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Unformatted text preview: event? Proper Scoring Rules 19 Combining informaNon is hard! •  If we have mulNple experts, how can we combine their informaNon? •  Some impossibility results on combining probability distribuNons. –  T(f1, f2, f3, …, fn) –  External Bayesianity –  Independent of irrelevant alternaNves => dictatorship 20 Orange Juice Futures and Weather Trades of 15,000 pounds of orange juice solid in March •  Orange juice futures price can improve weather forecast! [Roll 1984] 21 Bet = Credible Opinion •  Q: Is Vinay Deolalikar’s proof of P≠NP correct? “If Vinay Deolalikar is awarded the $1,000,000 Clay Millennium Prize for his proof of P≠NP, then I, ScoF Aaronson, will personally supplement his prize by the amount of $200,000.” •  ScoF Aaronson: “I have a way of staNng my predicNon that no reasonable person could hold against me: I’ve literally bet my house on it.” 22 PredicNon Markets •  A predicNon market is a futures market (be`ng intermediary) that is designed for informaNon aggregaNon and predicNon. •  Payoffs of the traded item is associated with outcomes of future events. $11 Percentage of $1 if Patriots win $ ×if Obama Wins Vote Share That $f(x) $0 Otherwise $0 Otherwise Obama Wins T1 ­23 Intrade 24 FuncNon of Markets 1: Get InformaNon •  SpeculaNon price discovery price ≈ expectaNon of r.v. | all informaNon $1 if Obama wins, $0 otherwise Value of Contract ? Payoff a wins ) $1 P( Obam $P( Obama wins ) 1- P ( O bama wins ) $0 Event Outcome Obama wins Obama loses Equilibrium Price ≈ Value of Contract ≈ P( Obama Wins ) Market Efficiency 25 A Combinatorial Be`ng Example 51 outcomes, 2251 combinaNons 2 •  •  Allow parNcipants to bet on logical formulas –  Create contracts on the fly: $1 i...
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This note was uploaded on 04/11/2013 for the course EE 218 taught by Professor Vanderschaar,mihaela during the Winter '13 term at UCLA.

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