One Among Many

The self in social context

Jumping the line

Half of you will be in line longer than average.

~ Anonymous

At Six Flags you can buy a day’s worth of rides for a lot of money [\$]. During high season, lines are long and many clients end up riding less than they had hoped. Six Flags offers a FlashPass for a lot of money times two ([\$\$]. With a FlashPass, you can bypass the regular lines. What a brilliant move by Six Flags [SF] and what a dilemma for the heat-stroked rider [HSR]! SF hopes that many HSR will buy the pass. If all [N] do, SF makes N\$\$. The HSR hopes that few will buy the pass, regardless of whether he himself buys one or not.

The more individuals buy the pass, the worse each individual is off, regardless of which group, regular pass holders or FlashPass holders, he is in. How can this be? The total waiting time (per person times the number of people) is the same regardless of how many riders have a FlashPass. This must be so because the park’s capacity is not affected by the types of ticket held. There is no overall efficiency gain.

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Now consider what happens when the first person upgrades from regular to flash. The upgrader saves S minutes on the average ride. Each of the other individuals has to wait S/(N-1) minutes longer. The upgrader is a defector. His benefit is far greater than the loss visited upon the average cooperator (regular pass holder), but equal to the sum of their losses. The apparent paradox disappears when we turn to the next defector. This person gains less than the first defector did and he also lengthens that person’s average waiting time. Like the first defector, the second defector also lengthens the average waiting time for the remaining cooperators, although by not as much as the first defector did. And so on. As the number of defectors goes up, their individual gains decrease and so do the gains of the defectors who already have a pass. The individual losses of the remaining cooperators also increase, as they are pushed to the back of the line, but the size of these decrements also becomes smaller as the number defectors increases. To repeat with more precision, if individuals defect one at a time, they make everyone worse off by just a little bit, previous defectors and remaining cooperators. Only they themselves benefit. This individual benefit is only fully eradicated when there are no cooperators left. Hence, there is a strong incentive to defect, which is only checked by the price of the privilege pass.

Economists will be impressed by the brilliance of SF and note that they can derive an equilibrium at which the price is right, that is, the price for the FlashPass at which a stable proportion of HSR will pay extra, and no one, defectors or cooperators, will change their minds after that. Conversely, one can calculate the proportion of people who will defect once a particular price has been set for the FlashPass. Together, these two methods of optimizing yield a family of equilibria, which can be depicted as lying on a pretty concave curve with coordinates in a space defined by the proportion of FlashPass holders (X-axis) and price of the pass (Y-axis). From this, SF can figure out with simple multiplication how to price the FlashPass to maximize its profit.

The introduction of the FlashPass increases the provider’s profit while hurting the interests of most buyers (at the limit, it hurts all of buyers’ interests). To the buyers, the situation is complicated by the sequential nature of the game. Whereas early (and solvent) buyers stand to gain, subsequent buyers are increasingly motivated to buy (defect) not only by a pleasure-seeking motive (greed), but also by the motive to guard against relative disadvantage (fear). Steadfast cooperators see the value of their pass erode with any additional FlashPass defector. I conclude with the suspicion that Six Flags is getting something for nothing. It did not, after all, increase its capacity or made rides more enjoyable on average.

A free-market enthusiast may counter that I am ignoring the arbitrariness with which the situation is framed. He could argue that the equilibrium, consisting of proportion p of regular passes at price \$ and 100-p of FlashPasses at price \$\$, which SF derived, is the true reflection of what a day at the park is worth to the collective HSR. If SF only offered regular passes, it would make a loss (either in absolute terms or relative to the profit they could make). In this frame, the regular pass is discounted relative to that grand average price, and the FlashPass is sold with the added premium for privilege. By analogy, one could argue that gas for cash and gas for credit is respectively cheaper and more expensive than the grand average market value of gas.

To this, I can only respond with a historical argument. A logical argument is not at hand because the free-market argument is tautologically true, and hence immune to the charge of incoherence. The historical argument is that SF seemed to be doing just fine before it introduced the FlashPass. Only then did it occur to them that they could make an extra profit without also improving services. This is why I think the frame I took is the right one. It is not the case that all tickets were originally offered at the price of the FlashPass and that then disounted tickets were introduced to those who were willing to wait longer. Finally, the economists doing the math for SF probably assume that their equilibrium solutions are realized by a collective of rational HSRs. But the assumption of rationality in a population of heat-stroked, thrill-addled adolescents is wildly optimistic. Irrational levels of greed and fear, both pushing individuals toward the costly pass, may raise SF’s profits even beyond the level predicted by the economists. Whether this happens, is an empirical question. If is does, SF can raise the price of the pass to induce a reduction in the number of buyers, and thus restoring equilibrium. Meanwhile, the average rider at Six Flags remains as modestly rational as ever.

Airlines separate their clients into the privileged (first and business class) and the rest of us (steerage). They play a game that forces them to be fairer than businesses like SF. They have a limited number of spacious seats. When they’re gone, they’re gone. The airlines can only use price as a variable. The average flyer need not worry that more and more passengers will defect to first class, thereby pushing him ever deeper into the back of the plane.

Businesses that, like SF, can print passes of privilege at no cost to them, can exploit the average person’s desire to be a little better off than the next person (see Bertrand Russell, 1930; Leon Festinger, 1954, for classical references, or Anderson et al., 2012, for recent empirical work). In a zero-sum game (fixed capacity of service), someone must be bumped back for everyone who moves up, and they’re all paying for it (see Robert Frank’s  book on the Darwin economy for more on this matter).

Getting groceries

How would you feel about having a fast-track check-out line at the supermarket? Why not use the Express Lane if you have “15 items or less” [sic]. You probably appreciate the convenience, as I do, irrationally. Let’s assume that the market has a fixed number of cashier lanes [N], and dedicates one of them to the quick shopper. This shopper is whisked through and finds happiness. There is a noticeable savings in time for him. He does not realize that the other shoppers, who have more items, have to each wait a little bit longer now, perhaps imperceptibly so. The lines these shoppers now form comprise only shoppers with 16 items or more. These shoppers are now distributed over N-1 lanes instead of N. Hence the longer wait. From a technical standpoint, the express lane does nothing. There is no efficiency gain, because we are again dealing with a zero-sum game – a fixed pie, in grocery parlance. Nevertheless, the opening of an express lane may be a clever move for the market because it banks on the idea that individual shoppers will irrationally appreciate it. They experience more choice, and they weight the occasional perceptible gain in speed more than the barely perceptible, but more frequent, loss. Everyone wins in this game of shared illusions.

Now suppose the market emulates Six Flags. How about FlashPasses for shoppers? There is no counter-argument an economist would accept as rational. Indeed, the economist might argue that if FlashPasses were sold at some equilibrium rate, the market would make a larger profit and might even be persuaded to return some of that to the customer. If so, and in this semi-far-fetched utopia, food might actually become cheaper for those willing to wait. Why shouldn’t this work? I can see 2 objections. One is that lines do not form as often in food markets (but then again, why have the express lanes for those with 15 times or fewer?). The other is that buying food is a necessity, whereas consuming thrills at the amusement park is, well, amusement. The poor and vulnerable will not be victimized at the park because they barely go anyway. Everyone goes to the market, though, and may expect fair treatment. This is just an hypothesis. It could be tested. Another hypothesis is already refuted, namely the idea that forming lines on a first-come-first-serve basis is a basic feature of civil behavior in the Anglo-Saxon tradition. Six Flags has taken care of this one.

Anderson, C., Kraus, M. W., Galinsky, A. D. (2012). The local-ladder effect: Social status and subjective well-being. Psychological Science. Published online first.

Festinger, L. (1954). A theory of social comparison processes. Human Relations, 7, 117-140.

Frank, R. H. (2011). The Darwin economy. Princeton, NJ: Princeton University Press.

Russell, B. (1930). The conquest of happiness. London. Allen & Unwin.

Joachim Krueger, Ph.D., is a social psychologist at Brown University who believes that rational thinking and socially responsible behavior are attainable goals.

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