Cardinal Measures and Ordinal Measures ________________________________________________________________________________________________________________________________________________ cardinal measurement: A variable is cardinally measurable if a given interval between measures has a consistent meaning, i.e., if the measure corresponds to points along a straight line. For example, height, output, and income are cardinally measurable. ordinal measurement: A variable is ordinally measurable if ranking is possible for values of the variable. For example, a gold medal reflects superior performance to a silver or bronze medal in the Olympics, or you may prefer French toast to waffles, and waffles to oat bran muffins. All variables that are cardinally measurable are also ordinally measurable, although the reverse may not be true. ________________________________________________________________________________________________________________________________________________ Cardinal versus ordinal utility Early economists assumed that people are able (perhaps only subliminally) to assign meaningful utility numbers (utils) to their satisfaction in one situation vis-à-vis their satisfaction in an alternative situation. For example, the utils generated by each brownie you eat or book you read would be recorded as if you have utilometer imbedded in your frontal lobe. Cardinal measurement of utility Satisfaction, like temperature or distance, is assumed measurable in meaningful, absolute numbers. Cardinal measures are possible when incremental units are constant and reasonably objective, but utility is roughly measurable at best. As far as we know no one is born equipped with a utilometer to precisely measure satisfaction. In the 1930s, Nobel prize-winner Sir John Hicks followed the leads of Vilfredo Pareto and Francis Y. Edgeworth to develop indifference analysis, an underpinning for the theory of consumer behavior that dispenses with cardinally-measured utility. Hicks argued that ranking our preferences is the best we can do—I prefer a slice of cherry pie to a vanilla ice cream cone, a mountain bike to a pair of rollerblades, etc. Utility measured by rank alone is known as ordinal utility. Ordinal measurement of utility Satisfaction is not cardinally measurable. Instead, relative numbers provide rankings like first, second, tied, etc. Ordinal analysis assumes that between any two bundles of goods, a person either prefers one to the other or is indifferent between the bundles—i.e., individuals can provide an ordering of bundles. Thus, ordinal utility analysis cannot tell us, for example, that one fried chicken yields 147 utils more satisfaction for the president than a few pieces of dry white toast—all that really matters is that he prefers the chicken to the toast. As long as people can consistently rank different bundles of goods by the satisfaction generated, ordinal utility is sufficient to model consumer behavior. Notice that any cardinal measurement is also ordinal (fixed increments establish rank), but the reverse is not true. If we know rank, it does not follow that we know cardinal intervals between bundles A, B, C, etc. For example, if we know only the order of finish in a horse race, inferring that the winner beat the second place finisher by precisely as much time as the second horse beat the third would be an unjustified stretch.
________________________________________________________________________________________________________________________________________________ Author: Ralph Byrns
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