Imprecise probabilistic beliefs as a context for decision-making under ambiguity

Coherent imprecise probabilistic beliefs are modeled as incomplete comparative likelihood relations admitting a multiple-prior representation. Under a structural assumption of Equidivisibility, we provide an axiomatization of such relations and show uniqueness of the representation. In the second part of the paper, we formulate a behaviorally general “Likelihood Compatibility” axiom relating preferences and probabilistic beliefs and characterize its implications for the class of “invariant biseparable” preferences that includes the MEU and CEU models among others.     

Differentiating ambiguity and ambiguity attitude

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a general decision model. We introduce a relation derived from the DM's preferences, called “unambiguous preference”, and show that it can be represented by a set of probabilities. We provide such set with a simple differential characterization, and argue that it is a behavioral representation of the “ambiguity” that the DM may perceive. Given such revealed ambiguity, we provide a representation of ambiguity attitudes. We also characterize axiomatically a special case of our decision model, the “α-maxmin” expected utility model.     

Underestimation of probabilities modifications: characterization and economic implications

The aim of this paper is to propose a behavioral characterization of individuals who underestimate probabilities modifications and to characterize this behavior in the standard preferences representation models under risk (expected utility, dual theory, rank dependent utility theory and MaxMin expected utility). Our main results are the following. Underreaction to probabilities modifications is in general independent from standard risk aversion and prudence. In models involving probabilities transformation functions, it is characterized by the slope of the probability transformation function. In the MaxMin expected utility model under risk, it is related to the weights of the maximal and minimal consequences in the preferences representation function. Considering a simple prevention decision, consisting in the reduction in the probability of a monetary loss, we show that individuals who underreact to probabilities modifications, invest less in prevention than individuals who objectively evaluate these modifications. Underreaction to probabilities modification is thus a possible explanation for low investment in prevention.     

Existence,uniqueness and some comparative statics for ratio and Lindahl equilibria

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost share or ratio equilibrium. Finally, we indicate how it may be exploited to facilitate comparative static analysis of Lindahl and cost share equilibria.      

A variable threshold band approach to measuring market linkages

Uncertain and changing economic conditions can have substantial effects on price relationships in spatially separated, linked markets. Although numerous studies have analysed price relationships to characterize market linkage structures, most assume that the relationships and associated linkages are time invariant. This study extends the literature by modelling and estimating time-dependent market linkages that are conditional on changes in exogenous factors. The methodology is used to investigate price relationships in North Carolina (NC) corn and soya bean markets. Empirical results indicate that generalized market-linkage models provide a better representation of price relationships over time, improving the understanding of price discovery dynamics and marketing strategies.     

Ambiguity Without a State Space

Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyses a third domain of preference: sets of consequential lotteries. Using this domain, we develop a theory of objective ambiguity without explicit reference to any state space. We characterize a representation that integrates a non-linear transformation of first-order expected utility with respect to a second-order measure. The concavity of the transformation and the weighting of the measure capture ambiguity aversion. We propose a definition for comparative ambiguity aversion.     

Probabilistic assignment of objects: Characterizing the serial rule

We study the problem of assigning a set of objects to a set of agents, when each agent receives one object and has strict preferences over the objects. In the absence of monetary transfers, we focus on the probabilistic rules, which take the ordinal preferences as input. We characterize the serial rule, proposed by Bogomolnaia and Moulin (2001) [2]: it is the only rule satisfying sd efficiency, sd no-envy, and bounded invariance. A special representation of feasible assignment matrices by means of consumption processes is the key to the simple and intuitive proof of our main result.     

The dual theory of the smooth ambiguity model

This paper studies the “dual” theory of the smooth ambiguity model introduced by Klibanoff et al. (Econometrica 73:1849–1892, 2005). Unlike the original model, we characterize attitudes toward ambiguity captured by second-order probabilities. First, we give a set of axioms to derive a dual representation of the smooth ambiguity model. Second, we present a characterization of ambiguity aversion. Last, as an application of our dual model to a portfolio problem, we conduct comparative static predictions which give sufficient conditions to guarantee that an increase in smooth ambiguity aversion decreases the optimal portfolio.     

David Hume's model of man: Classical political economy as “inspired” political economy

Abstract

The purpose of this paper is to analyse David Hume's model of man. We show that three major elements characterize his representation of man: first the weaknesses and limitations of human rationality; second, the psychological foundations of human behaviour, with a particular focus on the role of association in human cognition; and third, the collective dimension of individual learning through a process of communication based on sympathy. Therefore, we show that the theory of human nature and human cognition Hume proposes is different from the narrow view of man as homo ?conomicus that is used by mainstream economists.     

Minimal belief change, Pareto-optimality and logical consequence

Summary. A rational agent changes her beliefs in response to new information; a widely held idea is that such belief changes should be minimal. This paper is an overview of the theory of minimal belief revision. I employ a decision-theoretic framework to compare various principles for minimal belief revision. The main topics covered include the AGM postulates for belief revision, belief contraction, Grove's representation theorem, axioms for conditionals, and the connections between minimal belief change and questions in formal logic. I characterize under what conditions belief revision functions are consistent with the Levi Identity, and under what conditions belief contraction functions are consistent with the Harper Identity. Received: August 20, 2000; revised version: March 19, 2001     

An axiomatic approach to choice under uncertainty with catastrophic risks

This paper analyses decision under uncertainty with catastrophic risks, and is motivated by problems emerging from global environmental risks. These are typically low-probability events with major irreversible consequences. For such risks, the Von Neumann–Morgenstern (NM) axioms for decision making under uncertainty are not appropriate, since they are shown here to be insensitive to low-probability events. The paper introduces an alternative set of axioms requiring sensitivity to both low- and large-probability events. Through a new representation theorem in functional analysis, the results characterize all the operators whose maximization leads to the fulfillment of these axioms. They involve a convex combination of expected utility and a criterion based on the desire to avoid low probability and potentially catastrophic events. It is shown that the new axioms help resolve the Allais paradox. Open questions about risk aversion, games under uncertainty and calculus of variations are discussed.     

Multidimensional generalized Gini indices

Summary. The axioms that characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.Received: 20 August 2003, Revised: 26 May 2004, JEL Classification Numbers: D63. Correspondence to: John A. WeymarkWe are grateful to our referee for his or her comments.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

Attitude toward imprecise information

This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability–possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors—just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153]. However, unlike the MEU representation, the representation here also delivers a mapping, , which links the probability–possibility set, describing the available information, to the set of revealed priors. The mapping is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability–possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability–possibility set, i.e., is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the “mean value” of the probability–possibility set, and (ii) shrinking the probability–possibility set toward the mean value to a degree determined by preferences.     

Ordinal aggregation and quantiles

Consider the problem of aggregating a profile of interpersonally comparable utilities into a social utility. We require that the units of measurement of utility used for agents is the same as the units of measurement for society (ordinal covariance) and a mild Pareto condition (monotonicity). We provide several representations of such social aggregation operators: a canonical representation, a Choquet expectation representation, a minimax representation, and a quantile representation (with respect to a possibly non-additive set function on the agents). We also isolate an additional condition that gives us a quantile representation with respect to a probability measure, in both the finite and infinite agents case.     

Local representation and strategic voting: Evidence from electoral boundary reforms

We analyze whether voters value local political representation by exploiting municipal mergers, which increase the number of candidates available to voters and intensify political competition. In the Finnish open-list proportional representation system, voters rank the candidates within parties, and thus, concentrating votes to local candidates increases the extent of local representation. Using a difference-in-differences strategy, we find that the vote distributions become more concentrated in municipalities less likely to gain local representation after the mergers. Moreover, the effect is much larger in municipalities where the benefits of local representation to voters are large. The latter result disentangles voters' responses from the responses of other political actors. The results are important also for designing local government mergers, which are an important policy tool in many countries. They highlight that concerns over deteriorating local democracy due to mergers have merit, because voters have preferences for local representation. At the same time, the vote concentration patterns we find alleviate these concerns.     

Ranking investment projects

Summary. This paper describes conditions under which one investment project dominates a second project in terms of net present value, irrespective of the choice of the discount rate. The resulting partial ordering of projects has certain similarities to stochastic dominance. However, the structure of the net present value function leads to characterizations that are quite specific to this context. Our theorems use Bernstein's (1915) innovative results on the representation and approximation of polynomials, as well as other general results from the theory of equations, to characterize the partial ordering. We also show how the ranking is altered when the range of discount rates is limited or the rate varies period by period. Received: January 5, 2002; revised version: October 29, 2002 RID="*" ID="*" We thank Robert Driskill, Andrea Maneschi, Roy Radner, and participants of seminars at NYU, Notre Dame, Purdue, and Washington University for helpful comments. The present version of the paper has benefited from comments by a referee and the editor. Foster is grateful for support from the John D. and Catherine T. MacArthur Foundation through its network on Inequality and Poverty in Broader Perspective. Correspondence to: T. Mitra     

Female political representation and substantive effects on policies: A literature review

The share of women in political offices has increased considerably over the past few decades in almost every country in the world. Does this matter for policy outcomes? This is the first paper to provide a literature review on the substantive effects of female representation on policies. In developing countries, the increase in female political representation has caused a better provision of public goods, especially with regard to education and health. In developed countries, higher female representation has not affected public policies as measured by spending patterns. However, more recent evidence shows that female representation has induced changes in parliamentary deliberations and specific policy choices (e.g. more public child care) that may not be reflected in the observable composition of public spending. Finally, higher female representation has improved institutional quality by reducing corruption and rent-extraction by those in power.     

Political openness and armed conflict: Evidence from local councils in Colombia

In this paper, I empirically investigate how the openness of political institutions to diverse representation can impact conflict-related violence. Regression discontinuity estimates that exploit plausibly exogenous variations in the number of councillors in Colombian municipalities show that political openness substantially decreases conflict-related violence, namely the killing of civilian non-combatants. Empirical evidence suggests that the lower level of political violence stems from parties with close links to armed groups having greater representation on larger municipal councils. Using data about the types of violence employed by these groups, and government representation, I argue that armed violence has decreased not because of power-sharing arrangements involving armed groups linked to the parties with more political representation, but rather because armed groups with more political power deter other groups from initiating certain types of violence.