We axiomatize, in an Anscombe-Aumann framework, the class of preferences that admit a representation of the form V(f) = µ – ρ(d), where mu is the mean utility of the act f with respect to a given probability, d is the vector of state-by-state utility deviations from the mean, and ρ(d) is a measure of (aversion to) dispersion that corresponds to an uncertainty premium. The key feature of these mean-dispersion preferences is that they exhibit constant absolute uncertainty aversion. This class includes many well-known models of preferences from the literature on ambiguity. We show what properties of the dispersion function ρ(•) correspond to known models, to probabilistic sophistication, and to some new notions of uncertainty aversion.
This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals’ judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow’s impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.
Machina & Schmeidler (1992) show that probabilistic sophistication can be obtained in a Savage setting without imposing expected utility by dropping Savage’s axiom P2 (sure-thing principle) and strengthening his axiom P4 (weak comparative probability). Their stronger axiom, however, embodies a degree of separability analogous to P2. In this note, we obtain probabilistic sophistication using Savage’s original axiom P4 and a weaker analog of Savage’s P2.
We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi’s impartial observer theorem. To do this, we reformulate Harsanyi’s problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (first) Diamond’s critique concerning fairness and (second) Pattanaik’s critique concerning differing attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi’s utilitarianism.
Keywords: D63, D71
JEL Classification: Generalized utilitarianism, Impartial observer, Social welfare function, Fairness, Ex ante egalitarianism
Savage motivated his Sure Thing Principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, then it should be preferred overall. The idea that it should be possible to decompose and recompose decision problems in this way has normative appeal. We show, however, that it does not require the full separability across events implicit in Savage’s axiom. We formulate a weaker axiom that suffices for decomposability, and show that this implies an implicit additive representation. Our decomposability property makes local necessary conditions for optimality, globally sufficient. Thus, it is useful in computing optimal acts. It also enables Nash behavior in games of incomplete information to be decentralized to the agent-normal form. None of these results rely on probabilistic sophistication; indeed, our axiom is consistent with the Ellsberg paradox. If we assume probabilistic sophistication, however, then the axiom holds if and only if the agent’s induced preferences over lotteries satisfy betweenness.
We provide necessary and sufficient conditions for a dynamically consistent agent always to prefer more informative signals (in single-agent problems). These conditions do not imply recursivity, reduction or independence. We provide a simple definition of dynamically consistent behavior, and we discuss whether an intrinsic information lover (say, an anxious person) is likely to be dynamically consistent.
We compare the Skiadas approach with the standard Savage framework of choice under uncertainty. At first glance, properties of Skiadas “conditional preferences” such as coherence and disappointment seem analogous to similarly motivated notions of decomposability and disappointment aversion defined on Savage “ex ante preferences.” We show, however, that coherence per se places almost no restriction on the structure of ex ante preferences. Coherence is an `external’ restriction across preferences whereas notions of decomposability in the Savage framework are ‘internal’ to the particular preference relation. Similarly, standard notions of disappointment aversion refer to ‘within act’ disappointments. Skiadas’s notion of disappointment aversion for families of conditional preference relations neither implies nor is implied by standard notions of disappointment aversion for ex ante preferences.
We provide a model of a primitive state whose rulers extort taxes for their own ends. This ‘predatory’ state can result in lower levels of both output and popular welfare than either organized banditry or anarchy. The predatory state may provide public goods, such as protection or irrigation, and hence may superficially resemble a contractual state. But, the ability to provide such goods can actually reduce popular welfare after allowing for tax changes. We compare the revenues raised by taxation with those from banditry to get an idea when primitive states are likely to emerge.
We then consider interactions between bandits and the state. ‘Corrupt’ side-deals are bad for output and popular welfare, but good for revenue. Even in the absence of such collusion, the existence of a ‘mafia’ and of the state can be good for each other. Competition between organized crime and the state, however, typically reduces popular welfare and pushes the volume of banditry close to its anarchy level. Finally, we extend the basic model to allow the populace to form expectations of tax set by a long-lived king. Our relatively pessimistic conclusions about predatory states extend to this dynamic setting.
What is the relationship between an agent’s attitude towards information, and her attitude towards risk? If an agent always prefers more information, does this imply that she obeys the independence axiom? We provide a substitution property on preferences that is equivalent to the agent (intrinsically) liking information in the absence of contingent choices. We use this property to explore both questions, first in general, then for recursive smooth preferences, and then in specific recursive non-expected utility models. Given smoothness, for both the rank dependence and betweenness models, if an agent is information-loving then her preferences can depart from Kreps and Porteus’s (1978) temporal expected utility model in at most one stage. This result does not extend to quadratic utility. Finally, we give several conditions such that, provided the agent intrinsically likes information, Blackwell’s (1953) result holds; that is, she will always prefer more informative signals, whether or not she can condition her subsequent behavior on the signal.
We survey recent theoretical research on the effects of short-term share-price based marginal incentive schemes. Such schemes can induce inefficient managerial behaviour in both hidden action and hidden type contexts. These problems arise from informational asymmetries: managers take actions to manipulate the information flow rather than to maximize firm value. More generally, imperfect transmission of information between managers and shareholders or between managers of different firms can lead to similar distortions even when the parties’ interests are aligned.
We use a simple, graphical moral hazard model to compare monitored bank lending versus non-monitored bond issues as sources of external funds for industry. We contrast the conditions that theoretically favor each system, such as the size and number of firms, with conditions prevailing when these financial systems were developed during the British and German Industrial Revolutions. Then, to address the question why different systems have persisted, we embed the model in an entry game in which firm size and number are endogenous. We show that multiple equilibria can exist if financiers take the industrial structure as given and vice versa. Finally, we compare these equilibria in welfare terms.