Combinatorial Designs and related Discrete Combinatorial Structures
A Combinatorial Prediction Market for the U.S. Elections
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Transcript of A Combinatorial Prediction Market for the U.S. Elections
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A Combinatorial Prediction Market for the U.S. ElectionsMIROSLAV DUDÍK, SEBASTIEN LAHAIE,
DAVID M. PENNOCK, DAVID M. ROTHSCHILDMicrosoft Research
Thanks: Dan Osherson, Arvid Wang, Jake Abernethy, Rafael Frongillo, Rajiv Sethi, Rob Schapire, Jenn Wortman Vaughn
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An ExamplePrediction Market
• A random variable, e.g.
• Turned into a financial instrument payoff = realized value of variable
$100 if $0 ifI am entitled to:
Will Obama win 2012 Presidential election?(Y/N)
Obamawins
Romneywins
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Trade elections like stocks
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Trade elections like stocks
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Prediction Likelihood
VA: Romney 98.7%
MA: Romney 99.6%
VT: Romney 97.5%
ID: Romney 95.7%
GA: Gingrich 98.0%
OH: Romney 82.6%
OK: Santorum 88.6%
ND: Romney 72.1%
AK: Romney 82.6%
TN: Santorum 57.1%
• Predictions as of2:52 p.m. ETMonday, March 5, 2012
Super Tuesday
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Prediction Likelihood
VA: Romney 98.7%
MA: Romney 99.6%
VT: Romney 97.5%
ID: Romney 95.7%
GA: Gingrich 98.0%
OH: Romney 82.6%
OK: Santorum 88.6%
ND: Romney 72.1%
AK: Romney 82.6%
TN: Santorum 57.1%
• Predictions as of2:52 p.m. ETMonday, March 5, 2012
Super Tuesday
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Prediction Likelihood
VA: Romney 98.7%
MA: Romney 99.6%
VT: Romney 97.5%
ID: Romney 95.7%
GA: Gingrich 98.0%
OH: Romney 82.6%
OK: Santorum 88.6%
ND: Romney 72.1%
AK: Romney 82.6%
TN: Santorum 57.1%
total 872.5%
Expected num correct
8.725
• Predictions as of2:52 p.m. ETMonday, March 5, 2012
Super Tuesday
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Conditional probability“logistic regression”“combinatorial prediction markets”
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Prediction Likelihood
VA: Romney 98.7%
MA: Romney 99.6%
VT: Romney 97.5%
ID: Romney 95.7%
GA: Gingrich 98.0%
OH: Romney 82.6%
OK: Santorum 88.6%
ND: Romney 72.1%
AK: Romney 82.6%
TN: Santorum 57.1%
total 872.5%
Expected num correct
8.725
• Prior to MI primary, Santorum favored in Ohio: leading polls by wide margin
• Within hours of Romney winning MI, our OH prediction swung to Romney
• New York Times Nate Silver’s poll-based forecast a couple days behind at least
Super Tuesday: Polls vs Markets
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1. Real-time reaction to big events.
2. Romney dominating when others led the polls.
Real-Time!
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GOP Primary: Polls vs Markets
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Answering ?-mark headlines with data
• Reuters: “The dominant narrative, the day after the presidential election, is the triumph of the quants.”
• Mashable: “here is the absolute, undoubted winner of this election: Nate Silver and his running mate, big data.”
• ReadWrite: “This is about the triumph of machines and software over gut instinct”
[Santorum’s] odds of winning the nomination rose slightly, to a non-negligible 11.3 percent likelihood to Romney's 79.5
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Intrade = Predictions x100
• Presidential – National• Presidential – State-by-state• Presidential – Electoral College• Senate• House• Gubernatorial
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PredictWiseQ = Predictions 100
• 22% chance Romney will win in Iowa but Obama will win the national election
• 75.7% chance the same party will win both Michigan and Ohio
• 48.3% chance Obama gets 300 or more Electoral College votes
• 12.3% chance Obama will win between 6 and 8 states that begin with the letter M
• Path of blue from Canada to Mexico
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Some Counting
• 54 “states”: 48 + DC + Maine (2), Nebraska (3)• 254 = 18 quadrillion possible outcomes• 2254 1018008915383333485 distinct predictions
More than a googol, less than a googolplex• NOT independent
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A combinatorial question:How pivotal was Ohio?
• Day after 1st debate (October 4)• If Obama wins Ohio, 90% he’ll win the election• If Obama wins Florida, 95%; Virginia, 92%• If Romney wins Ohio, 41% he’ll win election;
Florida, 32%; Virginia 31%• If October jobs report bleak, will Romney win?
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PredictWiseQ• In theory, combo PM yields billions more predictions “for free”.
What about in practice?• A combinatorial prediction market for the election: http://PredictWiseQ.com
• Fully working beta & field test– Sep 16 – Nov 6, 2012– 680 users; 437 made at least one trade– 3137 trades in all 23 possible prediction categories– 514 distinct security types were bought
261 of these were traded by a unique user– Empirical paper to appear in ACM EC’13– Market maker algorithm details in ACM EC’12
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Why Expressiveness?
• Dem Pres, Dem Senate, Dem HouseDem Pres, Dem Senate, GOP HouseDem Pres, GOP Senate, Dem HouseDem Pres, GOP Senate, GOP House...
• Dem PresDem HouseDem wins >=270 electoral votesDem wins >=280 electoral votes...
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Standard vs Combinatorial
• Industry standard: Ignore relationshipsTreat them as independent markets
• Las Vegas sports bettingKentucky horseracingWall Street stock optionsHigh Street spread betting
• Combinatorial– Automatic information propagation: reward traders
for information, not computational horsepower
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Consistent pricing
0
1
0 1
A&B’&C
A&B&C
Independent markets
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Consistent pricing
0
1
0 1
A&B’&C
A&B&C
Independent markets
Prices p
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Consistent pricing
0
1
0 1
A&B’&C
A&B&C
Independent markets
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Consistent pricing
0
1
0 1
A&B’&C
A&B&C B = 0.6
A = 0.8C = 0.9
Independent markets
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Consistent pricing
0
1
0 1
0.6 B = 0.6
0.8 A = 0.8
A&B’&C
A&B&C
0.9 C = 0.9
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Consistent pricing
0
1
0 1
0.6 B = 0.6
0.4
0.8 A = 0.8
0.8A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Consistent pricing
0
1
0 1
0.6 B = 0.6
0.4
0.8 A = 0.8
0.8A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Approximate pricing
0
1
0 1
0.6 B = 0.6
0.4
0.8 A = 0.8
0.8A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Approximate pricing
0
1
0 1
0.6 B = 0.6
0.4
Prices p0.8 A = 0.8
0.8A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Approximate pricing
0
1
0 1
0.5 B = 0.5
0.5
Buy NotBPrices p0.8 A = 0.8
0.8A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Approximate pricing
0
1
0 1
0.5 B = 0.5
0.5
Prices p0.8 A = 0.8
0.8A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Approximate pricing
0
1
0 1
0.8
0.5
A = 0.8
B = 0.55
0.5 0.8
Prices p
A&B’&C
A&B&C
0.9 C = 0.9
0.9
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Does it work?
Tested on over 300K complex predictions from Princeton study
Budget
10 States
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Does it work?
Tested on over 300K complex predictions from Princeton study
Budget
Log Score
50 States
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Does it work?
Tested on over 300K complex predictions from Princeton study
Revenue
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User activity, Mean daily profit
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Focal predictions
Top singleton securities• Federal, 43K• FL, 26K• OH, 17K• VA, 15K• CO, 12K• Electoral votes, 10K• NC, 10K• Senate, 8K
Top combinatorial securities• VA, WI = Dem• CO, IN, NH, OH, VA = Dem• Fed, OH = Rep• OH, VA = Dem• FL=Rep, Fed=Dem• FL, NC = Rep• FL, Fed, OH = Dem• NH, NV, OH, VA, WI = Dem
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Return
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Types of securitiesby user return
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“Diversification” by user return
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Accuracy
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Accuracy
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Full distributions
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Counterfactuals
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Further reading
Our paper in ACM EC’13coming soon: email me
Our paper in ACM EC’12http://research.microsoft.com/apps/pubs/default.aspx?id=167977
Blog post on PredictWiseQhttp://blog.oddhead.com/2012/10/06/predictwiseq/
Blog on gory details: What is (and what good is) a combinatorial prediction market?http://bit.ly/combopm
Guest post on Freakonomicshttp://bit.ly/combopmfreak
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NYSE 1926
http://online.wsj.com/article/SB10001424052748704858404576134372454343538.html
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NYSE 1987
http://online.wsj.com/article/SB10001424052748704858404576134372454343538.html
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NYSE 2006-2011
•2011 Deutsche Börse AG
•2007 Euronext
•2006 Archipelago, ipo
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NYSE 7pm Sep 10, 2012
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New markets, same old CDA
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A Better Way(Or,... Bringing trading into digital age)
• Expressiveness– Linear programming– Bossaerts, Fine, Ledyard: Combined Value Trading
Fortnow et al.: Betting Boolean Style– http://bit.ly/multipm
• Expressiveness + Liquidity– Automated market maker– Always quote a price on anything– Downside: requires subsidy/risk