## 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?

## Huckabee and Trump Depart the Race

Within the past week, both Mike Huckabee and Donald Trump announced that they would not seek the Presidency in 2012. The prediction markets had plenty to say about these candidates both before and after they dropped out of the running. Both men's likelihood of winning the Republican nomination peaked at nearly 9%, but the markets show that the end of their campaigns came about under very different circumstances. Below is a chart of Mike Huckabee's likelihood of winning the Republican nomination, where the red line marks the moment when he made the announcement he was not running during his weekly Fox News TV show. One day before his on-air announcement, when rumors of an impending announcement on his campaign began to spread, this market tanked rather quickly. The market was reasonably quick to recognize that he was going to drop out of the race. However, it appears as though the market began to second-guess itself over the following 24 hours – perhaps due to conflicting rumors – and by the time of his announcement, the Huckabee contract regained about 1/3 of the value lost during the previous day.

Donald Trump's likelihood of winning the Republican nomination peaked just before President Obama released his long-form birth certificate on April 27, and began its precipitous decline just as Obama announced the death of Osama Bin Laden on May 1. The final drop on May 17 coincided with his announcement that he will renew his job as a television personality, rather than run for President. While Huckabee was an extremely viable candidate prior to his announcement, Trump had already been trending towards irrelevancy, even before his announcement.

I regret that we had not been tracking Jon Huntsman's chances until very recently, but the other two candidates who clearly benefited the most probability of victory with the Huckabee announcement were Mitt Romney and Tim Pawlenty. As I note in the first chart there are really two separate noteworthy events in Huckabee's withdrawal from the race. The first occured when rumors of an impending announcement were circulating and the second occurred a day later when his decision was announced. The first reaction of the market was to assume that Romney was going to really benefit from Huckabee's departure. After the rumors began, going into the formal announcement (where the red line is located), Romney had absorbed almost all of the Huckabee's total loss. Yet Romney gained little from the formal announcement while Pawlenty, who had already fallen back down to his pre-rumor level, got a nice boost from the actual announcement. One thing is clear from this analysis: the market is undecided on who benefited from the Huckabee announcement.

## Death of Osama on 2012 Election

A key question in political circles over the last few days has been the effect of the death of Osama Bin Laden by the U.S. armed forces on the outcomes of the 2012 election. Indubitably, the event is beneficial to the Democratic party and President Obama in particular. Polls conducted in the days following the event gave Mr. Obama at 9 percentage point increase in approval. There are a few points to consider on the prediction market's reaction to the event.

First, it definitely increased President Obama's probability of victory in 2012. On average his probability of victory has gone from around 60% to around 63%. Second, both Intrade and BetFair, the two leading markets, took a surprising amount of time "digesting" the information. Today, seven days after the event, they are still moving sharply. Prior to Mr. Obama's press conference announcing the death of Osama, the probability is relatively flat for weeks, but after the event there is a distinct trend in both markets that is still visible. Third, the two markets ultimately disagreed on the trajectory of the "digesting". Betfair is digesting the news by moving even further in favor of an Obama victory and Intrade, from an almost identical position, is moving back toward the pre-Osama death probability of victory. I am not going to discuss here the true underlying value of Osama's death, beyond the values provided by the markets, but I can state that in a few days arbitrage will bring these two markets together and we can have a clearer picture of what the markets feel is the underlying value of Osama's death on the 2012 Presidential election.

There appears to minimal effect on the House. The probability of the Democratic party regaining the House remained flat through the last two weeks.

## Government Shutdown

The table is now not as useful as a chart of the evening. The deal was struck at 10:30 PM and the probability derived from Intrade's prices moved just as the deal was being announced. That being said, it was generally moving in that direction as some information was dispersed. At 10:30 PM HuffingtonPost and others were still giving very neutral headlines, while Intrade was in its steady march downward towards no shutdown.

Watch this number as we approach midnight! It is currently at 55% with 6 hours to go …

## Libya and Gaddafi

The dotted line you see here represents the exact point in time that the UN passed its resolution for a no-fly zone over Libya. The interesting thing about this line is that the price for a contract on Gaddafi not being in power past the end of the year reached a local peak as it passed, not after. The reason is that Intrade did a good job here incorporating the information about the UN and the actual passage became a fete-de-complete. More important, the price has been impressively stable even as events swirl back and forth on the ground in Libya. The contract is for the end of the year and I take the stability as a sign of a mature and liquid market, where Intrade had, in the past, had issues with dramatic volatility in similar situations … Finally, what most people really care about, I would translate the current price (at 1:00 PM EST on Thursday, March 31) into a probablity of 85% that Gaddafi does not make it into the New Year as the ruler of Libya.

## Mrs. Palin's Political Trouble from Saturday's Massacre

Immediately in the aftermath of Saturday's assassination attempt on Congresswoman Gifford, that resulted in the death of six people including a federal judge and a nine year old girl, the media began speculating on the political fallout to Sarah Palin's 2012 Presidential aspirations. In March she had put out an advertisement with a target on Congresswoman Gifford and then told asked that her followers "Don't Retreat, Instead – RELOAD!" Thus, after the massacre people began to discuss her contribution to both the specific target and the general heated atmosphere in politics; regardless of her complicity, and thus far there is no direct evidence the assassin followed Mrs. Palin, talk of it has political consequences. As several blogs have already noted, the market for her 2012 Republican nomination responded immediately … on Intrade. She lost over 1/3 of her probability in the immediate aftermath of the massacre. Yet, the movement a different market, Betfair, was much smaller, as it was already trading lower for Mrs. Palin; Betfair has consistently had less confidence in Mrs. Palin's viability as the Republican nominee. The chart is below:

## Repeal of "Don't Ask, Don't Tell"

The Senate votes today on the repeal of the "Don't Ask Don't Tell" law.  News of the vote caused PredictWise's likelihood of repeal to skyrocket to 88%, implying that the controversial law is very likely to be over-turned today.

## Obama and the 2012 Nomination &#8230;

When you think about 2012 Presidential nominations you are likely thinking about Palin, Romney, and the Republicans. But, as the year comes to close and the 111th Congress end on December 17th or so, I urge you keep an eye on the Democratic ticket. An editoral in today's Washington Post urges a Democrat to run to the left of the President to force him to hold firm on taxes, war, and social issues. First, it would be difficult for Biden to do that from within the adminstration and Clinton is not that person, thus for this to happen it would have to be an outside option. We will make sure to add that person, and you will see it coming with Obama falling. Second, notice the discrepencies between Betfair and Intrade  on Hillary and Biden.

## Market to Watch: DADT

The probability of Don't Ask Don't Tell being eliminated by the end of the year tanked to just above 10% after the Democratic defeat on Election Day. But, today brought good news to those trying for repeal, the Democrats are making a top priority in the lame duck session …