Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply.To this end, we present a framework that allows for “shades of gray” of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.

From Chicago to Paris

Chapter 11 studies the second phase of the debate on expected utility theory (EUT), which commenced in May 1950, when Paul Samuelson, Leonard J. Savage, Jacob Marschak, Milton Friedman, and William Baumol initiated an intense exchange of letters. These economists argued about the exact assumptions underlying EUT, quarreled over whether these assumptions are compelling requisites for rational behavior under risk, and debated the nature of the cardinal utility function u featured in EUT. This correspondence modified the views of all five economists and transformed Samuelson into a supporter of EUT. In a prominent conference in Paris in May 1952, Friedman, Savage, Marschak, and Samuelson advocated EUT in the face of attacks from Maurice Allais and other opponents of the theory. The Paris conference and the publication of an Econometrica symposium on EUT in October 1952 marked the emergence of EUT as the mainstream economic model of decision-making under risk.

Cardinal Utility

Chapter 6 reconstructs the progressive definition and stabilization of the current notion of cardinal utility as utility unique up to positive linear transformations. This notion was the eventual outcome of a long-lasting discussion, inaugurated by Vilfredo Pareto, regarding an individual’s capacity to rank transitions among different combinations of goods. This discussion continued through the 1920s and early 1930s and underwent a decisive acceleration from 1934 to 1938, that is, during the conclusive phase of the ordinal revolution. In this latter period, the main protagonists of the debate were Oskar Lange, Henry Phelps Brown, Roy Allen, Franz Alt, and Paul Samuelson. In the discussions that led to the definition of cardinal utility, some of these utility theorists began to envisage a broader notion of measurement according to which utility can be measurable even if no utility unit is available. Until the mid-1940s, however, cardinal utility remained peripheral in utility analysis.

When Unit-Based Measurement Ruled the World

In order to illustrate the broad intellectual context within which the early discussions of utility measurement took place, chapter 1 reviews the history of the understanding of measurement in philosophy, physics, psychology, mathematics, and areas of economics before and beyond marginal utility theory. This review reveals that between 1870 and 1910, all these disciplines were dominated by the unit-based or, equivalently, ratio-scale conception of measurement. According to this conception, measuring the property of an object consists of comparing it with some other object that is taken as a unit and then assessing the numerical ratio between the unit and the object to be measured. This chapter also shows that late-nineteenth-century discussions of measurement in mathematics established the cardinal–ordinal terminology that later passed into economics. However, the mathematical concept of cardinal number is different from the economic concept of cardinal utility, which entered the scene only in the 1930s.

What Is That Function?

Chapter 10 reconstructs the first part of the American debate on expected utility theory (EUT), which ranges from 1947, when the second edition of John von Neumann and Oskar Morgenstern’s Theory of Games was published, to April 1950. In this period, a number of eminent American economists, including Milton Friedman, Leonard J. Savage, Jacob Marschak, Paul Samuelson, and William Baumol, wrote papers in which they took stances on the validity of EUT and the nature of the cardinal utility function u featured in the expected utility formula. Friedman, Savage, and Marschak supported EUT, although for different reasons, while Samuelson and Baumol rejected it. Regarding the nature of the cardinal utility function u, however, they all shared the view that it is interchangeable with the utility function U that the earlier utility theorists had used to analyze choices between riskless alternatives.

Is There a Unit of Utility?

Chapter 2 discusses how William Stanley Jevons, Carl Menger, and Léon Walras addressed the issue of the measurability of utility. The three founders of marginal utility theory identified measurement with unit-based measurement and, accordingly, searched for a unit of utility that could be used to assess utility ratios. The outcomes of this search were diverse and ranged from Jevons’s idea that a unit to measure utility, although not available at present, may become so in the future to Walras’s assertion that although utility cannot be measured, constructing economic theory as if it were measurable is a scientifically legitimate procedure. The final section of the chapter explains why the current notion of cardinal utility is inadequate for understanding the utility theories of Jevons, Menger, and Walras and accordingly contends that the three founders of marginal utility theory were not cardinalists in the modern sense of the term.