This preview shows page 1. Sign up to view the full content.
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...
View
Full
Document
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.
 Winter '13
 vanderSchaar,Mihaela

Click to edit the document details