Lebesgue measure and social choice trade-offs

Summary An Arrovian social choice rule is a social welfare function satisfying independence of irrelevant alternatives and transitivity of social preference. Assume a measurable outcome spaceX with its (Lebesgue) measure normalized to unity. For any Arrovian rule and any fractiont, either some individual dictates over a subset ofX of measuret or more, or at least a fraction 1–t of the pairs of distinct alternatives have their social ordering fixed independently of individual preferences. Also, for any positive integer (less than the total number of individuals), there is some subsetH of society consisting of all but persons such that the fraction of outcome pairs (x, y) that are social ranked without consulting the preferences of anyone inH, whenever no individual is indifferent betweenx andy, is at least 1–1/4.We are grateful to Roy Mathias and Daniel Waterman for help with some technical matters, and to chairman Jim Follain and the Syracuse University Economics Department for financing the exchange that launched this project. Campbell's research was funded by National Science Foundation grants, SES 9007953 and SES 9209039.     

Another Graphical Proof of Arrow's Impossibility Theorem

Arrow's (1951) Impossibility Theorem is the idea that, given several well-known assumptions, the social orderings of particular alternatives that are meant to reflect individuals' preferences must match the preferences of an arbitrary individual (the dictator). A social-choice rule other than dictatorship is impossible. Following from Fountain (2000), the author presents another graphical proof of the theorem that is intended to be more accessible to students and teachers of economics. The principal strength of this approach is that the patterns of agreements and conflicts over all possible combinations of two individuals' rankings of alternatives are transparent; appreciating these patterns is the key to intuitively understanding Arrow's theorem. A self-test for readers (or a classroom exercise for students) is included.     

Preference revelation with a limited number of indifference classes

Suppose that g is a strategy-proof social choice rule on the domain of all profiles of complete and transitive binary relations that have exactly m indifference classes. If and the range of g has three or more members, then g is dictatorial. If m = 2, then for any set X of feasible alternatives, there exist non-dictatorial and strategy-proof rules that are sensitive to the preferences of every individual and which have X as range.     

Condorcet cycles in bipartite populations

Summary. Simple majority voting between pairs of alternatives is used to aggregate individual preferences. The occurence of Condorcet cycles is limited thanks to a principle of homogeneity on individual preferences. The restrictions induced on the domain of the latters are weak: among the n! possible orderings of n alternatives, more than one half are admissible within a domain. The resulting aggregated preference has then a neglectable probability of showing up cycles. We show moreover that the set of individual preferences can be `naturally' partitioned into two such domains. Received: June 17, 1996; revised version: April 15, 1997     

Characterization of the private alternatives domains admitting arrow social welfare functions

An n-person social choice problem is considered in which the alternatives are n dimensional vectors with the ith component of such a vector being the part of the alternative effecting individual i alone. Assuming that individuals are selfish (i is indifferent between any two alternatives that have the same ith component) we characterize all the families of permissible individual preferences that admit nondictatorial Arrow-type social welfare functions. We also show that the existence of such a function for a given family of preferences is independent of n provided that is greater than one.     

Public decisions: Solidarity and the status quo

A public decision model specifies a set of alternatives, a variable population, and a common set of admissible preferences. We study the implications of the principle of solidarity, for social choice functions in all such models. The principle says that when the environment changes, all agents not responsible for the change should either all weakly win, or all weakly lose. Under weak additional requirements, but regardless the domain of preferences, each of two formulations of this principle, population-monotonicity and replacement-domination, imply coalition-strategy-proofness; that the choice only depends on the set of preferences that are present in the society, but not on the number, nor on the labels of agents having particular preferences; and that there exists an alternative always weakly Pareto-dominated by the alternative selected by the rule. Replacement-domination is generally at least as strong as population-monotonicity.     

CONSUMPTION EXTERNALITIES, PREFERENCE CHANGES AND THE 'SAMARITAN'S DILEMMA'

This paper examines the desirability of an exogenously induced change in the preferences of individuals in an economy characterized by (i) asymmetrical, localized positive consumption externalities, (ii) private, non-market, negotiation-free transfers, and (iii) the ‘Samaritan's dilemma.’ A model is analysed in which a benefactor (individual 1) makes an unrestricted voluntary transfer to a beneficiary (individual 2) who ran use the transfer to increase 2's consumption of either a purely private good x or a good y that generates external benefits for 1. Once 1 makes a transfer to 2, 1 cannot control how 2 spends it. If 2 fails to take into account this externality, then good y is under consumed and a loss in social welfare results. When such externalities and their concomitant welfare losses arise, conventional solutions are frequently inappropriate, impractical or impossible. This power shows that exogenously inducing the adoption of new externality internalizing preferences by the benefactor and the beneficiary not only increases the benefactor's transfer and the beneficiary's consumption of good y but also produces a ‘socially superior’ state. The welfare improvement is measured in terms of a welfare criterion that is based on the initial and new preferences of each individual     

Scoring rules: an alternative parameterization

This note presents an alternative parameterization of any scoring rule that satisfies the score-expansion property. This parameterization is based on the vector that specifies, for every number of alternatives k, k ≥ 3, the minimal size of a coalition that can veto an alternative which is preferred by everybody outside the coalition. Our result sheds new light on the commonly used plurality and Borda rules, as well as the inverse plurality rule and any “vote for t alternatives rule”.     

Discounting Nordhaus

This paper evaluates Nordhaus's neoclassical complaints about the Stern Review from the vantage point of classical growth theory. Nordhaus criticizes the Stern Review because it uses a discount rate that is well below the market rate of return on capital. From the perspective of classical growth theory, Nordhaus's belief in choosing preference parameters for the social planner based on observed market rates of return is equivalent to assigning the preferences of the capitalist agents to the social planner. This equivalence is an implication of the Cambridge Theorem, which interprets the Ramsey equation as the saving function of the capitalist agents.     

Strategy-Proof Voting on Compact Ranges

Strategy-proof social choice functions are characterized for societies where the space of alternatives is any full dimensional compact subset of a Euclidean space and all voters have generalized single-peaked preferences. Our results build upon and extend those obtained for cartesian product ranges by Border and Jordan (1983). By admitting a large set of non-Cartesian ranges, we give a partial answer to the major open question left unresolved in this pioneering article. We prove that our class is composed by generalized median voter schemes which satisfy an additional condition, called the intersection property [Barberà, Massó, and Neme (1997)].Journal of Economic LiteratureClassification Number: D71.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

Quasitransitive social preference: why some very large coalitions have very little power

Summary. If only the strict part of social preference is required to be transitive then Independence of Irrelevant Alternatives implies that there is a coalition containing all but one individual that cannot force x to be socially ranked above y for at least half of the pairs of alternatives (x,y). Received: August 29, 1996; revised version: March 24, 1997     

Nash Equilibrium and Welfare Optimality

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A , where the subset is interpreted as the set of "welfare optima". A game form (or "mechanism") implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game form (implying, in particular, that a Nash equilibrium exists) and, (ii) all Nash equilibria are welfare optimal. The main result of this paper establishes that any SCR that satisfies two properties—monotonicity and no veto power—can be implemented by a game form if there are three or more individuals. The proof is constructive.     

A unifying impossibility theorem

This paper identifies and illuminates a common impossibility principle underlying a number of impossibility theorems in social choice. We consider social choice correspondences assigning a choice set to each non-empty subset of social alternatives. Three simple axioms are imposed as follows: unanimity, independence of preferences over infeasible alternatives, and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our axioms is serially dictatorial. A number of known impossibility theorems—including Arrow’s Impossibility Theorem, the Muller–Satterthwaite Theorem, and the impossibility theorem under strategic candidacy—follow as corollaries.     

Robustness of simple menus of contracts in cost-based procurement

We consider a model of cost-based procurement in which the principal faces Knightian uncertainty about the agent's preferences for cost reduction. We show that a particularly simple incentive scheme—a menu comprising a fixed-price contract and a cost-reimbursement contract—minimizes the maximum expected payment, where this maximum is taken over the set of possible agent preferences. For some parameters of the problem, a range of alternative incentive schemes also satisfy this criterion. We show that the simple incentive scheme is not weakly dominated by any of the alternatives: there does not exist an alternative mechanism for which the expected payment is no higher for all realizations of the agent's preferences and strictly lower for some realization.     

PERCEIVED INTENTIONALITY IN 2 × 2 EXPERIMENTAL GAMES

We test experimentally whether decisions in 2 × 2 games with mixed equilibria depend on the co‐player being nature or a human agent. Controlling for social preferences, we find differences in decisions in the chicken game and battle of the sexes but not for stag hunt and matching pennies. We attribute these to subjects' perception of the other's intentionality and disapproval avoidance in particular.     

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.     

Model Uncertainty, Optimal Monetary Policy and the Preferences of the Fed

Monetary policy in the US is characterized by a substantial degree of inertia. While in principle this may well be the outcome of an optimizing central bank behaviour, the ability of any derived policy rule to match the data relies on so large weights for interest rate smoothing into policy makers' preferences as to be theoretically flawed. In this paper we investigate whether such a puzzle can be interpreted as resulting from the concern of monetary authorities for potential misspecifications of the macroeconomic dynamics. Accordingly, we propose a novel thick modelling approach that incorporates model uncertainty into the identification of central bank's preferences. The thick robust policy rule shows the kind of smoothness observed in the data without resorting to implausible values for the preference parameters.     

Euclidean individual preference and continuous social preference

Assume a finite society, a standard space of allocations of public goods, and an open and connected domain of profiles of Euclidean individual preferences. (There is an additional technical restriction on the domain.) If a social welfare function f satisfies Arrow's independence axiom and generates social preferences that are continuous and transitive, then f is constant or dictatorial or inversely dictatorial.     

Adaptive Preferences and Capabilities: Some Preliminary Conceptual Explorations

The Capability Approach (CA) as developed by Amartya Sen and Martha Nussbaum, has in part been a response to the problem of adaptive preferences. Their argument says that people might adapt to certain unfavorable circumstances and any self-evaluation in terms of satisfaction or happiness will in this case necessarily be distorted. To evaluate people's well-being in terms of functionings and capabilities guarantees a more objective picture of people's life. Next to this strong criticism on subjective measurements of well-being, we observe an increasing interest in Subjective Well-Being (SWB) or Happiness studies that are included in the broader field of Hedonic Psychology. In this paper, we thus revise the original critique of adaptive preferences and compare it with a more detailed analysis of adaptation as it is presented in hedonic psychology. It becomes clear that adaptation can be a positive as well as a negative phenomenon and that the adaptive preference critique had a particular narrow view on adaptation. However, this does not mean SWB-research is not any longer susceptible to this critique. An alternative way to assess people's subjective well-being, but which could be considered to be more in line with the CA, is proposed by Daniel Kahneman's Objective Happiness. These are all relatively new considerations, especially in economics. Therefore much more research needs to be done on the positive and negative aspects of adaptation to understand its consequences on well-being – especially when evaluated within the capability-space.