# Explaining the Favorite-Longshot Bias in Prediction Markets

To illustrate the favorite-longshot bias, assume that, six months before an election, an investor believes the Democratic candidate has a 95% chance of winning. There are several reasons why this investor would not pay a full \$0.95 for a contract that pays off \$1 if the Democratic candidate wins. First, there is an opportunity cost of the bet being held for upwards of 6 months, because there is limited liquidity in many markets. The investor's money is tied up in this market, when it could be out doing something else: sitting in a bank, providing capital for a startup, being used to consume something, etc. The cost is literally the opportunity to be doing other things with the money while it held up in the market. Secondly, there are transaction costs of around \$0.015 per \$1 invested, thus the investor will actually bid up to whatever she determines is the optimal price minus the transaction cost that will be lost when the bet is processed. Finally, if there are two bets that are equal in expectation, the investor gains more utility from betting on a longshot. It is not clear to researchers whether investors are risk loving (i.e., they gain utility from doing risky things) or beset by misconceptions or Prospect Theory (i.e., they overvalue small probabilities and undervalue high probabilities), but it is accepted in the academic literature that they are not risk neutral.

All this brings me to the subject of Intrade's market for the Democratic Nominee for President of the United States in 2012. Currently, Mr. Obama is trading at a bid of \$0.910 per \$1 and an offer of \$0.937 per \$1 for a price of \$0.924 per \$1. If this seems too low to you, let's examine why you might be correct.

(I should note that the rules of the market specifically state that the contract is voided if any nominee in the market passes away, so that is not an issue.) Let us consider our three remaining causes of the favorite-longshot bias:

First, the market will not settle until September of 2012 (i.e.,15 to 16 months from now). This means that any money tied up in this market is lost for a consider amount of time. Thus, there is a large liquidity cost.

Second, Intrade has just switched to a flat fee model, while there are still transaction costs, they are much lower for Intrade than for any other market, so this is not a big factor in the low price.

Third, people get more utility out of holding (and dreaming about) the longshot Mrs. Clinton to be the nominee, with a bid at \$0.030 and an ask at \$0.040 per \$1, than the favorite Mr. Obama, so they are willing to bid more than is realistically likely in order to own the contract. Again, I am not sure if it is the utility of dreaming about/holding onto longshots, or is it because people are miscalculating long odds. Yet, if an investor deemed an investment in Obama and Clinton equal in their likely payout, they are going to gain more utility from the Clinton investment.

While the direct translation of these prices would say that Mr. Obama has 92.4% likelihood of the nomination and Mrs. Clinton a 3.5% likelihood of the nomination, my calculations would place it closer to 99% and 0.2%. Which one seems more realistic to you?