Why do we need cardinal utility (instead of ordinal ranking)?

Question

The reasons I've been thinking about:

1. Without cardinal utility, the strength of preference does not make sense.
2. In social welfare function, if we don't have the strength of preference, then we have Arrow's impossibility.
3. Cardinal utility allows quantitative analysis, such that the utility values make sense.

My questions: what are some strong reasons for using cardinal utility on preference instead of ordinal rankings?

How do I argue that having a cardinal utility is important?

Answer 1

Using cardinal utility is justified if you think that the axioms of Expected Utility Theory are plausible, because then your choice behavior can be described by maximizing the expected value of a cardinal utility function.

Answer 2

Without using cardinal utility almost whole field of poverty, inequality, welfare and public economics becomes impossible. With ordinal utility benefits of redistribution or various policies between two individuals are incomparable.

Most of micro would probably be fine with ordinal utility, but subfields that study (analytically) poverty, inequality, welfare and public economics would virtually vanish if the concept of cardinal utility would stop being used.

Answer 3

One way to argue that cardinal utility is important is to ask whether the law of diminishing marginal utility is plausible. For example:

1. If you eat (at one sitting) one doughnut, then a second, then a third, and so on, does your additional satisfaction from eating an additional doughnut become less with each doughnut?
2. Comparing a person with an annual income of \$10,000 and one with an annual income of \$100,000, would an increase of \$1,000 be worth less to the latter than to the former?

If someone accepts the answer 'yes' to questions such as these, then they are acknowledging the plausibility, in at least some circumstances, of the law of diminishing marginal utility. You can then point out that the concept of marginal utility (whether diminishing or not) makes no sense without that of cardinal utility (mathematically, $\frac{\Delta U}{\Delta x}$ and $\frac{dU}{dx}$ are undefined unless $U$ (and $x$) are numerical variables).

Answer 4

I largely agree with Adam's answer.

To build off of his answer- There are key practicalities to consider when understanding why we use cardinal utility. In addition to Adam's points, you could also point to the consumer welfare maximization problem. Many "standard" problems in economics frame household tradeoffs as a consumer maximization problem. It's necessary to construct cardinal preference measures, despite their ordinal interpretation, as a means to make use of the dynamic programming/analytics tools afforded by applied mathematics.