

  • Under diversification


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Choice Overload

  • Jam samples in supermarket

    • Consumers sample jam

    • Can buy with coupon

  • Case 1: 6 jams

    • 30 percent redeem coupons

  • Case 2: 26 jams

    • 3 percent redeem coupons


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Information Overload

  • Decision makers have lots of information

  • Need to decide what is relevant

  • Emergent patterns on irrelevant information

    • Sunspots


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