# Does Paul Krugman Understand Arithmetic?

Charles N. Steele

Issue CCLXXVII - February 14, 2011

A friend pointed out to me a recent post by Paul Krugman that begs for a response.

Krugman comments on the recent Pew poll regarding public attitudes towards budget cutting, and notes that while a majority polled wants federal speding to be cut, when people are polled on specific programs, a majority opposes cutting any particular program area.  (Read Krugman's post.)  Krugman suggests this means people think the laws of arithmetic can be repealed.  I think it means Krugman doesn't understand arithmetic, nor does he understand social choice theory.  Consider this simple example.

Suppose the population is three people, there are three federal government programs (A, B, and C), and one dollar is spent annually on each program for a total budget of \$3.  One hundred percent of the population might believe that the budget should be slashed by one third, to \$2.  When polled, one person says "cut A," one says "cut B," and one says "cut C."  The polls will show a majority (unanimous!) wants the federal government cut, but a majority wants to save every program.

So Dr. Krugman argues that the laws of arithmetic are to be repealed, and that people are confused and don't know what they want?  I think he doesn't understand simple math himself.

Let's look further at this.  Suppose everyone agrees that the highest priority is cutting the budget, that avoiding national bankruptcy or higher taxes or whatever results without cuts is the paramount concern.  They simply disagree over what the least-cost way of doing this is, where cost is understood to mean the full opportunity cost, not simply monetary expenses.  The poll reveals the issues that need to be debated -- exactly which cuts should be made, what comprises and tradeoffs should be chosen, and how will the costs be distributed.  Rather than illustrate a confused public and a hopeless dilemma, it illustrates a classic problem in social choice theory, the Arrow Possibility Theorem (usually called the impossibility theorem).  In effect, the theorem shows that there's no rule which can systematically assemble individuals' rankings over options into a consistent social ranking of those options.  In the case at hand, it's still very possible that a majority would agree to some compromise, if that were the option they had been asked about.  That's the debate we need to have.

Also there's a problem with what's called "framing," i.e., the particular language used to ask a question.  Respondents were asked if they wanted to cut spending on agriculture, and only 23% wanted to decrease it.  Well, what is "spending on agriculture?"  If it is basic research on better crops and better yields, maybe I can understand why majority would not want it cut.  But had these same people been asked about cutting agricultural subsidies, would that have answered the same way?  Or consider "combatting crime."  If instead the option were cutting spending on the war on drugs, answers might have been quite different.

Krugman holds a Ph.D. in economics, so it is not too much to expect that he would be familiar with basic social choice theory, with framing effects (Nobel Prizes in Economics were awarded for work in both of these areas before Krugman ever got his), and use of percentages. I can only conjecture that he was in such haste to "prove" the irrationality of those who favor a reduction in the federal government that he forgot basic economics and arithmetic.

This article originally appeared on the Hillsdale-econ.com blog, a new forum for the expression of economic ideas by professors Charles Steele and Gary Wolfram of Hillsdale College.

Dr. Charles N. Steele is the Herman and Suzanne Dettwiler Chair in Economics and assistant professor at Hillsdale College in Hillsdale, Michigan. His publications include papers on the Soviet economy and economics of transition, economic growth, and institutional change.  He received his Ph.D. in economics from New York University in 1997, and has subsequently taught economics at the graduate and undergraduate levels in the People’s Republic of China (China Agricultural University), the Russian Federation (Moscow State University), Ukraine (Economics Education and Research Consortium, National University Kyiv-Mohyla Academy), and the United States (Montana State University). He has also worked as a private consultant in design and review of USDA crop insurance programs with Watts and Associates, Inc.

In addition to economics, Steele's interests include trail running, mountaineering, snowshoeing, and similar outdoor pursuits. He's completed 26 ultramarathons, ten triathlons, and is a nine times finisher of The United States' oldest 50 mile race, the Le Grizz Ultramarathon.

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