What do Lance Armstrong, Abraham Lincoln, and a group of Wall Street bankers have in common?

This is not the opening line of an incredibly unfunny joke.* Rather, this is an economist’s story of how Abraham Lincoln indirectly forced Lance Armstrong to come clean about cheating. It’s also the story of why detecting fraud by Wall Street bankers may prove more difficult.Economists study incentives. We know that if the price of rice goes up, the incentive to produce and supply rice increases. The same is true in the market for private information about fraud. If whistle-blowing behaviour is rewarded, the incentive to supply private information about dishonest or illegal behaviour also increases.

In the United States, if an individual has private information that persons or companies have committed fraud against the federal government, then that individual can file a private lawsuit on behalf of the government against the fraudulent person or company. If fraud is proven and damages awarded, the whistleblower bringing the suit stands to receive a substantial portion of the total damages (up to one quarter of the total damages).

This law was introduced during the American Civil War when a large number of unscrupulous contractors were defrauding the government. Because it was introduced during the presidency of Abraham Lincoln, it is referred to as “Lincoln’s Law”. It is commonly accepted that Lincoln’s Law has been highly successful at both encouraging whistle blowing and deterring fraud.

What does this have to do with Lance Armstrong? The truth about Lance Armstrong’s doping became public, in part, because of information released by his former teammate, Floyd Landis. Landis won the 2006 Tour de France, but was later stripped of his victory because he doped during the Tour. Landis pleaded innocence for years, but in 2010, he openly admitted to cheating. He also accused Lance Armstrong of doping. Armstrong strenuously denied the allegations; the International Cyclist Union stated that Floyd Landis’s allegations were “completely untrue” and he was merely seeking revenge. Alarmed at the lack of response, Floyd Landis filed suit against Lance Armstrong on behalf of the United States government under Lincoln’s Law.

How did Lance Armstrong defraud the federal government? Between 2002 and 2004, Lance Armstrong and Floyd Landis were teammates on a team sponsored by the United States Postal Service, a branch of the U.S. federal government. This sponsorship was worth about $30 million. Floyd Landis claimed that the sponsorship money was obtained fraudulently. If he could show that Lance Armstrong received this money by promising that he did not use drugs, Floyd Landis stood to receive about $20 million by being the first to blow the whistle on Lance Armstrong.

Let’s turn to game theory to analyse why Lincoln’s Law is so successful. Lincoln’s Law provides an excellent example of what game theorists call “screening”. The law enables the government – who is poorly informed about the existence of fraud – to extract private information from better-informed individuals, such as employees of firms committing fraud.

Let’s suppose there are two types of potential whistleblower. First, there are whistleblowers with very strong information that fraud has occurred. They may, for example, have been involved in defrauding the government. Second, there are whistleblowers with very weak information. These whistleblowers are merely guessing that fraud has occurred, but they may report this information in order to seek revenge against their former employer. The government wants to encourage whistleblowers with strong information to come forward; it wants to discourage whistle blowing by individuals with weak information.

The government may incentivize whistle-blowing behaviour by providing very large rewards to whistleblowers. This may, however, have a perverse effect of encouraging all potential whistleblowers – both strong information types and weak information types – to come forward. Such a reward scheme generates what is known as a “pooling equilibrium”: Whistleblowers with strong information and whistleblowers with weak information behave exactly the same way. The government will be no better informed than they were before.

Lincoln’s Law provides very large rewards that are contingent upon successfully proving fraud, but it also incurs large private costs on the whistleblower. There are significant monetary and reputational costs to bringing suit. The costs are even greater for bringing a failed suit. These private costs help generate a “separating equilibrium”: Only those individuals sufficiently confident of victory – those with strong information – will be incentivized to file suit. Individuals with weak information will not be willing to bear these costs of filing suit given the low likelihood of receiving a reward. The law, therefore, “screens” the quality of the whistleblower’s information.

There have been attempts to replicate the success of Lincoln’s Law in other whistleblower schemes. These new schemes, however, recreate only the reward scheme; they do not require whistleblowers to file a lawsuit. Take, for example, recent changes to securities regulation in the United States. The government introduced a new whistleblower scheme to deter fraud by Wall Street bankers. This new law merely requires the whistleblower to bring the information to the regulator. If the case against the fraudulent bank proves successful, the whistleblower stands to gain an enormous reward; but if the case proves unsuccessful, the whistleblower may be granted anonymity and he bears little private cost.

A game theoretic analysis suggests that this high-reward, low-cost incentive structure used to detect fraud on Wall Street may prove counter-productive. The new rules may incentivize disgruntled employees with poor information to report their information to the regulator in the hope of hitting the jackpot.

*   Of course, if you do have humorous punch lines for these “jokes”, please feel free to post them below in the comments section.