Ordinal Utility

Suppose Jane has a free afternoon and all three options are available. She prefers a walk, then the cinema, then a book at home. This distinguishes what she prefers without telling us whether the walk narrowly beats the cinema while reading comes far behind both. Here, economic utility represents how alternatives are valued, not a measured volume of pleasant feelings. The relationship between options matters, rather than a distance on an imagined ruler. [1] [3]

Assign the walk, cinema and book the numbers 3, 2, 1, with higher numbers indicating preferred options. The numbers 100, 20, 10 express exactly the same ordering. Jane has not changed her mind, although the numerical gaps have changed greatly. A strictly increasing transformation is a renumbering that preserves both rankings and any ties. Doubling an ordinal number therefore does not mean doubling satisfaction. [3]

Seeing Jane on a walk does not establish that she preferred the park to the cinema. The cinema might have been closed or unaffordable. Understanding the decision requires knowing the available options and their conditions. In Human Action, Mises connects value rankings with actual action, rather than an unchanging list hidden in someone’s head. Today’s choice may not hold tomorrow, when Jane is tired, rain arrives or another film appeals to her. [1]

A standard economic model assumes alternatives can be compared and preferences are transitive. If Jane prefers walking to cinema and cinema to reading, she also prefers walking to reading. Models can include ties; an indifference curve connects equally valued alternatives. These are explicit assumptions and a way of describing choice. One afternoon’s decision does not prove that a real person has complete, stable preferences for every future situation. [3] [5]

If Jane and Peter both assign an experience 10, that does not give us a common scale of satisfaction. Each person’s numbers could be changed differently while preserving their own ranking. Adding those numbers does not itself measure collective happiness or establish who benefits more from a change. This does not rule out discussing social benefit. It means comparisons between people need further rules, information and justification that rankings alone cannot supply. [1] [2]

When ordinal utility is written as a mathematical function, renumbering can change its slope and numerical increments while preserving preferences. For advanced reading, even a derivative of that function — its rate of change — does not automatically measure emotional intensity. The related Marginal Utility explains the importance of another unit or a use that would be forgone. In calculations, distinguish the choice from the numbers of its chosen representation. Analysis remains useful, provided we know what its numbers represent. [3]

Jane may also choose between options with uncertain outcomes, such as a trip where she might get caught in the rain and an indoor activity. Expected Utility models weight outcomes’ utilities by their probabilities. They add assumptions, so we cannot arbitrarily change the utility numbers assigned to outcomes and then average again expecting the same conclusions. The expected-utility form is preserved by a positive affine transformation a·u+b, where a>0: multiply every utility by the same positive number and add the same constant. This extra structure still does not itself create a shared happiness scale across people. [4]

To spend bitcoin, a wallet uses private keys: secret numerical data used to create a digital signature authorizing a payment. One user prioritizes protecting keys, another everyday payment convenience, and another purchase cost. Wallets therefore need not rank the same for everyone. A score of 80 against 40 does not mean twice the personal benefit. Budgets expressed in money can be added, but that does not make them a scale of feelings. Ask which criteria a comparison uses, who set their weights, and whether the available options match your circumstances. For Bitcoin too, a tidy score is an aid, not a substitute for explanation. [1] [2] [6]