Fisher's Contribution

Chapter 4, Section 3: Fisher's Contribution

Nowadays, the utility numbers economists use are mostly ordinal measure. Numbers of ordinal measure are not additive, but they can be ranked. Ranking is measuring. For an unadditive ranking, the margins between numbers are not comparable. 101 is greater than 99, and 99 is greater than 89. The former margin is 2, while the latter is 10, since the numbers are not cardinal measure, we cannot say the latter margin is five times larger.

Let's have some examples. In a Miss Hong Kong contest, the champion wins a score of 88, the runner-up 82, and the third place 79, then the ranking is settled. But we cannot say the margin between the champion and the runner-up is two times as large as that between the runner-up and the third place. Another example, when students take an exam, the teacher ranks them by scores. When I was studying in UCLA, one student asked the teacher how test scores were calculated. The teacher answered: "Test scores is just an arbitrary ranking, teachers that don't do this would be too stupid to teach in UCLA." The scores for essay questions are ordinal measure.

Ranking utilities with ordinal numbers doesn't have any logic problem. The assertion that someone takes A over B because the utility for A is larger, if relevant constraints properly handled, explains the behavior sufficiently. But when measuring utility with ordinal numbers, we know neither what the margin between A and B means, nor where a total utility for that man can be used. More than twenties years ago, the father of a Hong Kong middle school student called me, and said his son cannot answer the teacher's question about the use of total utility and thus failed an exam. The father asked for the answer, yet I asked in reply: "Does your son really not know the answer?" "No, he doesn't." "Good, your son actually knows more than his teacher!"

In 1892, I. Fisher (1867-1947), who later became the greatest economist of the twentieth century, published his doctoral dissertation, part of which is about utility theory. That's a genius book, and a key point in it is, to explain behaviors, cardinal ranking of utility is totally unnecessary, because at margin, cardinal ranking and ordinal ranking are of no difference, while for behavior explanation "margin" is sufficient. "Marginal" utility means the numerical change of utility brought by the increase or decrease of an item. When viewed at margin, neither addition into a total utility is necessary, nor comparison among different margins.

The idea that changes at margin suffice for behavior explanation originated from W. S. Jevons (1835-1882), and thrived due to Fisher's cherishing. In 1946 Stigler pointed out, if two products are produced through a single process, the average cost for each would be unable to know, yet the variation of marginal cost is knowable. To explain production behaviors, the information of average cost is unnecessary.

Later on when I was engaged in transaction cost research, I'd start only from changes at margin in any analysis. In the real world, transaction cost is not easy to measure. A viable means to explain behaviors is to see under different scenarios whether the transaction cost would go up or down. Change means "margin", and if there is no change, a behavior can never be explained. In dealing with transaction cost via changes at margin, it doesn't matter whether cardinal measure or ordinal measure is used. We cannot say cardinal measure is more accurate either, because accuracy here depends on the acceptance of observers, not the thoroughness of numbers.

Let me stress once again. Utility is just a free name for the ranking numbers of options, aiming at explaining a man's choices. This is what my teacher Alchian has said. Stigler has said: "Whether we assume one maximizes wealth, religious belief, elimination of love song singers, or his waistline, for rigorous demand theory it just makes no difference." R. H. Strotz has said: "Obviously, we don't have to find out whether the measurement of utility is in money, leisure time, octave, or inch, not to mention a psychological unit." These are all wisdom in the fifties of last century.