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Winner Take All

The President of the United States earns far less money than the CEOs of mid-sized corporations. Should we worry that we are not paying him enough to attract qualified applicants? Probably not—for two reasons. First, the perquisites of the presidency yield a real pay vastly greater than the official salary. Second, the presidency is an example of a winner-take-all competition and this type of competition has a tendency to over-attract entrants.1

The argument that winner-take-all contests tend to over-attract entrants closely parallels the argument that the problem of the commons yields inefficiency: people respond to average benefit rather than to marginal benefit. An example may help explain the logic involved.

Suppose that we have a two-occupation world. The inhabitants of Nirvana can be peasants, at which they all are equally good and produce output valued at $1000 per person. (We can assume that there is an export market to avoid the problem of diminishing marginal utility and a downward-sloping demand curve.) Or, they can compete to be the ceremonial chief, which has benefits to the winner of $100,000 and nothing at all to the losers. The value of the chief to the inhabitants depends on the quality of the chief.

Suppose further that each year the inhabitants have to make a decision to be peasants or to compete to be chief. Also assume that at the beginning of each year no one has any reason to believe he is any more or less likely to be able to win the competition, even though abilities are not equally distributed for this task. How many people should compete for this job? If all were equally able or if we could identify the best candidate from the start, the answer is, "Only one." If all were equally able, we could select one by lottery, and if we could identify ability with a simple test, we could use that test to select the winner. But suppose that the situation is more complex, and that only after a year of intensive training will the best candidate be apparent. The larger the group of persons who compete for the position, the more talented the winner can be expected to be. (For the same reason we expect a high school that has 10,000 students to dominate athletic competition with a high school with only 100 students—the bigger the pool of possible athletes, the more likely it is that one with exceptional talent will emerge.) What is the best number—the economically-efficient number—of candidates?

Using marginal principles, we can see that the society should continue adding candidates to the pool as long as adding another increases the expected return by more than $1000 (the value of the candidate as a peasant). If a pool of 10 candidates can be expected to yield a chief whose value in the job is $70,000, and a pool of 11 applicants can be expected to yield a winner who provides $72,000 worth of value, it is in the interests of the society to have at least 11 competing. If adding the eleventh candidate increases the expected yield only to $70,900, then the society would get more value if the eleventh applicant remained a peasant. As the pool gets bigger, adding an additional person can be expected to yield diminishing returns.

How will the applicants see the competition? Suppose that there are only 10 in the pool. Would another person find it attractive to join knowing that the value of the position to the winner will be $100,000? If each thinks he has an equal chance to get the prize, the expected value of entering is $10,000, and this would draw in additional people if they are not bothered by the risk. In fact, if they were risk-neutral and understood the payoffs, 100 people would want to be in that pool because they will keep joining as long as the average expected value is greater than $1000. But because the average expected value will fall as more people join, the marginal expected value must lie below the average. Hence, if the value of being chief as perceived by the society is not much smaller than the value of being chief as seen by the winner, there will be a tendency for too many candidates to compete for chiefdom. Nirvana would be better off if some them remained peasants.2

Political offices, NBA basketball careers, and lives as Hollywood movie stars are examples of competitions that are either winner-take-all competitions or very close to winner-take-all situations. There is a fixed number of players on the rosters of the NBA teams. Although there is not a fixed number of movie stars, the number that the public can pay attention to and that can be featured in the tabloids is quite limited. Do we see too much effort expended competing for these positions? Many observers believe so. For every person who makes it into one of these financially rewarding positions, there are hundreds or thousands who, despite great effort and sacrifice, do not make it.

So back to our original question—do we pay the president enough? The answer is, "Yes, unless the value to the citizens of a good president is considerably bigger than the value the president gets from holding the office." Perhaps you find the argument that the value of having a good president is so large that we need even more people wanting to be president, but I do not.

Any discussion of income distribution seems to lead into a discussion of fairness.

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1 For an entertaining and provocative look at winner-take-all markets, see The Winner-Take-All Society by Robert H. Frank and Philip J. Cook (New York: The Free Press, 1995).

2 If the value of the ceremonial chief to society were $10,000,000 but the winner only received a value of $100,000, it is likely that the competition would attract too few rather than too many entrants. Winner-take-all competitions that vastly underpay may exist in the area of innovation. The person who invents a new product or technique has a chance to capture rich rewards as a result, but the history of innovation is full of those who were able to capture only a tiny amount of their innovation's value. For example, Philo T. Farnsworth never became fabulously wealthy and you may not even have heard of him, though he has had a tremendous influence on your life. In fact, without him you probably would not be reading this text on your computer screen because he invented key technology on which television —and hence the computer terminal—is based. The disruptions of World War II delayed his efforts to get a broadcasting business up and running by about five years, and when his crucial patents expired in the late 1940s, the field was then open for others to enter—and enter they did. He and his team of researchers managed to capture a few million dollars of the billions of dollars of value they created.

Copyright Robert Schenk