Saturday, April 14, 2012

Jimmy McNulty and the Economics of the Baltimore Serial Killer

In HBO’s ‘The Wire’ drug kingpin Stringer Bell was an economics student, but unfortunately for him he did not live to see possibly the most interesting illustration of economic theory the show had to offer. In season five, police detective Jimmy McNulty misleads his department, the mayor’s office and the media by fabricating evidence that several unconnected murders are the handiwork of a mysterious serial killer in Baltimore. At first this seems like utter madness, but as the season goes on one can see why McNulty’s gambit might indeed be a rational response to the issues facing the police department, and why society might even benefit from it.

The optimization problem

In economic theory the optimization problem is that rational economic agents try to maximise their utility subject to their budget constraints. Utility is essentially a measure of what the agent values and dislikes. The budget constraint is the set of resources available to the agent.

In season five of ‘The Wire’ the police department is operating under severe budget constraints, with many officers owed back pay for overtime worked. Less money for the police department also means less money to spend on cases and combatting crime. Baltimore’s mayor, Tommy Carcetti, is reluctant to seek extra funds for his “broke-ass” city because he believes it will lower his chances of becoming Governor of Maryland down the track.

With this scenario before us, let’s look at the optimization problem for each of the major players:

McNulty: McNulty’s utility is positively related to his ability to bring bad guys to justice. In season five McNulty is primarily concerned with bringing drug kingpin Marlo Stanfield and his crew to justice for their drug dealings and murders. The problem for McNulty is there are not sufficient funds available to the police department to do this. McNulty therefore needs to expand the budget set available to him so as to be able to reach a higher level of utility. By manufacturing a serial killer, McNulty is able to leverage a sensitive political issue in order to obtain more funds for the department and expand this budget set.

There are arguably other utility gains to McNulty from being able to expand the budget set. As we see McNulty is able to allocate resources to other “real” cases, therefore increasing the chances of bringing more bad guys to justice. He also gets the satisfaction of outsmarting his superiors and the mayor’s office, but despite McNulty’s smirk let us assume that this results in only a minor utility gain.

On the other hand McNulty’s utility is negatively related to the chance that he will get caught for fabricating evidence and therefore be kicked off the force and even go to jail. He may also potentially lose the support and respect of his family and friends, with best friend Bunk Moreland being a particular critic of McNulty’s scheme. McNulty therefore needs to put in measures to reduce the likelihood of these negative outcomes. This is explained further in the section on game theory below.

Carcetti: Carcetti’s utility is positively related to his chances of becoming Governor of Maryland. It would also be positively related to the wellbeing of the city, but through his decision to forgo funds he has revealed a preference for his political ambitions over the city’s health. Conversely his utility is negatively related to anything that diminishes his chances of becoming governor, such as political scandal. Carcetti’s budget constraint is the city’s balance sheet, which has been left in poor health by the time he gains office.

The Baltimore police officers: Like McNulty all of the work of the Baltimore police officers is being constrained by the limited funds available to the department. Many police officers have things to gain or lose from McNulty’s serial killer hoax, but the three most interesting cases are Cedric Daniels, Lester Freamon, and Bunk Moreland. Daniels has been promised by Carcetti that he will be the next police commissioner. Daniels’ utility is positively related to his level of authority and his ability to ‘do the right thing’ (and negatively related to the absence of these things). Freamon is working the Marlo case, and his potential gains and losses are fairly similar to those of McNulty’s. Moreland’s are similar as well, but he reveals a preference for keeping his job, staying out of jail and maintaining the respect of the department over potentially bringing Marlo to justice. He therefore takes no part in McNulty’s scheme and even actively discourages McNulty to drop it.

Game theory

Given the utility functions and constraints of each of the major players what are their best strategies? We can work this out using a bit of game theory.

For McNulty there is some probability that he will get caught. If there is no chance he will get caught his best strategy is to fabricate a serial killer, since it increases the chance of bringing the bad guys to justice and brings in money for the police department (though it does lose him some respect with Moreland). But if there is a chance he does get caught this is not so clear – he may lose his job and go to jail. McNulty’s best strategy then will depend upon the chance he gets caught, as well as the likelihood that he loses his job and the likelihood he goes to jail.

As it turns out McNulty does get caught but he does not (technically) lose his job or go to jail. The reason is that, when Carcetti finds out, he decides to continue to play along with the hoax. For Carcetti, once he finds out the killer is a fake this is his best strategy. If word gets out that he has been directing funds to catching a fake serial killer his chances of becoming governor are substantially reduced, and he has to fire Daniels, who is his first choice to become Commissioner. If the hoax is covered up then Carcetti’s chances of becoming governor remain roughly the same, and he is able to appoint Daniels (or so he thinks).

Whether McNulty planned it or not he has locked Carcetti into a particular strategy. Once Carcetti has committed to chasing the serial killer booting McNulty off the force and indicting him is no longer a credible threat. Given this is the case the expected payoff for McNulty of fabricating a serial killer is even higher; even in the case where McNulty does get caught the probability of him going to jail is low and so it is clear that this is the best strategy. Once again Carcetti’s political ambitions have given McNulty the incentive to deceive the mayor’s office. To avoid this situation Carcetti needed to convince others that he cared more about the integrity of his city’s institutions than his political ambitions (even if in truth he didn’t). This would have increased McNulty’s estimation of how likely he was to go to jail if he got caught.

For Freamon the best strategy is also to maintain the fiction of a serial killer for the same reasons as McNulty. Further Freamon probably cares less than McNulty about losing his job given he has an excellent “outside option” – that is another source of income. For Bunk the probability of losing his job and going to jail is too high for his liking to become a co-conspirator.

For Daniels the best strategy, when he learns the truth about the serial killer, is less clear. If he covers it up he increases the chances of bringing the bad guys to justice but is not doing what he perceives to be ‘the right thing’. If he does not cover it up he does ‘the right thing’ but raises his chances of being fired. Given that he does come forward to Carcetti with the truth perhaps he too perceives that Carcetti firing him is not a credible threat.


In the end did McNulty’s strategy result in better outcomes for all concerned? For McNulty and Freamon they didn’t go to jail but they were prevented from ever doing police work again. They brought some of the bad guys to justice and effectively crippled Marlo’s organization, although it’s clear that other drug dealers are ready to take Marlo’s place. For Freamon, because of his older age and alternative source of income, it could be argued that he came out slightly ahead. For McNulty, he possibly came out behind, given he is banned from ever doing police work (therefore being unable to bring further bad guys to justice) and he lost the respect of Daniels, and to some extent Greggs and Moreland. Moreland meanwhile also came out slightly behind given he lost his best pal McNulty from Homicide (yes we’ll count that as a loss).

Of the police officers Daniels was the biggest loser. While Daniels was not fired by Carcetti the incident made it less likely that Daniels would cover up other things in the future, as shown soon after when he refuses to tweak the crime statistics. The result is that Daniels never gets the chance to become Commissioner (again we’ll count that as a loss), and is instead replaced by Major Valchek.

Carcetti also came out behind. In terms of his chances of becoming governor these were barely harmed due to the cover-up, and in the end he does become the Governor of Maryland. But given that he also cares about the city’s health he does suffer a hit in utility in that he is forced to replace Daniels with the rather less competent Valchek.

So all up most of the individuals lose out from McNulty’s strategy. Does this mean that McNulty should not have done it? No, from McNulty’s standpoint it was the best thing for him to do. Although things turned out worse for him because he was caught, given there was some probability that he would never be caught the expected gains from his gambit outweighed the expected losses. Essentially Carcetti contributed to making this the best strategy for McNulty when he made the cuts to the budget of the police department.

Further, while the individuals lost out it is possible that the city of Baltimore gained as a result. Essentially McNulty’s ‘serial killer’ directed funds towards bringing the bad guys to justice and away from other public goods. If the value of bringing the bad guys to justice outweighed the value of these other public goods then society gained as a result. But did they? One of the main reasons Carcetti wasn’t directing funds to the police department was because he was directing it to schools. Which has the greater public value? McNulty thought it was the police department, but I’ll have to leave each viewer to make up their own mind on that one.

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