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 it is interesting to check this by looking at the data.

To do this we need to describe how the Tradesports betting works. We illustrate how this in terms of betting that Hillery Clinton will be nominated as the democratic candidate for the 2008 presidential election.

Betting at Tradesports is made through contracts. You can buy or sell contracts. In this example the a contract has a price between 0 and 100. A contract with price 0 is worthless. A contract with price 100 is worth $10.

Until the nomination is determined you can offer to buy or cell contracts at specific prices. If your offer to buy matches another persons offer to sell you can bid for a contract. Tradesports makes the initial price for a contract and after this it is determined by offers to buy and sell them. Thus Tradesports is simply a match maker though there are some fees attached to this which are explained here

As of December 23 Hillery contracts were given in the following table.

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

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At this is written the price of a contract is 50.3. This is interpreted to mean that Hillery has a 53% chance of being nomiated.

The closing price of a contract varies through time as illustrated by the following graphic:

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

Here are similar graphs for other leading cadidates for democratic and republican nominations as of Dec. 5, 2006 that 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 and the question raised earlier: Assuming that the price of a contract the democrats will win a particuar state estimates the probability that they win this state, are the events that the they win two states independent. On might think that events such as the Folley scandal and his resignation in late september could influence the prices of both contracts. 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 publized 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 Missori prices(top) http://www.dartmouth.edu/~chance/forwiki/RhodeIslandOhio.jpg RhodeIland prices (bottom) and Ohio prices(top) http://www.dartmouth.edu/~chance/forwiki/MontannaPennsylvania.jpg Montanna prices (bottom) and Pennsylvania prices(top)

and consider the 33 Senate races.   The democrats had to win 24 or more of these races to win control the Senate.  Assuming that the indpendent candidates Joe Lieberman in  Connecticut and Bernie Sanders in Vermont will win their races and vote as democrates.  the democrates would have to win 22 or more of the remaining 31 races. 

We assume that the price of a contract for the democrats winning a particular state is an estimate for the probability they will win this state. If we could assume that the outcome of different states are independent the probability that the win a specified number of states would be the product of the probabilities for which each state. Then we coulc calculate probability that they would win 22 or more of the states. However, they are probability not independent, But, we can estimate the expected number of states the democrats will by simply adding the probabilities for states with contract price greater than 1/2.

Doing this using the closing price for each day from Jan 15 to November 6 we obtain the following graph:

http://www.dartmouth.edu/~chance/forwiki/demleads.jpg<\center>