Ordinal World and Cardinal Questions: Possibility, Impossibility and John Harsanyi

Decades have passed since Arrow (1951) published his groundbreaking theory, known as the first impossibility result in modern economics. Arrow formulated five appealing conditions – Pareto optimality, unrestricted domain, independence of irrelevant alternatives, non-imposition and non-dictatorship – and derived the disheartening conclusion that no social welfare function (with more than two alternatives) can simultaneously satisfy all of these conditions. Assuming that all conditions are attractive, this result has had a profound impact on the social choice literature, as it implies the unattainability of an ideal social welfare function. Consequently, numerous attempts have been made in the literature to overcome this unfavorable conclusion, with one notable endeavor being the weakening of unrestricted domain condition to single-peaked preferences by Duncan Black(1958). Over the years, Black’s theorem has emerged as the most influential solution to the impossibility problem. In contrast, another scholar, John Harsanyi (1979), has also demonstrated that under specific circumstances Arrow’s result can be avoided for a utilitarian social welfare function. Harsanyi introduced a novel approach, involving cardinal utilities and interpersonal utility comparison, instead of relaxing or discarding one or more of the original conditions, a standard practice in the literature. By reformulating Arrow’s five conditions within the cardinal paradigm, Harsanyi demonstrated that the utilitarian social welfare function avoids the impossibility results. Puzzlingly, Harsanyi’s proof went largely unnoticed and has had limited influence over the years. The focus of this thesis is to establish and demonstrate the fundamental differences between Arrow’s and Harsanyi’s approaches and to address the question of why Harsanyi’s possibility proof gained less traction within the field.