What is Utilitarianism? The answer is not obvious, and without and answer much that has been written about Utilitarianism is not meaningful. But measurement of hedonic value of episodes on a ratio scale opens up possibilities various kinds of product utilitarianism without interpersonal comparisons. And equilibration dynamics opens up the possibility of conventional interpersonal comparisons, and the use of the Utilitarian sum.
Interpersonal comparisons of utility can be conventional. Alternative conventions are possible. The (conventional) aggregate utility can be used for equilibrium selection. This solves the old Utilitarian problem of conflict between maximizing individual and group utility. Conditions on an equilibration dynamics leading to such a convention are given.
A theory of hedonic episodes is given. A representation theorem is given, which measures utility on a ratio scale.For aggregation of pleasures for a group, the product of individual utilities is meaningful without interpersonal comparisons. Common “counterexamples” to Utilitarianism turn out not to be meaningful. There are two distinct kinds of group expected utility: one violates group rationality, the other violates Pareto dominance.
Does neurobiology deliver a Utilitarian measurement of pleasure and pain? Much remains unknown, but enough is known to show that neurobiology just makes the problems more complex and difficult.
Extensive measurement from Helmholtz and Holder is the standard physical account. It gives a ratio scale. Stevens introduces interval and ordinal scales. Scott and Suppes give a representational foundation to Stevens’ scales. Suppes, Zinnes, Luce and Narens analyse meaningfulness.
This discusses the von Neumann-Morgenstern representation theorem. Preference orderings over chancy prospects are used to measure utility on an interval scale. Ramsey’s earlier theorem from the 1920s is also discussed.
Luce’s theory of semiorders resolve a problem with just noticeable differences - intransitivity of equality. Bisection measurement gives an alternative approach. This is related to Ramsey’s representation theorem for probability and utility. Stevens’ indirect magnitude production method can be given a rigorous analysis. Torgerson’s experiments suggest that subjects cannot distinguish between estimating equal intervals and equal ratios. Problems of cross-modality matching are explored.
