Tradesports predictions for 2006 elections
Can predictions markets be right too often?
David Pennock
Prediction map post mortem.
Robert Forsythe
We have discussed the use of betting markets to predict the outcomes of elections several times in Chance News. See for example Chance News 12.02
Lance Fornow Computer Scientist at the University of Chicago, David Pennock and Chen Yiling Research Scientists at Yahoo have carried out research to evaluate the ability of markets such as Tradesports, the Iowa Political Markets and other such markets to predict the outcomes of elections, sports events, Oscar winners etc.
In their discussion of the predictions relating to the 2006 Senate races, they provided the following map showing results as of about 9 AM CST election day.
In his analysis, Fornow wrote:
Every state colored blue was won by a Democrat and every state colored red went to a Republican. But also note the 69% given to GOP (Republican) Senate control although this election will give control to the Democrats. No outcome would have made all the states and Senate control agree with the 9 AM map.
Were the markets inconsistent? No, because the markets predict not absolutely but probabilistically. For example, the markets gave a probability of winning 60% for each of Virginia and Missouri, and the Democrats needed both to take the Senate. If these races were independent events, the probability that the Democrats take both is 36% or a 64% chance of GOP Senate control assuming no other surprises.
Of course the races were not independent events and there are other states involved making it more difficult to compare the probabilities of the individual races with that of Senate control.
So how did the markets do as predictors? Quite well as the outcome seems quite reasonable given the markets. Other outcomes would have also been reasonable such as the Democrats losing Virginia and the Senate remaining in Republican hands, a possibility that came very close to happening.
While it seems likely that the outcomes of individual state elections are not independent, we thought it would be interesting to explore this.
To do this we need to describe how the Tradesports betting works. As explained by WikiPedia:
Tradesports markets trades in the binary 0-100 format. If the event specified in a given contract occurs, the contract settles at 100 points, or $10 per contract or share; otherwise, the contract settles at 0. Thus, the current price of the contract can be imputed as the probability that the specified event will occur.
We will illustrate this in terms of a current event: will Hillary Clinton be nominated as the Democratic candidate for the 2008 presidential election?
Tradesports makes the initial price for a contract and after this the price is determined by offers to buy and sell the contracts. Thus Tradesports is simply a match maker, though there are some fees attached to this which are explained here
On December 23 Senator Clinton contracts were given in the following table.
.
A price of 53.0 is interpreted to mean that Senator Clinton has a 53% chance of being nominated. It would cost you $5.30 for this contract. Then you should win $10 with probability .53 and 0 with probability .47, giving you an expected winning of $5.30 and making it a fair bet.
For each day there is a closing price for a contract which varies through time as illustrated by the following graphic:
Here are similar graphs for other leading candidates for Democratic and Republican nominations as appeared in a New York Times article," '08 Candidates in a Virtual Market", Dec. 5, 2006.
http://graphics8.nytimes.com/images/2006/12/05/us/politics/1205-nat-webACTION.gif
Now we return to the 2006 election. There were a number of contracts you could bid for. We will concentrate on the contracts for the Democrats winning a particular state and contracts that they win control of the Senate.
We would like to see if the contract prices really act like probabilities. Here is an elementary test. When you buy a contract for the outcome of a particular state you have three choices for the contracts: The Democratic candidate will win, the Republican candidate will win, and some other cadidate will win. if the prices are really probabilities the prices for these three choices should add up to about 1. Of course these prices are themselves random variables so we cannot expect them to add up to exactly 100.
Here are the sums for some of the states that were considered important for the Democrats to control the senate.
State |
Democrat |
Republican |
Other |
Total |
|
Virginia |
66 |
35 |
.1 |
101.1 |
|
Tennessee |
15 |
85 |
1 |
101 |
|
Missouri |
55 |
48 |
1 |
104.9 |
|
Rhode Island |
79.3 |
23 |
2.6 |
104.9 |
Ohio |
94.8 |
5 |
.1 |
99.9 |
Montana |
67.9 |
39 |
.1 |
107 |
Pennsylvania |
96.9 |
6 |
.1 |
99.6 |
New Jersey |
91 |
8.5 |
.1 |
99.6 |
Washington |
92.2 |
8 |
.1 |
93.1 |