Critics and the other envious resent the staggering salaries and perks superstar athletes, CEOs, actors, politicians and other entertainers command.

Somehow, being paid hundreds of millions of dollars to kick or throw a ball, to pretend not to be yourself in front of a camera, to get a multi-million-dollar retirement package and frequently to paid such vast sums merely for distracting the public from the really important issues of the day seems unfair—even insane.

Lucrative, indeed grotesque endorsement payouts and post-political-career lecture-circuit fees are seen as compounding the injustice to the point of absurdity.

But, if fairness is to be the determining criterion of compensation packages, the argument for why paying somebody in short pants more than $100 million to chase, kick or throw a soccer ball or $20 million to portray some action movie hero is fair or unfair needs to be carefully laid out.

For openers, clearly, two of the most common notions of fairnessKarl Marx’s “from each according to his ability, to each according to his needs” and John Stuart Mill’s “the greatest good for the greatest number” are inadequate to this task.  

Low Marks From Marx, No Millions from Mill

A cursory examination of the skill set and real needs of major league ball players reveals that despite the fact that their abilities are rare, there is no evidence that those skills represent important and “socially useful labor” of the sort that Marx ranted on about. Ditto for those politicians who, after feeding at the public and lobbyist troughs, go to work for the same crony companies they benefited.

More importantly, the notion that their multi-million dollar paydays are scheduled and sized according to their needs is simply preposterous.

The utilitarian “greatest good for the greatest number” principle of  19th-century liberal British philosophers and reformers John Stuart Mill and Jeremy Bentham also fails to legitimize such huge payouts, to the extent that, on the face of it, the deals the superstars get seem to amount to “the greatest good for the smallest number”—namely the small populations of elite A-list actors, chart-topping music artists, superstar pro athletes and lavishly-pensioned politicians, to name but a few of the few.

Likewise, the capitalist mantra “what the market will bear” is, as a criterion of fairness, nonetheless arbitrary. Consider a scalper selling life preservers for thousands of dollars to flailing victims floating by in tsunami floodwaters. Do you really consider that “fair”—or ethical, given either the willingness or inability of the human flotsam to pay?

[Presumably what is fair should also be ethical, which hardly seems to be the case here, unless “what the market will bear” is arbitrarily defined as ethical.]

Thinking Beyond a Cost-Benefit Critique of a Cost-Benefit Approach

That said, some will argue that a dollar-denominated cost-benefit analysis is all that is needed to explain and justify such gargantuan salaries: the compensation that superstars command is offset by the colossal revenues they generate in virtue of the mass audiences and deep-pocket advertisers they attract or because of the favors they grant while in office.

But, here too, it is debatable that “financially justifiable” means “ethically justifiable”; hence, if “fair” is to imply “ethical”, a purely financial cost-benefit analysis as a justification for staggering salaries and perks is unlikely to satisfy anyone who believes “fair” is an ethical concept as well as, or instead of, a statistical or financial one.

However, apart from that account and independent of any mass-market effect, it may be that all that is needed to justify bloated compensation is some basic high school math and an understanding of what makes a game “fair”.

On one such analysis, all that is necessary for a salary or other payoff scheme to be fair is that on average the average payoff to the participants is zero. That’s a mathematical definition of a “fair game”: an “expected gain”, on average, of zero—meaning the average player is guaranteed neither a win nor a loss over averaged countless plays of the game.

If it were otherwise, the game, as a game of chance, would be unfair, even if on average the expected gain were greater than zero, since somebody would, on average, be paying out that payoff.

The Fairness of Zero

Hence, for any given occupation, if on average those within the profession average a zero payoff, many among them have to incur a net loss to offset the gains of those who come out ahead.

This is the case with many aspiring actors: While A-list superstars score big returns, the astronomical salaries paid these few are justified because the “game” of being an actor involves offsetting losses by the many—including not only lost savings, but also financial loss through underemployment, and financial costs imposed on parents and friends, to mention but a few. In this way, the average payoff to the average actor can become zero, i.e., “fair”.

Although the average payoff to actors, comprising the aspiring, unemployed, never employed and employed, is virtually certain not to be exactly zero, and most likely greater than that, if the actual expected gain averaged over all actors is considered—on one estimate I saw years ago, a barely survivable income—the huge incomes garnered by Hollywood superstars can be interpreted as a kind of lottery or crapshoot payoff or a risk incentive, i.e., an inducement to take the risk inherent in attempting to make a living as an actor.

 [Annual average salaries for actors are not calculated at the Bureau of Labor Statistics. All figures are hourly wages, given the irregularity of the work. That average expected gain on an hourly basis, for the 70,540 actors in the government data base, presumably including the Hollywood glitterati, had a median rate of $20.26 per hour—which hardly seems “unfair” or otherwise unreasonable, when compared to what is considered a living wage.]

Of course, it is right to ask why a zero average payoff defines “fair”. In considering this, imagine a game I’ll call “Lucky 13”: You win $13 if you draw any one of the four aces from a deck, but otherwise lose $1. Would this game be fair?

No, it wouldn’t. At least, it wouldn’t be fair to the casino. The reason is that [$13 x 4/52] – [$1 x 48/52] = $1- $0.92 =  $0.08 [rounded off] per play, as a payoff to the players, on average. To break even on this game, which means to make it fair, a casino would have to charge players $1.083 when the latter lose. 

Another Whack at Defining “Fair”

What about occupations with a very narrow spread of incomes, utterly unlike that of actors and athletes? Given that there are virtually no janitorial income superstars to offset the modest or low wages of the mass of janitors, by what expected-gain criterion could whatever wage an individual janitor gets be judged fair or unfair?

One way to apply expected gain when there is no wide variation in incomes within a given occupation —or indeed to apply it to any occupation, irrespective of its income spread—might be to imagine a lottery or game in which a “ticket” wins one of two prizes: One of the prizes, with a 50-50 chance of being won, is the average payoff for getting a non-janitorial job in the U.S. multiplied by the average probability of getting one of those jobs.

The other prize is a janitorial job and its average or specific annual salary multiplied by the probability of getting a janitorial job, but with a 50-50 chance of winning that ticket option, i.e., of winning a janitorial job, rather than any other job.

If the difference between the two lottery outcomes is zero, the janitorial salary would be absolutely fair—at least mathematically speaking, especially if the specific salary is used in the calculation, since for a given, specific job it may otherwise be unfair relative to the average for janitorial jobs in the aggregate.

Of course, in contemplating one’s own salary or wages, this kind of calculation would, if attempted, be impossibly complex—maybe impossible, period.

But if you are the one offering the salary, you can always suggest to the complaining or otherwise dissatisfied employee or job candidate that such a calculation would prove the compensation package is fair and shift the burden of proof to him or her.

This could be pulled off. Just be sure to make it clear which sense of “fair” you mean.

But don’t expect a superstar bonus for pulling it off.

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