The False Fairness of Percentages and Percentiles (Opinion)

My mother was the first member of her family to earn a high school diploma, and she never spent a day in college, but she was very sharp with figures. She explained mortgage amortization to me when I was about 12.

Mom worked as a school secretary, and even though my father was an administrator whose annual misery was negotiating with the teachers’ union, she sympathized with the teachers.

Something insidious was happening with school salaries, she told me: across-the-board raises. To give the higher-paid administrators the same percentage raise as teachers and support staff, she showed me with unassailable mathematical precision, was creating a wider income gap.

And yet it seems so fair. If everyone gets 3 percent or 5 percent, everyone’s standard of living is improving at the same rate, right?

Except 5 percent of $100,000 buys a lot more than 5 percent of $50,000. And next year, 5 percent of $105,000 will buy a lot more than 5 percent of $52,500, and so perpetually on.

While the difference between the two salaries stays in proportion, the difference between standards of living grows bigger with each raise. The people who have more get more, and the people who have less get less more.

Much fairer, my mother thought, would be equal raises in take-home pay.

Current events have reminded me of my mother’s lessons in basic finance, specifically Herman Cain’s 9-9-9 tax proposal and the Washington Post’s fascinating report about “peer benchmarking” in executive compensation. The story (published Oct. 3 and available online) relied on new transparency requirements by the Securities & Exchange Commission to show executive compensation at publicly traded companies is often more closely tied to the pay packages of other executives than to individual performance.

The result is something far more insidious than anything my mother observed in Arkansas school salaries of the 1970s.

Executives who are demonstrably below average in performance as measured by stock value are being rewarded because some other company rewarded its execs, who may have gotten a raise merely because yet another executive did. If our executive weren’t above the 50th percentile, he wouldn’t be our executive, right? If you look at it that way, it seems perfectly fair.

So does Herman Cain’s tax plan. The former pizza chain CEO presumably knows as much about finance as my mother, yet in his quest for the Republican presidential nomination, he has glommed onto yet another simplistic variation of the flat tax idea, in which everyone, would pay the same percentage of his income.

Every independent analysis of Cain’s still sketchy proposal that I’ve seen has found that it would bring in less federal tax money and thereby exacerbate the deficit, despite demanding 9 percent of the income of people who earn too little to pay federal income tax under the current system. It would do that by taxing the very wealthiest far less than they currently pay.

Cain would (with apologies to Finley Peter Dunne) comfort the comfortable and afflict the afflicted — but he would do it in a way that sounds so fair.