Who's Counting: It's Mean to Ignore the Median

Along various social dimensions, the dynamics underlying these laws may lead naturally to the development of stark inequalities, which increasingly seem to reign not just here but throughout the world. The United Nations issued a report a few years ago, for example, saying the net worth of the world's three richest families -- the Gateses, the Sultan of Brunei and the Waltons of Wal-Mart -- exceeded the gross domestic product of the 43 poorest nations.

Philosophy and a Little Game

Still, this lopsidedness is neither necessary nor inevitable, and it bodes ill for civil society. Almost 2,400 years ago Aristotle, seeing the discord between ancient Greece's rich and poor, applied his idea of the golden mean to call for an equitable (but not equal) income distribution. For purposes of stability, he favored establishing a strong middle class and government policies to assist in this establishment.

A little game from the field of behavioral finance illustrates the class resentment Aristotle described. The so-called "ultimatum game" generally involves two players: One is given a certain amount of money, say $100, by an experimenter, and the other is given a kind of veto. The first player may offer any nonzero fraction of the $100 to the second player, who can either accept or reject it. If he accepts it, he is given whatever amount the first player has offered, and the first player keeps the balance. If he rejects it, the experimenter takes the money back.

Viewing this in rational game-theoretic terms, one would argue that it's in the interest of the second player to accept whatever is offered, since any amount, no matter how small, is better than nothing. This is not what happens, however. The offers generally range from 5 percent to 50 percent of the money involved, but, when deemed too small, the offers are often rejected. Better to receive nothing, the resentful rejectors say, than to be humiliated. Notions of fairness and equity, as well as anger and revenge, seem to play a role.

Almost as if on cue, just as I finished writing this, the House passed a modest minimum wage bill but typically linked it to a significant cut in the estate tax. Once again, one for you, 10 for me. (It seems the bill will not make it through the Senate, however.)

So was Aristotle a card-carrying Democrat? No. I think he was just expressing some increasingly uncommon common sense. It's mean to ignore the median.

Professor of mathematics at Temple University, John Allen Paulos has written such best-sellers as "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.

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