The Sunk-Cost-Fallacy Fallacy

This post is mostly economics, but I promise a small bit of undead action at the end.

As both an economist and a screenwriter, I loved the Planet Money podcast’s recent episode on “The Scariest Thing in Hollywood.”  The episode shows how, from the standpoint of return on investment (ROI), making super-low-budget movies can actually be superior to making big-budget blockbusters.

However, I think the episode has one misstep:  it commits what I call the “Sunk-Cost-Fallacy Fallacy” — that is, the error of using the Sunk-Cost Fallacy to condemn choices that are (or at least may be) perfectly rational.

Here’s the context.  The show follows the production of the movie “The Boy Next Door.”  (As an aside, this movie is best known to me and my wife as the movie that features a “first edition copy of the Iliad.”  Ponder that for a moment.)  The movie was directed by Rob Cohen on a tiny budget of $4.2 million.  When it was done, focus groups delivered “meh” responses.  But Cohen believed that just a little more money — $300,000 — could fix a couple of key scenes and turn the movie into a hit.  The film’s producer, Jason Blum, said no.  One of his rules for making low-budget movies with high ROI is “never ever break your budget,” and he stuck by that rule.  However, Cohen persuaded the film’s distributor, Universal, to throw in the extra $300K.  And ultimately, despite lousy critical reviews, “The Boy Next Door” grossed over $50 million worldwide.

The episode characterizes Cohen’s desire to use $300K to rescue the movie as a case of the Sunk-Cost Fallacy.  But that characterization, I suggest, is itself a fallacy.

The Sunk-Cost Fallacy is usually defined as “failing to ignore costs that have already been incurred and cannot be recovered.”  Such costs are gone no matter what you do, and thus they should be irrelevant to your present decisions.  Only present and future costs and benefits are relevant.  There are a couple of different ways that you can commit the Sunk-Cost Fallacy:

  1. Because you have already invested (sunk) a bunch of money and resources into a project, you decide to spend more money to “bail out” your losses, i.e., to make benefits materialize that will justify the costs you’ve already incurred. This is the version of the fallacy that the episode’s producers are thinking of when they analyze Cohen’s decision.
  1. Because you have already invested (sunk) a bunch of money and resources into a project, you continue to count those costs in the present for making present decisions. That is, you evaluate your decision looking at “all revenues” versus “all costs,” when you should be looking at “present/future revenues” versus “present/future costs.”  This is the version of the fallacy that actually occurs in the episode — not when Cohen wants to spend more money, but when Blum refuses to break the budget under any circumstances.

Think about it this way.  The $4.2 million budget is already gone.  So the relevant question is this:  How much will another $300K increase the movie’s revenues?  Let’s suppose that, without the extra $300K, the movie would have grossed $49.9 million.  The $300K infusion raises the take to $50 million.  In that case, the $300K is a bad investment because it reduces the net by $200K.

On the other hand, suppose that without the extra $300K, the movie will only gross $20 million, whereas with the extra $300K it will gross $50 million.  In that case, the $300K is an awesome investment because it increases the net by $29.7 million.

So there are really two possible errors here:  overestimating the added revenue, or underestimating it.  Now, it’s entirely possible that Cohen was engaged in some wishful thinking.  Maybe the movie would have grossed $50 million even without the “fixes” he had in mind.  But it’s certainly not fallacious to contemplate the possibility that some changes will generate added revenues that more than cover the added cost.  What is fallacious is assuming that can never happen, as Blum’s “never break the budget” rule suggests.

Now, Blum’s rule may have a good justification.  It may help him to resist wishful thinking that exaggerates the possible gains from added spending.  Following the rule ruthlessly might make it easier for him to say “no” to every director (like Cohen) who wants to spend a little more.  But the rule also has the downside of shutting down some potential improvements that lead to net gains.

Okay, I promised some undead action, so here goes.  In Chapter 2 of Economics of the Undead, “Human Girls and Vampire Boys, Part 2,” I discuss some of the reasons that a human girl might choose to stay with her vampire boyfriend despite some bad behavior on his part.  Included in those reasons is the value of certain relationship-specific investments she’s made in the relationship — value that will diminish or disappear if the relationship ends.  Now, this might sound like the Sunk-Cost Fallacy, but it’s not.  Here’s what I say in the chapter:

In considering the value of continuing a relationship versus walking away, you should be careful not to fall prey to the sunk cost fallacy. Sunk costs are costs that have already been incurred and cannot be recovered, and the fallacy is letting them influence your choices. For instance, suppose you’ve bought a nonrefundable ticket to see a concert (Vampire Weekend, naturally) on Sunday night—and then you get invited to a True Blood viewing party on the same night. In deciding what to do, the $100 you’ve already spent on the concert ticket is irrelevant, because you can’t get it back anyway; the only thing that matters is whether you would enjoy the concert or the party more. Likewise, the time and effort you’ve spent building a relationship are sunk costs. You’re never getting them back, no matter what you do. But what does matter is what your time and effort have bought you: the shared routines, memories, home, and so on, whose value will decrease or vanish if you break up. The value of these relationship-specific assets might, indeed, be enough to justify continuing your cross-the-grave romance.


I will be speaking on three panels at Westercon68 in San Diego, including a panel on “The Working Dead” and “Economic Recovery After the Zombie Apocalypse.” If you’re attending, please come by and introduce yourself!

Urban Zombies, Rural Apocalypse

I’ve been meaning to give my thoughts on physicist Alex Alemi’s model of a national zombie outbreak. I haven’t checked the math, but the conclusions seem to be solid given the assumptions. (As Bishop, Tufte, & Tufte make clear in Chapter 6 of Economics of the Undead, “What Happens Next? Endgames of the Zombie Apocalypse,” various assumptions about zombie and human behavior can lead to quite different outcomes.) But I want to draw attention to one prediction of Alemi’s model:

But unlike the movies, which often depict diffuse saturation and numerous locations simultaneously affected, a true outbreak wouldn’t work like that. It would take hours, days, months and even years to spread into every underpopulated nook and cranny of the United States.

“New York City would fall in a matter of days, but Ithaca, where I am — it would take weeks for the zombies to make their way up here,” Alemi said. “It would be a situation where you’re watching chaos on television, but where you are everything would remain unchanged.”

Indeed, watching the virus seep across the United States is like watching a flame seek out its next source of oxygen. The spots with heavy populations are gobbled up at a dizzying rate, but the virus slows in underpopulated regions, leaving them more or less protected. If the disease were to begin in the heart of New York City, other big cities such as Boston and Washington, D.C., would be gone within days, if not hours. But in more isolated places, like the northern reaches of Vermont and New Hampshire, there wouldn’t be a zombie in sight.

The conclusion that urban areas will be more vulnerable, and more fully saturated with undead, makes a great deal of intuitive sense. Furthermore, it’s a major contributing factor to the economic collapse that typically accompanies a zombie apocalypse. As discussed in various chapters of Economics of the Undead (especially chapters 3, 4, and 5), the prosperity of the modern global economy depends crucially on a vast interconnected web of specialization and trade. Cities provide the hubs, or most significant nodes, within that web. Take out the hubs, and the web will start to disintegrate.

And that is why I have to quibble with Alemi’s statement that in less populated areas “everything would remain unchanged.” Ithaca’s well-being depends on New York City, Boston, and many other centers of specialization and trade. If the big cities fell to the zombies, the rest of the country (and world) would almost immediately begin to suffer, even before the arrival of the undead horde.

Are You Insured Against a Zombie Invasion?

CareFirst, a health insurance provider, thought referencing the zombie apocalypse would be a good way to sell insurance:

Naturally, this invited much ridicule from the Twitterverse. As many tweeters rightly noted, insurance is unlikely to pay out any claims in a zombie apocalypse. This point was also made by Eleanor Brown and Robert Prag in Ch. 9 of Economics of the Undead, “Zombification Insurance.” Brown and Prag observe that “None of those people running screaming through the streets in World War Z are looking for their claims adjusters. … In a full-blown zombie apocalypse, then, anybody who wants to run screaming through the streets in search of her claims adjuster should be heading for the courthouse where the insurers are filing their bankruptcy papers.”

But if that were the end of the story, Brown and Prag’s chapter would have been very, very short. It turns out that insurance might indeed play an important role in how we deal with zombies – just not during a full-blown zombie apocalypse. If zombies fail to cause the collapse of civilization and instead become more of an ongoing threat, much like car accidents and house fires, then we might well see the emergence of a market for zombification insurance. It might be stand-alone insurance to cover expenses from zombie infections and other undead damage, or it could be packaged with other forms of insurance such as life insurance, health insurance, and homeowner’s insurance. Depending on the contractual language, it’s possible that you’re already covered against zombie-related damage under your current policy!

One potential problem with zombification insurance, unmentioned by CareFirst, is that insurance can create moral hazard: the tendency of people to take greater risks when insured against losses. For instance, people with zombification insurance might not be as diligent about decapitating and disposing of the infected bodies of loved ones. It’s a tough thing to do anyway, and if there’s a chance Granny isn’t really infected, or if you think there’s a chance of a cure (or, as Brown and Prag suggest, cryonic preservation until such time as a cure is invented), you might take a chance on waiting. The insured might also take a chance on love with a zombie, as in the movie Warm Bodies. To deal with such contingencies, insurance providers might require substantial deductibles and copayments in order to expose the insured to some portion of the risk they create and provide an incentive to contain it.

Peak Blood?

Third of three guest posts by Enrique Guerra-Pujol

A final and potentially devastating argument against blood markets is that such markets would be self-defeating or self-destructive. Some of my Freakonomics commentators noted that “vampirism is contagious” and that “vampires procreate via their bite.” Or as Glen Whitman ominously puts it in his essay “Tragedy of the Blood Commons” (in chapter 15 of Economics of the Undead), “At present, humans are plentiful and vampires relatively rare—but that pleasant condition may not last forever.

Why not? Because if vampires procreate via their bite, then each vampire bite converts a potential blood seller into a blood consumer (i.e. a fellow vampire) and thus every vampire bite reduces the aggregate supply of blood. At some point, vampires (blood buyers) will not only outnumber humans (potential blood sellers) but the number of humans or sellers will dwindle to zero and the market for blood will collapse.

This notion of “peak blood” is similar to the familiar and oft-lamented problem of “peak oil” — the point in time when the maximum rate of extraction of petroleum is reached after with the rate of petroleum extraction is expected to enter terminal decline.

But this line of reasoning is actually an argument for legal markets, not against them! With legal markets based on well-defined property rights, owners of blood will have a powerful incentive to manage and conserve their blood resources; without such legal markets, we run the risk of a tragedy of the commons. For my part, I favor assigning rights to human blood to humans, but such rights could just as well be assigned to vampires!  [Note: Ownership of humans by vampires is the solution proposed by the vampire-economist author of Chapter 15, mentioned above. – GW]

Lastly, notice that the “peak blood” argument assumes that markets move toward some equilibrium or end state. But, frankly, I don’t think this standard equilibrium assumption is warranted. What if, instead, markets are open-ended, evolutionary, creative processes?

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Blood Markets and Blood Culture

Second of three guest posts by Enrique Guerra-Pujol

It’s the natural order. [We] are predators. You and your kind are prey, that’s all. To survive, we must feed on your blood.

– Arkley the vampire in David Wellington’s Laura Caxton Vampire Series

In my previous post, I considered human-centered arguments against blood markets: either we don’t believe in vampires or we fear them. Now, let’s consider a different set of arguments against blood markets and the possibility of human-vampire trade generally — not from our human point of view, but rather from the point of view of the vampires!

Vampire superiority complex

Won’t vampires see bargaining with humans as beneath them? I call this the “vampire superiority complex.” One commentator (Owen), for example, wrote that “most vampires consider themselves to be superior beings to humans … and as such have no compunction about ‘stealing’ blood to feed them[selves].” Along the same line, another commentator (Davo) identified a “critical error” in my market argument. “In most vampire lore,” Davo wrote, “[vampires] are a different (more advanced) species.” In support of this claim, Davo produced my favorite comment — perhaps the most memorable one in the entire Freakonomics thread — “Asking vampires to buy human blood is like asking humans to buy a ham hock off a pig.”

This line of argument offers an alternative explanation of vampire violence. Vampires are violent not because of the lack of blood markets (my claim in my essay “Buy or Bite?” in chapter 12 of Economics of the Undead) but rather because they are culturally and biologically superior to humans. Because of their superiority, vampires view humans as prey. Consider, by way of example, this statement by Arkley the vampire in David Wellington’s Laura Caxton Vampire Series: “It’s the natural order. [We] are predators. You and your kind are prey, that’s all. To survive, we must feed on your blood.” In other words, predators don’t negotiate with prey; they hunt and kill them instead.

Certainly, I do not deny that vampires are an accomplished and talented lot. Nor do I deny that most vampires probably view humans as prey and not as possible trading partners. Let us assume, then, that vampires are not only a different species but also a more advanced species than us humans. What effect would these assumptions have on the market for blood? Do such innate vampire feelings of superiority inhibit such trade or make such markets more likely to occur?

I could be wrong, of course, but my conjecture is that vampires will prefer trading to hunting precisely because of their cultural superiority. In other words, the cultural superiority argument strengthens — not weakens — the case for human-vampire trade! Here’s why:

If vampires are so smart, they will immediately grasp the advantages of trading over hunting. Simply put, the prospect of hunting for human blood is not an attractive one because such behavior invites lethal retaliation from vampire slayers. A legal market, by contrast, promises to supply the vampire race with regular and stable supply of blood at the best possible price.

In other words, even if vampires are somehow culturally or biologically superior to humans in every possible way, why would any individual vampire want to waste time and effort hunting for blood or invite the risk of deadly retaliation if a safer and more attractive option (legal markets) were available to him or her?

But what if vampires prefer the thrill of the hunt to the security and stability of a legal market? What if vampires prefer raiding to trading?

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Order and Chaos in Zombie Society

Mathematician Thomas Woolley and coauthors claim that mathematical modeling can help us understand the movement of zombies, and thus how best to avoid encounters with them.  Naturally, we here at Economics of the Undead applaud the application of theoretical models to zombies.  But Woolley’s model provides an excellent example of why theory has to be tested against data – in this case, the observed behavior of zombies in film and fiction.

According to Woolley et al., zombie movement can be described as a “random walk,” a notion that has been employed in theoretical models in both physics and economics.  Basically, the idea is that each step of a zombie is a random draw:  he could move one step in any direction, and then another step in any direction from there, and so on.  Over time, Woolley and his coauthors argue, this should lead to diffusion of zombies over the available domain.

But this is inconsistent with how zombies actually behave, if existing zombie narratives can be taken as any guide.  Rather the diffusing over the landscape, zombies tend to appear in clusters and mobs, even long after the initial invasion.  In a conflict between observation and theory, it pays to look for a better theory.  And fortunately, there is one available.  In Chapter 7 of Economics of the Undead, “Order, Coordination, and Collective Action among the Undead,” Jean-Baptiste Fleury and Alain Marciano suggest that zombies do not simply wander about randomly attacking people, but in fact display a range of behaviors that allow them to coordinate their behavior for mutual advantage (with other zombies, not with humans).  Among other things, zombies tend to flock together for strength in numbers — the best-known example being the famous “zombie ant-pile” seen in the movie World War Z.

“Actually, the very fact that zombies gather in large and stable flocks, as most accounts will confirm, is evidence of an ordered society,” Fleury and Marciano argue.  “If zombies were not ordered, they would wander chaotically and scatter into the wilderness, like particles of smoke into the air.”  That description sounds a lot like Woolley’s prediction.  “But such chaotic behavior would seriously undermine zombies’ ability to hunt and eat human flesh,” they add, supporting their claim with evidence from various zombie narratives:

Due to limited agility and cognitive abilities, a zombie is not much of a threat when hunting alone. Many action sequences in The Walking Dead TV series illustrate this point: Rick and his friends are generally pretty effective when it comes to fighting with roaming individuals as well as small groups of zombies. But when attacked by hordes of “walkers,” as in the last episode of the second season, Rick and his friends are quickly overwhelmed and eventually escape only at great cost. As confirmed in many accounts, such as Romero’s Night of the Living Dead, flocks of zombies are most dangerous to humans: they can exert tremendous collective pressure so as to break down manmade barriers and barricades. Thus, zombies tend to gather in stable groups, which help them maximize their chance of success in case of confrontation with humans.

But what could be the source of such cooperative tendencies?  Fleury and Marciano suggest three possibilities.  First, zombies may retain some basic tendencies written into their human DNA, including the basic desire to congregate with others of their kind.  Second, they may retain some rudimentary memories of their prior human existence and cultural background.  (In Romero’s Dawn of the Dead, one character famously explains the convergence of zombies on a shopping mall as resulting from “a kind of instinct, a memory [of] what they used to do” because “this was an important place in their lives.”)  Third, the zombie virus itself may endow its hosts with any number of tendencies beyond the obvious craving for human flesh.  It is well-known that parasites can affect the behavior of hosts – the most famous example being toxoplasma gondii – so it shouldn’t be surprising to find the zombie virus does so as well.

Whatever the cause, Fleury and Marciano’s claim is borne out in countless zombie narratives.  Despite their shambling gait, zombies do not appear to follow a random walk.  By all indications, zombies are guided instead by a tendency to flock with other zombies in a manner that increases their efficacy in confronting their much-smarter human prey.

Reopening the Case for Blood Markets

First of three guest posts by Enrique Guerra-Pujol

Freakonomics Radio recently broadcast a highly-entertaining program on Economics of the Undead on 30 October 2014 (“What can vampires teach us about economics?”). Among the topics discussed on that podcast was the possibility of legal markets in blood, a topic near and dear to me — see my essay “Buy or Bite?” in chapter 12 Economics of the Undead.

In addition, the discussion of blood markets on Freakonomics Radio generated a number of original and insightful comments. Many commentators objected to the possibility of blood markets, offering several thoughtful objections specific to vampires and their way of life. I have thus decided to write this post to respond to these various objections.

Let me first restate these objections in the words of the Freakonomics commentators themselves:

  1. “Y’all know that … vampires aren’t real, right?” [Comment by Truth & Beauty.] Let’s call this the “hypothetical entities” argument.
  1. “would you accept to work extra hours [with your boss] … if your boss is one of them?” [Comment by carlosmx37.] Call this the “fear factor” argument.
  1. “most vampires consider themselves to be superior beings to humans … and as such have compunction about ‘stealing’ blood to feed them[selves].” [Comment by Owen.] Call this the “vampire superiority complex” argument.
  1. “taking blood by force may be so culturally ingrained among vampires that … there is cultural barrier against [trade].” [Comment by Cuylar Conly.] The “cultural path dependence” argument.
  1. “Vampires ‘procreate’ via their bite” and “Vampirism is contagious” [Comments by scott fowler and Cuylar Conly, respectively.] The “peak blood” argument.

Before proceeding, notice how these various anti-choice arguments build on each other. 1. Vampires do not exist, so the idea of markets in blood is ipso facto preposterous. 2. Even if vampires were real, most people fear such cunning creatures and would thus be reluctant to engage in any sort of voluntary trade with them. 3-4. Even if we could overcome our fear of the undead, vampires prefer raiding to trading. 5. And even if we could incentivize vampires to buy our blood on a consensual basis – instead of taking it by force – vampires would overuse or oversuck their human resources and turn us all into vampires.

I will focus on the first two objections in this blog post and then address the remaining objections in a future post.

Hypothetical entities

The crux of this objection is that vampires are not worthy of academic study because vampires are not real — they are hypothetical entities.

But is this objection correct? Or, in the words of one commentator (James), “how do [we] know there are no real vampires?”

In any case, even if vampires are imaginary creatures, thought experiments about them are still useful because they help clarify our thinking by revealing anomalies and logical inconsistencies. In the words of the historian of science Thomas Kuhn (The Essential Tension, 1977, p. 252), a thought experiment, or the careful analysis of an “imagined situation,” is useful because it confronts its audience with unanticipated consequences of our ordinary way of thinking, and thus thought experiments, especially outrageous and far-fetched ones, are often capable of producing the new insights.

But why is my particular thought experiment about blood markets any good? Because this particular example illustrates a larger problem, the problem of “legal failure” or legal barriers that prevent trade and stifle markets. We call such legal barriers to trade “legal failure” because such barriers not only make us worse off; they often lead to violence and exploitation.

Vampires and humans are rarely depicted in cooperative terms. We rarely, if ever, see vampires bargaining with humans to buy and sell blood. Instead, vampires are usually depicted as cunning and stealthy predators, and conflict between humans and most vampires is the norm. My thought experiment, by contrast, presents an alternate vampire world, one in which blood markets are legal, and poses a new hypothetical question: what would happen to the level of vampire violence in a world in which the purchase and sale of blood was legally enforceable? Would vampire violence go up, go down, or stay the same? However one answers this hypothetical question, my simple thought experiment requires one to explain and defend one’s reasoning. Therein lies the value of thought experiments generally.

In short, just because vampires are fictional or imaginary creatures doesn’t mean we should ignore them. Even if vampires are make-believe, the vampire world is still worth studying because it invites us to think about the nature and sources of violence.

What about the “fear factor,” however? That is, why should anyone trust a vampire?

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Zombies in the Classroom

Guest Post by Michael O’Hara

No, I don’t mean the kind of reanimated corpses you encounter when you teach an 8:30am econometrics class. On a recent day in my natural resource economics class, I set the students free to construct an economic model of zombies as a recreational hunting species. These students have spent the semester so far analyzing models of resource use including how to efficiently and sustainably use renewable resources such as fish or deer. But ultimately what I want to teach them is a way of analyzing issues that can be applied to new problems. In my chapter in Economics of the Undead, “Zombies as an Invasive Species: A Resource Economics Perspective”, I suggest that in the inevitable event of a zombie invasion, a possible control method might be to encourage zombie hunting for sport. Building upon this idea, I set the students loose to think through the problem of how to make the best use of zombies as an economic resource.

I gave the students minimal guidance, letting them take the discussion in any direction they chose, and they had to make many choices and assumptions along the way. Since the idea of allowing free-range zombies was understandably a little troubling to them, they chose to build upon an idea I raise in my chapter: private zombie-hunting preserves. This keeps the zombies in check so that humans are not in danger, but it also raises an interesting problem: if zombies are contained, then there is no natural reproduction to maintain the zombie stock as there is in most of our bioeconomic models. Assuming that zombie hunting is a popular sport and we want to continue it in a sustainable way, this would require a steady stream of new zombies. As mentioned in my chapter, one way would be to limit head shots in some way so as to prolong the hunting value, but students recognized this as only a short-term fix. They needed some other way to replenish the herd.

Unlike my own (perhaps dated) concept of zombies being created by a bite from another zombie, most students were familiar with a more modern idea of zombies from The Walking Dead, in which anyone who dies is reanimated as a zombie. Making this assumption, they decided that deceased humans would be delivered to the preserve to restock the zombie population. Working through the implications of the model, this led the students to the logical conclusion that the rate at which we could sustainably harvest zombies would be constrained directly by the mortality rate of humans outside the preserve. Oddly (to me), students took this rate as given. The larger question of whether altering this rate could result in an improvement in economic welfare was not investigated.

Students truly enjoyed this exercise and it was very instructive for them to have to build a model of a new situation and see how the assumptions they put into the model lead to the conclusions at the end. Several of the students have told me since then that they were a little skeptical of the exercise at the start, but that it turned out to be one of their most memorable days of class.

Michael O’Hara is an assistant professor of economics at Colgate University, where he teaches and publishes in environmental and resource economics and econometrics.

Econ Undead on Australian Radio

Last week I was interviewed on Australia’s RN Sunday Extra, where I talked about the tragedy of the blood commons, zombies as an invasive species, legal vs. black markets in blood, and cross-the-grave dating, among other topics. You can listen to the whole thing here.