Generic impossibility of Arrow’s impossibility theorem

Our major objective is to show that if there are infinitely many alternatives and society can be decomposed into the sum of two non-negligible coalitions, the set of all Arrovian collective choice rules that satisfy the ultrafilter property (its set of decisive coalitions form an ultrafilter), is nowhere dense in the set of all Arrovian collective choice rules. This result entails that (1) almost all Arrovian collective choice rules are non-dictatorial and (2) in any neighborhood of a dictatorial Arrovian collective choice rule, a nondictatorial Arrovian collective choice rule can be found, i.e., the property of admitting a dictator is not a locally stable property for Arrovian collective choice rules in the sense that the property does not withstand a small perturbation.     

Limiting Dictatorial rules

We consider the preference aggregation problem in infinite societies. In our model, there are arbitrarily many agents and alternatives, and admissible coalitions may be restricted to lie in an algebra. In this framework (which includes the standard one), we characterize, in terms of Strict Neutrality, the Ultrafilter Property of preference aggregation rules. Based on this property, we define the concept of Limiting Dictatorial rules, which are characterized by the existence of arbitrarily small decisive coalitions. We show that, in infinite societies which can be well approximated by finite ones, any Arrovian rule is limiting.     

Strategy-proof fuzzy aggregation rules

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategy-proof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategy-proof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.     

Reduction-consistency in collective choice problems

We consider the problem of choosing a subset of a feasible set over which each agent has a strict preference. We propose an invariance property, reduction-consistency, of choice rules and study its implications. The property is a natural expression for the problems of a general principle of consistency having been studied extensively in resource allocation problems. We show that no scoring rule satisfies reduction-consistency, and base a characterization of the top rule on the property. We also investigate the minimal extension of a rule needed to recover reduction-consistency, and identify the minimal extensions of several rules including the Borda and plurality rules.     

Weighted majoritarian rules for the location of multiple public facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on efficiency, object-population monotonicity and sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically — anonymity — respects some form of coherence across collective decision problems — reinforcement — and only depends on peak information — peak-only — is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the interest groups and specific weights attached to locations. We give an explicit account of the richness of this class of rules.     

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

We consider the problem of finding an efficient and fair ex-ante rule for division of an uncertain monetary outcome among a finite number of von Neumann–Morgenstern agents. Efficiency is understood here, as usual, in the sense of Pareto efficiency subject to the feasibility constraint. Fairness is defined as financial fairness with respect to a predetermined pricing functional. We show that efficient and financially fair allocation rules are in one-to-one correspondence with positive eigenvectors of a nonlinear homogeneous and monotone mapping associated to the risk sharing problem. We establish relevant properties of this mapping. On the basis of this, we obtain a proof of existence and uniqueness of solutions via nonlinear Perron–Frobenius theory, as well as a proof of global convergence of the natural iterative algorithm. We argue that this algorithm is computationally attractive, and discuss its rate of convergence.     

ON THE UNIMODALITY OF GENERALIZED POISSON DISTRIBUTION

Abstract. The unimodality property is very important in many statistical problems. In this paper, it is shown that the generalized Poisson distribution is unimodal. Upper and lower bounds to the mode are given.     

On stable rules for selecting committees

A voting rule is said to be stable if it always elects a fixed-size subset of candidates such that there is no outside candidate who is majority preferred to any candidate in this set whenever such a set exists. Such a set is called a Weak Condorcet Committee (WCC). Four stable rules have been proposed in the literature. In this paper, we propose two new stable rules. Since nothing is known about the properties of the stable rules, we evaluate all the identified stable rules on the basis of some appealing properties of voting rules. We show that they all satisfy the Pareto criterion and they are not monotonic. More, we show that every stable rule fails the reinforcement requirement.     

Linear learning in changing environments

The decision maker receives signals imperfectly correlated with an unobservable state variable and must take actions whose payoffs depend on the state. The state randomly changes over time. In this environment, we examine the performance of simple linear updating rules relative to Bayesian learning. We show that a range of parameters exists for which linear learning results in exactly the same decisions as Bayesian learning, although not in the same beliefs. Outside this parameter range, we use simulations to demonstrate that the consumption level attainable under the optimal linear rule is virtually indistinguishable from the one attainable under Bayes’ rule, although the respective decisions will not always be identical. These results suggest that simple rules of thumb can have an advantage over Bayesian updating when more complex calculations are more costly to perform than less complex ones. We demonstrate the implications of such an advantage in an evolutionary model where agents “learn to learn.”     

Opportunity Evaluation as Rule‐Based Decision Making

We draw from cognitive science literature on rule‐based thinking to develop and empirically test a theoretical framework of entrepreneurial opportunity evaluation. We argue that entrepreneurs make use of socially constructed rules to discern the attractiveness of an opportunity, for them, specifically. Using conjoint analysis data of 498 decisions made by 62 entrepreneurs, we find that entrepreneurs' use of rules regarding opportunity novelty, resource efficiency, and worst‐case scenario significantly influences entrepreneurs' evaluations of opportunities and that individual differences in opportunity market and technology knowledge augment the effect of the rules on opportunity attractiveness. Additionally, we document that the worst‐case scenario diminishes the positive effect of other rule criteria (e.g. novelty, resource efficiency) on opportunity evaluation and that market and technology knowledge further influence the negative effects of the worst‐case scenario.     

Why and How Do Employees Break and Bend Confidential Information Protection Rules?

Organizations cannot function effectively if their employees do not follow organizational rules and policies. In this paper, we explore why and how employees in two high‐tech organizations often broke or bent rules designed to protect their employers' confidential information (CI). The CI protection rules sometimes imposed requirements that disrupted employees' work, forcing employees to choose between CI rule compliance and doing their work effectively and efficiently. Employees in these situations often broke the rules or bent them in ways that enabled employees to meet some of the rules' requirements, while also satisfying other expectations that they faced. We discuss implications of our findings for practice and for future organizational scholarship on rule following.     

城市制度:城市发展的核心构架

讨论了城市制度的本质、结构、功能及我国城市的发展模式 ,提出城市制度不完善是我国城市发展滞后的重要原因 ;建构与转换城市制度是城市发展进入自觉阶段的根本标志。我国城市要实现跨越式发展 ,应以制度创新为先导     

A test for multimodality of regression derivatives with application to nonparametric growth regressions

This paper presents a method to test for multimodality of an estimated kernel density of derivative estimates from a nonparametric regression. The test is included in a study of nonparametric growth regressions. The results show that in the estimation of unconditional β‐convergence the distribution of the partial effects is multimodal, with one mode in the negative region (primarily OECD economies) and possibly two modes in the positive region (primarily non‐OECD economies) of the estimates. The results for conditional β‐convergence show that the density is predominantly negative and there is mixed evidence that the distribution is unimodal. Copyright © 2009 John Wiley & Sons, Ltd.     

On properties of division rules lifted by bilateral consistency

We consider the problem of adjudicating conflicting claims in the context of a variable population. A property of rules is “lifted” if whenever a rule satisfies it in the two-claimant case, and the rule is bilaterally consistent, it satisfies it for any number of claimants. We identify a number of properties that are lifted, such as equal treatment of equals, resource monotonicity, composition down and composition up, and show that continuity, anonymity and self-duality are not lifted. However, each of these three properties is lifted if the rule is resource monotonic.     

A policy-based rationalization of collective rules: Dimensionality,specialized houses,and decentralized authority

We offer a policy-basis for interpreting, justifying, and designing (3, 3)-political rules, a large class of collective rules analogous to those governing the selection of papers in peer-reviewed journals, where each referee chooses to accept, reject, or invite a resubmission of a paper, and an editor aggregates his own and referees’ opinions into one of these three recommendations. We prove that any such rule is a weighted multicameral rule: a policy is collectively approved at a given level if and only if it is approved by a minimal number of chambers — the dimension of the rule — where each chamber evaluates a different aspect of the policy using a weighted rule, with each evaluator’s weight or authority possibly varying across chambers depending on his area(s) of expertise. These results imply that a given rule is only suitable for evaluating finite-dimensional policies whose dimension corresponds to that of the rule, and they provide a rationale for using different rules to pass different policies even within the same organization. We further introduce the concept of compatibility with a rule and exploit its topological properties to propose a method to construct integer weights corresponding to evaluators’ possible judgments under a given rule, which are more intuitive and easier to interpret for policymakers. Our findings shed light on multicameralism in political institutions and multi-criteria group decision-making in the firm. We provide applications to peer review politics, rating systems, and real-world organizations.     

On probability models in voting theory

This paper illustrates the use of probability models to study properties of voting rules. In particular, a simple occupancy distribution and its limiting Dlrichlet form are introduced, corresponding to simplifying assumptions about voters' preferences. We use as illustrations the occurrence probability of the Condorcet Paradox, a vintage problem in social choice theory, along with the related concept of Condorcet efficiency, a measure of goodness for voting rules. Further examples include properties of a lottery rule and the vulnerability of certain voting rules to strategic manipulation. Prospects for future work are indicated.     

Note on ‘Loss of monetary discretion in a simple dynamic policy game’

Jensen (1994a) finds that loss of monetary discretion leads to lower welfare. However, by extending his model we show that if real base money holdings are relatively low, as is likely to be the case for modern economics, a zero-inflation rule may well be preferable to monetary discretion. If the emphasis on achieving the output and public spending targets falls, a zero-inflation rule is more likely to be preferred. The increased support for binding policy rules thus conforms with a less tolerant attitude towards inflation.     

The Theory of Socially Embedded Games: The Mathematics of Social Relationships,Rule Complexes,and Action Modalities

In their classic work, Von Neumann and Morgensterndefined a game as simply the totality of the rules which describe it. Theydid not, however, elaborate a theory of rules. Such considerations lead toconceptualizing rules and rule configurations as mathematical objects, specifyingthe principles for combining rules, developing the theory of revising,replacing, and, in general transforming rules and rule complexes. Themathematics is based on contemporary developments at the interface ofmathematics, logic, and computer science. This article, drawing on themathematical theory of rules and rule complexes, extends and generalizes gametheory (GGT). The theory of rule complexes is used to conceptualize andanalyze diverse social relationships, roles, and games as particulartypes of rule complexes. A social role, for instance, is the major basisof an individual's action in a game. It consists of at least four majorcomponents – which are mathematical objects – in the determinationof action: value complex, model of reality (including beliefs and knowledgebases), a repertoire of acts, routines, programs, and strategies, and modalities,role-specific algorithms for determininig or generating action in gamesettings. The article focuses on three types of action modality routineor habitual, normative, andinstrumental modalities. The theory: (1) provides a cultural/institutionalbasis for a theory of gameswhere games, social relationships, and rolesare formalized in terms of rule complexes; (2) explains human action as a formof rule application or rule-following action, which underlies allmodalities of action; (3) formulates the theory that actors construct an action or make choices amongalternative actions by making comparisons and judging similarity (ordissimilarity) between an option or options considered and their norms and values,and, in general, determine whether or not, and to what degree, a value,norm, or goal will be realized or satisfied; (4)reconceptualizes ``game' as a social form and makes a distinction between open and closed games.     

Efficiency in complementary partnerships with competition

The objective of this paper is to show how efficiency can be implemented in a market with strictly complementary inputs when the productive firms undertake unobservable effort. The observable output is a joint undertaking by a partnership consisting of two types of firms. It is shown that simple linear sharing rules cannot implement socially optimal effort, but a modified linear sharing rule can implement the first‐best outcome provided that commitment to the proposed sharing rule is possible. This is so even when the sharing rule is proposed by one of the active partners. When opening up for the possibility of renegotiating sharing contracts that have undesirable properties for one or more of the firms, it becomes more difficult to implement socially efficient solutions. Implementation of the socially efficient outcome requires that the sharing rule is proposed by an outsider to the partnership. Copyright © 2008 John Wiley & Sons, Ltd.     

The Borda class: An axiomatic study of the Borda rule on top-truncated preferences

The Borda rule, originally defined on profiles of individual preferences modelled as linear orders over the set of alternatives, is one of the most important voting rules. But voting rules often need to be used on preferences of a different format as well, such as top-truncated orders, where agents rank just their most preferred alternatives. What is the right generalisation of the Borda rule to such richer models of preference? Several suggestions have been made in the literature, typically considering specific contexts where the rule is to be applied. In this work, taking an axiomatic perspective, we conduct a principled analysis of the different options for defining the Borda rule on top-truncated preferences.