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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.
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
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