Musical Chairs, Ski Lifts, Thermostats, and Other Mental Models — Thomas Schelling

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Musical Chairs, Ski Lifts, Thermostats, and Other Mental Models — Thomas Schelling

Musical chairs and phone calls

There is something inherently futile about the game of musical chairs. Every child knows that he or she must be quick to stave off elimination. Yet among the group, it does not matter how fast everyone moves. When the music stops, somebody will be removed. As Thomas Schelling observes in Micromotives and Macrobehavior, peculiar invariances can arise here: “If we keep adding new players equal to the number evicted, replenishing players rather than removing chairs, we can calculate the average number of rounds that anybody will get to play before being caught chairless and evicted. The average is mathematically predetermined.”

Similar predeterminations emerge elsewhere. Schelling points, for example, to telephone calls. Yes, some people are more chatty than others. Extroverts will make more outgoing calls than introverts. One call may spur another as gossip and news make their rounds. Yet, among the collective in a closed system, the total number of calls made must equal the total number of calls received. As Schelling notes, musical chairs and telephone calls illustrate “propositions that are true in the aggregate but not in detail, and true independently of how people behave.” 

Christmas cards and bad drivers

These examples remind us that there can be dualities, invariances or equivalences in systems. In economics, these often take the form of “accounting statements”. Respectively, one person’s output, income, debit, or export, for example, is another’s input, spending, credit, or import. So when somebody tells you that there is a lot of selling on the stock market, you should tell them that there must be a lot of buying too. As Schelling writes, “we cannot all get rich by not spending our money, any more than at Christmas time, we can all receive more value than we give by spending less on each other’s presents.”

Clearly, we have to pay attention to the features and constraints of the system. So when most drivers believe that they have above-average driving skills, or when every parents tell us that their child boasts above-average intelligence, something peculiar must be going on. As Schelling notes, either: (1) a minority of drivers or children are so bad that the majority is indeed above average; (2) adults are ranking their driving or children on distinct and incomparable criteria; or (3) a good number of parents and drivers are simply deluding themselves. Studies suggest indeed that the latter case of overconfidence is probable.

Ski-lifts and traffic jams

Another class of issues in systems relates to bottlenecks. Schelling points, for example, to the problems of downhill skiing. In particular, skiers hate waiting in line for the lifts to the mountaintop. They spend much of their time in queues, only for the downhill exhilaration to be over in a matter of minutes, and for the waiting to commence again. A quick fix, perhaps, might be to increase the speed of the lifts. However, if other factors, like the lift’s loading times and carrying capacity, as well as the total time patrons spend skiing, remain unchanged, the proposal alone might have no effect. You may end up instead with more people in the waiting lines. 

The issue is comparable, Schelling notes, to traffic jams. Widening one part of the highway may serve only to push every car into the next bottleneck. In fact, these problems are everywhere. Greater public splurging in tertiary education, for instance, may yield a weak social return on investment if the serious pain points in early childhood and primary learning go unaddressed. Similarly, better policing may have a weak effect on criminal activity if the justice system, welfare system, employment services, and related institutions are unable to cope with recidivism. What we have here, Schelling notes, are conservative quantities and systems. Holistic solutions are usually necessary.

Thermostats and epidemics

One useful mental model for systems thinking, Schelling shares, is that of the simple thermostat. When room temperature falls below some desired level, the thermostat will activate a furnace to heat the water inside the radiators that warm the air. And when the temperature is above the preferred level, the furnace simply stays off. But because the heating and cooling of water and air takes time, there is a tendency for the rise and fall in temperature to overshoot and undershoot its mark under a simple thermostat. As a result, a cyclic process around the desired room temperature emerges.

Economics is likewise replete with such cycles. For instance, according to behavioral finance, a mixture of conservatism and representativeness may explain the overreaction and underreaction that recurs in financial markets. That is, investors may be slow to incorporate new information, and wrongly assume that recent trends are reflective of the future. Similarly, governments are usually reactive to shortages in workforce supply. One common response is to expand the pool of incoming graduates. But because it can take many years to attract and develop new workers, the workforce needs may change entirely by the time the policy is ready to take effect. Moreover, if the market happens to find a substitute during that time, the industry might find itself with a surplus of unneeded graduates. As Schelling notes, “the thermostat reminds us to look for the time lag, or for an accumulated inventory like the hot water.”

Funeral attire and atomic piles

Indeed, these systems are complicated because elements of the system are responding to the system itself, or to other responding elements. Sometimes, such systems can also display a sort of all-or-nothing characteristic. Dress codes are a classic example. Most self-conscious adults, I suspect, are unlikely to attend a funeral or wedding in bright leggings or beach sandals when everyone else is attending in formal attire. The result, for the most part, is a homogeneously dressed group.

Similar feedback or “tipping” processes may also occur in the patterns of neighborhood migration. Schelling shows, for instance, in a simple geospatial model, that if enough people express a preference for living in a neighborhood in which their culture or ethnicity is in the majority, then it is possible for segregation to emerge over time. Here, the minorities in each neighborhood depart for another in which their neighbors will be more like them. Such mechanisms may apply not only to neighborhoods, but to clubs, professions, politics, churches, and other self-organizing groups.

The process, Schelling notes, is also related to the concept of “critical mass” in physics. An “atomic pile goes ‘critical’ when a chain reaction of nuclear fission becomes self-sustaining;… [for] an atomic bomb, there is some minimum amount of fissionable material that has to be compacted together to keep the reaction from petering out.” Fashion fads, human stampedes, religious currents, political protests, and other social movements may similarly arise when some critical number of adherents is reached within the collective.

Self-fulfilling prophecies

Social systems face further complications because their agents are continuously forming and updating their beliefs, expectations, and response rules in a context-dependent way. However, their macro behaviors may, under the right conditions, converge in predictable ways. For example, beliefs and expectations can sometimes be self-fulfilling in the sense that they provoke the very behaviors that reinforce the beliefs that give rise to them. For example, if the majority is racist and deems some minority group unfit for positions of leadership, then minorities are unlikely to be recruited or voted into said positions. In turn, they will lack the opportunity to demonstrate their ability and experience, thereby reinforcing the prejudices of the ill-informed.

Self-displacing and self-negating

Similarly, if shoppers believe that toilet paper and other essentials will be in shortage during a crisis, they may hoard and panic-buy during the crisis itself, generating the very shortage that they feared in the first place. Similarly, if investors grow pessimistic and begin to sell their shares in anticipation of a downturn, their collective behavior may generate the fall in asset prices and confidence that led to the very downturn that they sought to preempt. As Schelling notes, “if everybody believes you have to go early to get a good seat, you will have to go early to get a good seat.”

Sometimes, the effects are “self-displacing”. If every chief executive demands a compensation package that is above the average, then executive benefits are likely to rise. If students, companies, athletes, and researchers are each endeavoring to outdo their peers, then the qualities on which they compete are likely to intensify. But the processes can also be “self-negating”. When policymakers believe that a serious financial crisis is imminent, they may take preventative action to mitigate the damage. But if they believe that such a crisis is impossible, their casualness may bring about a disaster that they are ill-prepared for. As Schelling notes, “if everybody expects everybody else to bring food but no drinks, everybody will bring drinks but no food.”

Social contracts and structures

Indeed, much of society, Schelling reminds, “consists of institutional arrangements”—formal, informal, and hidden sets of “self-enforcing”, “self-confirming”, and “self-correcting” conventions—that bind us to each other. We drive on one side of the road and abide by many traffic rules without question because everyone else does too. Failure to comply is usually met with punishment, accident, or both. Other examples, Schelling adds, include our synchronized clocks, linguistic rules, mathematical notations, social etiquette, and so on. We attend birthday parties and send festive cards to one another, not because the majority of us love to do so, but because non-participation is socially difficult once the collective behavior is underway. 

As I hope the examples have shown, “these [social] patterns and structures”, Schelling writes, “impose a certain discipline on the variables.” They “[reduce] the ‘degrees of freedom’ that related activities can enjoy, [limit] the arrangements and outcomes that are mathematically possible, and [make] some equivalences hold among events or activities or distributions.” Of course, “it would be helpful to have a logical scheme or exhaustive taxonomy for all of these closed systems, conservative quantities, paired events, reciprocal flows, accounting statements and transition matrices.” Unfortunately, Schelling and other experts “know of none, and would not be sure where to draw the line if [they] did.” For now, we have to content ourselves in knowing that obvious and non-obvious rules and structures tether our microinteractions to our macrobehavior.

Sources and further reading