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.

http://weblog.fortnow.com/media/election-day-2006-map.JPG

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.

http://www.dartmouth.edu/~chance/wikivideos/clintonbidask.jpg

.

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:

http://www.dartmouth.edu/~chance/wikivideos/clintongraph.jpg

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.

http://www.dartmouth.edu/~chance/forwiki/tradesportstable.jpg

These look reasanoble but if you really believed that these were the true probilities you could buy contracts on all three of the possible outcome of the

Next we would like to see if the prices for contracts that the Democrats will win two different states are independent. One way to look at this is to compare plots of the prices of two different states. We do this for three pairs of states chosen from the six states widely publicized as states the Democrats would have to win to win control of the Senate.

http://www.dartmouth.edu/~chance/forwiki/VirginiaMissouri.jpg Virginia prices (bottom) and Missouri prices (top) http://www.dartmouth.edu/~chance/forwiki/RhodeIslandOhio.jpg Rhode Island prices (bottom) and Ohio prices (top) http://www.dartmouth.edu/~chance/forwiki/MontannaPennsylvania.jpg Montana prices (bottom) and Pennsylvania prices (top)

Well, they do seem to follow each other and so we can say that they are not independent but this may not be completely convincing.

were 33 Senate races. The Democrats had to win 24 or more of these races to win control the Senate. It was pretty clear that the Independent candidates Joe Lieberman in Connecticut and Bernie Sanders in Vermont would win their races and vote as Democrats, so the Democrats would have to win 22 or more of the remaining 31 races.

If the prices of individual states are not independent we cannot estimate the probability that the Democrats win 22 or more races. But, we can estimate the expected number of states the Democrats will win by simply adding the probabilities for states with contract price greater than 1/2. Doing this, using the closing price for each day from January 15 to November 6, we obtain the following graph:

http://www.dartmouth.edu/~chance/forwiki/demleads.jpg

This suggests that only in the last days of the race did the Democrats appear to have a chance of winning the required 22 states.

Tradesports did not have a contract that the Democrats would win control of the Senate, but they did have a contract that the Republicans would; so we can determine the probability that the Democrats win control of the Senate from this. Here is Tradesports graph of the closing prices for the contract that the Republicans would win control of the Senate:

http://www.dartmouth.edu/~chance/forwiki/repSenatecontrole.jpg

While the probability that the Republicans would win control of the Senate decreases as the election gets closer, even the day before the election we would still predict that it is unlikely that the Democrats would win control of the Senate. This is not consistent with our conclusion using the estimates for the expected number of states they did have a good chance of winning control of the Senate.