Factoring out the impossibility of logical aggregation

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow's and arguably enhances its paradoxical value.     

A note on introducing a "zero‐line" of welfare as an escape route from Arrow's theorem

Since Sen's insightful analysis of Arrow's Impossibility Theorem, Arrow's theorem is often interpreted as a consequence of the exclusion of interpersonal information from Arrow's framework. Interpersonal comparability of either welfare levels or welfare units is known to be sufficient for circumventing Arrow's impossibility result. But it is less well known whether one of these types of comparability is also necessary or whether Arrow's conditions can already be satisfied in much narrower informational frameworks. This note explores such a framework: the assumption of (ONC + 0), ordinal measurability of welfare with the additional measurability of a "zero‐line", is shown to point towards new, albeit limited, escape routes from Arrow's theorem. Some existence and classification results are established, using the condition that social orderings be transitive as well as the condition that social orderings be quasi‐transitive.     

Neutrality in arrow and other impossibility theorems

Summary. Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.Received: 13 April 2000, Revised: 6 December 2002, JEL Classification Numbers: D71, C70.I thank Salvador Barberá, Luis Corchón, Cesar Martinelli, Eric Maskin, Tomas Sjöström, Ricard Torres, José Pedro Ubeda, and an anonymous referee for feedback. The proofs of Arrow's theorem and two Wilson's theorems come from a note I wrote in 1987 at Universitat Autónoma de Barcelona (Ubeda [16]). In 1996 Geanakoplos [7] wrote a proof of Arrow's theorem similar but not identical to mine. All work in this paper is independent of his.     

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.     

On the independence from irrelevant alternatives in probabilistic choice models

Probabilistic choice models often invoke a behavioral assumption referred to as the independence from irrelevant alternatives. The implications of this condition have not been fully developed in probabilistic choice contexts. It is well known that nonpathological preferences may not exhibit the independence from irrelevant alternatives, which is apparently an assumption of convenience; and the obvious question is then whether the assumption is very restrictive. This paper addresses this question. A common model of probabilistic choice is constructed. A measure of the likelihood that independence from irrelevant alternatives holds is seen to arise naturally in this model. Given this measure, it is demonstrated that the condition will almost always fail to hold.     

Revealed group preferences on non-convex choice problems

Summary. This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that while no continuous choice function can satisfy strong Pareto optimality over the class of all compact and comprehensive choice problems, strong Pareto optimality, Arrow's choice axiom, upper hemicontinuity and a weak compromisation postulate turn out to be necessary and sufficient to represent choice correspondences by continuous, strictly increasing and quasiconcave real-valued functions. Some applications of our main findings to axiomatic bargaining theory are also studied. Received: December 2, 1996; revised version: February 27, 1998     

The economic implications of learning-by-doing for population size and growth

This paper criticizes Arrow's research on learning-by-doing. The authors use a model like Arrow's to conclude that population growth--and, even more important, population size--may have positive effects on economic growth through positive effects on the rate of technical progress, on reasonable assumptions about the likely capital-output ratios with different demographic structures, but negative effects with other capital-output ratio difference. In a comparison of 2 worlds that have different population sizes, but that are otherwise alike including their capital-labor ratios and the initial per worker outputs, the larger world will come to have higher per worker output because of learning-by-doing. This conclusion is unlike the conclusion implicit in Arrow's model of learning-by-doing because Arrow looked at steady-state rates of growth rather than changes in the level of income from the starting point. Arrow's analysis also is confused by using the capital stock rather than cumulative output as the measure of experience, though output is the variable used in the empirical analyses that are the basis of this line of work.     

Arrow's Possibility Theorem for one-dimensional single-peaked preferences

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow's requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2^N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave.     

The impossibility of a weakly path independent Paretian liberal

This paper shows that the conflict between two well cherished values related to moral and political philosophy, namely the Pareto optimality and the libertarian principle, cannot be resolved as long as a social choice function is required to satisfy a rationality-consistency condition which ensures some kind of path independence, however, weak.     

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.     

A note on the independence of irrelevant alternatives in probabilistic choice models

The purpose of this note is to show that there is no necessary relationship between the independence of irrelevant alternatives (IIA) property and stochastic independence of the errors in probabilistic choice models.     

On the frontier between possibility and impossibility theorems in social choice

This paper attemts to make precise the frontier between possibility and impossibility theorems in social choice. It is shown that some criterion of rejection of some alternative is the critical factor. In the absence of such a condition, it is possible to construct a fairly wide class of “democratic” decision rules which satisfies a class of consistency conditions. Any one of these, together with the criterion of rejection, generates a power structure similar to the ones discovered by Arrow, Gibbard, and others when the decision rule is required to satisfy the weak Pareto principle and the independence condition.     

The strategy-proof provision of public goods under congestion and crowding preferences

We examine the strategy-proof provision of excludable public goods when agents care about the number of other consumers. We show that strategy-proof and efficient social choice functions satisfying an outsider independence condition must always assign a fixed number of consumers, regardless of individual desires to participate. A hierarchical rule selects participants and a generalized median rule selects the level of the public good. Under heterogeneity in agents’ views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.     

Knowledge, economic geography, and growth in a two-group island economy

This paper proposes a two-group urban model with endogenous capital and knowledge accumulation in an isolated island economy. The model examines the dynamic interdependence among knowledge utilization, creativity, transportation conditions, savings behavior, location choice, and residential pattern in a just two-group island economy. Although it is constructed with some strict assumptions, the model is quite general in the sense that the well-known models, such as the Solow-Swan model, the Kaldor-Pasinetti two-group model, and the Alonso model, can be considered, from a structural point of view, as its special cases. The knowledge accumulation in our model is based upon Arrow's learning-by-doing model. It is proved that the system may have a unique or multiple equilibria and each equilibrium may be stable or unstable, depending upon knowledge utilization and creation characteristics of the two groups. We also examine the impact of changes in the population and knowledge creation efficiency of two groups on long-run growth, wealth distribution, and residential structure.     

Judgment aggregation: (im)possibility theorems

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore suggest restricting independence to “premises”, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent.     

The optimal choice of central bank independence and conservatism under uncertainty

This paper examines the optimal monetary delegation arrangement of central bank independence and conservatism in the presence of uncertainty about the central bank’s output objective. We show that full independence is no longer optimal with uncertain central bank preferences, and that optimal delegation involves the choice of both independence and conservatism. Further, we find that the usual trade-off between independence and conservatism no longer necessarily holds. Consequently, high central bank independence may also require a high level of conservatism.     

The Supporting Line Property and the Additive Choice Function for Two-Dimensional Choice Problems

The paper provides an axiomatic characterization of the additive choice function using the additivity property. It is seen that, along with Pareto optimality, symmetry, and a supporting line property, the additivity axiom uniquely characterizes the additive choice function. The additive choice function as defined in this paper does not satisfy Nash's assumption of the independence of irrelevant alternatives. This raises the question of when a choice function is representable, an issue addressed in an appendix.     

公司治理与管理层机会主义会计选择——基于新会计准则的实证分析

2007年1月1日开始实施的新会计准则为上市公司提供了更多的会计选择空间,诱发了管理层的机会主义动机。本文以新会计准则下金融资产分类为例,结合2007～2008年中国A股上市公司数据,实证检验了公司治理安排对管理层机会主义会计选择的影响。研究发现,国家控股和两职合一的公司更倾向于机会主义会计选择,独立董事比例和管理层持股比例与机会主义会计选择显著负相关。并且,独立董事和股权激励制度对管理层机会主义会计行为的约束作用在国有企业中更加显著。本研究丰富了会计选择的研究文献,有助于监管部门了解新会计准则的实施效果及影响机制。     

Do Capital Controls Enhance Monetary Independence?

International monetary policy trilemma—the tradeoff among exchange rate stability, monetary independence, and unrestricted capital mobility—is an important constraint for policy makers in an open economy. This paper investigates an aspect of the hypothesis that has received relatively less attention: whether a decrease in capital mobility through imposition of capital controls, while holding the degree of exchange rate stability constant, will enhance monetary independence. Using a panel dataset covering 88 countries for the 1995–2010 period and the generalized method of moments (GMM) estimation, we find that: (1) capital controls help improve a country's monetary independence; (2) the effectiveness of capital controls depends on the types of assets and the direction of flows that are imposed; and (3) the choice of exchange rate regime has an important impact on the effectiveness of capital controls on monetary independence.     

The Possibility of Issue-Specific Decisions on Multiple Social Choice Issues

This paper considers an aggregation rule when each alternative consists of elements of multiple issues. I assume that each issue-specific aggregation rule can be applied to each issue and explore whether various different issue-specific aggregation rules are compatible. When the set of alternatives has some structure (which we call a set connected by loops), there exists a powerful individual whose preference always coincides with the social ordering in every issue. As a corollary, Arrow's General Possibility Theorem is obtained.