On some suggestions for having non-binary social choice functions

The various paradoxes of social choice uncovered by Arrow [1], Sen [10] and others have led some writers to question the basic assumption of a binary social choice function underlying most of these paradoxes. Schwartz [8], for example, proves an important theorem which may be considered to be a generalization of the famous paradox of Arrow, and then lays the blame for this paradox on the assumption of a binary social choice function. He then proceeds to define a type of choice functions which, like binary choice functions, define the best elements in sets of more than two alternatives on the basis of binary comparisons, but which, as he claims, have an advantage over binary choice functions, in so far as they always ensure the existence of best elements for sets of more than two alternatives irrespective of the results of binary comparisons. The purpose of this paper is to show that even a considerable weakening of the assumption of a binary social choice function does not go very far towards solving some of the paradoxes under consideration, and that if replacing the requirement of a binary social choice function by a Schwartz type social choice function solves these paradoxes, it does so only by violating the universally acceptable value judgment that in choosing from a set of alternatives, society should never choose an alternative which is Pareto inoptimal in that set (i.e., the socially best alternatives in a set should always be Pareto optimal). This argument is substantiated with the help of an extended version of Sen's [10] paradox of a Paretian liberal, and thus a by-product of our analysis is a generalization of the theorem of Sen [10]. The argument itself, however, is more general and applies also to the impossibility result proved by Schwartz [8].We are extremely grateful to Amartya Sen for his helpful comments.

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Implementation without rationality assumptions

Hurwicz (Social Choice and public decision making. Essays in honor of Kenneth J. Arrow, Cambridge University Press, Cambridge, 1986) was the first to study an approach to implementation theory based on choice functions instead of preference relations. We argue that the solution concept used by him, the generalized Nash equilibrium, is not really compatible with the idea that individual behavior is describable by a choice function. A new solution concept that better fits the choice function framework is then introduced. Using this, we investigate what behavioral assumptions are needed for the full characterizations of Nash implementable social choice correspondences to still hold. We will show that a condition known as Property α is central.     

现代国有企业制度与管理层的外部选择

政府对国有企业管理层的外部选择既不是现代国有企业制度不完善的表现,也不可能取代国有企业的制度改革,相反,外部选择和现代企业制度特别是企业治理结构都是保证国有企业性质和绩效不可或缺的有机组成部分.只有二者形成事前选择与事后监督的动态制约体系,才能克服国有企业中的制度失灵和管理者行为的不一致性问题.事实表明,国有企业管理者行为的不一致的原因主要在于国有企业制度不完善,因而改正的办法是深化制度改革,而不是简单地代之以强化外部选择.     

Aggregation theorems and multidimensional stochastic choice models

In many choice situations, the options are multidimensional. Numerous probabilistic models have been developed for such choices between multidimensional options and for the parallel choices determined by one or more components of such options. In this paper, it is assumed that a functional relation exists between the choice probabilities over the multidimensional options and the choice probabilities over the associated component unidimensional options. It is shown that if that function satisfies a marginalization property then it is essentially an arithmetic mean, and if the function satisfies a likelihood independence property then it is a weighted geometric mean. The results are related to those on the combination of expert opinion, and various probabilistic models in the choice literature are shown to have the geometric mean form.     

Reference Wealth Effects in Sequential Choice

It is argued that in order to accommodate experimentally-observed choice patterns, it is not enough to model the utility function as being dependent on changes from a reference wealth point. Instead, individuals should be modeled as treating decisions as part of an identifiable sequence of decisions, and utility should be a function of reference wealth, income so far from the sequence, and payoffs from the current decision. The three-argument utility function allows for risk aversion over gains and risk seeking over losses for the first choice in the sequence, and for the house money and break-even effects in later decisions.     

Rationality and Order-Dependent Sequential Rationality

We show that an individual using a choice function is sequentially rational and the decisions he makes are independent of the order of implementation of the rationales if and only if he is rational with the union of the rationales as a base binary relation. When he makes his decisions following a choice correspondence, the sufficiency part of this claim still holds, the necessity part of it does not.      

Common ratio using delay

We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing.     

Choice and constraint in budget-making

A theory of the budgetary process within public resource allocation has to recognize that decision rules may vary over time and program. Our findings based on a new econometric approach indicate that various different decision mechanisms operate in different categories of public resource allocation. Variation over time is particularly difficult to accommodate within the incrementalist approach as incremental decision rules imply structural stability over time. We find the opposite to be true of the programs analysed.A model of the public expenditure process has to take choice into account to a larger extent. The attempt to make budget-making a function of constraints violates the occurrence of shiftpoints that is typical of the data. The existence of a base and the resort to mechanical rules for the derivation of the yearly increments implies a deterministic interpretation of budgetary behavior. Budgets are made in choice processes where the principal actors employ various decision rules meaning that budget-making is more voluntaristic than deterministic. The choice rules employed for the derivation of requests and appropriations are not mechanistic decision rules.     

The aggregation of preferences: can we ignore the past?

The article shows that a Paretian social welfare function can be history independent and time consistent only if a stringent set of conditions is verified. Individual utilities must be additive. The social welfare function must be a linear combination of these utilities. Social preferences are stationary only if, in addition, all individuals have the same constant discount rate. The results are implemented in two frameworks: deterministic dynamic choice and dynamic choice under uncertainty. The applications highlight that the conditions are unlikely to be met by individual preferences, and that they severely restrict social preferences.     

Subjective Probability Weighting and the Discovered Preference Hypothesis

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. I thank Peter P. Wakker for useful comments and suggestions.     

Weakly implementable social choice rules

Previous investigations have shown that a social choice function which is partially implementable must be characterized by pervasive veto power. This paper investigates how much additional latitude in the design of social choice functions, and how much relief from this vetoers result, can be achieved by examining multi-valued social choice rules and relaxing the requirement of partial implementability to a requirement that we call weak partial implementability. We find that the power structures which characterize partially implementable social choice functions, including the veto properties, also characterize weakly partially implementable social choice rules. The conclusion is that invoking multi-valuedness and implementation of appealing social choice rules in strong Nash equilibria. Our results apparently exhaust the possibilities for implementation in strong Nash equilibrium. If any implementation possibility results are to be achieved, they can apparently come only by weakening the equilibrium requirement.     

Hidden information acquisition and static choice

This note explores the consequence of hidden information acquisition for static choice theory. We show that any choice function in the observable problem can be consistent with some well-behaved choice function in a metaproblem with unobservable costly information acquisition. This illustrates how choices may not satisfy consistency conditions because a decision maker's decision process (in this case, information acquisition) depends on her feasible set. It also illustrates the importance of modeling the source of violations of consistency conditions, rather than simply weakening axioms on preferences.     

R&;D cooperation in emerging industries,asymmetric innovative capabilities and rationale for technology parks

Starting from the premise that firms are distinct in terms of their capacity to create innovations, this article explores the rationale for R&D cooperation and the choice between alliances that involve information sharing, cost sharing or both. Defining innovative capability as the probability of creating an innovation, it examines firm strategy in a duopoly market, where firms have to decide whether or not to cooperate to acquire a fixed cost R&D infrastructure that would endow each firm with a firm-specific innovative capability. Furthermore, since emerging industries are often characterized by high technological uncertainty and diverse firm focus that makes the exploitation of spillovers difficult, this article focuses on a zero spillover context. It demonstrates that asymmetry has an impact on alliance choice and social welfare, as a function of ex-post market competition and fixed costs of R&D. With significant asymmetry no alliance may be formed, while with similar firms the cost sharing alliance is dominant. Finally, it ascertains the settings under which the equilibrium outcome is distinct from that maximizing social welfare, thereby highlighting some conditions under which public investment in a technology park can be justified.     

Are Quasi‐markets in Education what the British Public Wants?

In the context of inconclusive evidence on the extrinsic successes of quasi‐markets, policy defences of school choice and competition in education have often discussed the intrinsic, empowering value of choice for consumers, arguing that school choice for parents is ‘what people want’. Discourses often imply that choice is desired for its own sake rather than merely as a means by which families can escape what are deemed to be poor quality schools. Support for an idealistic, abstract notion of ‘choice’ is also taken to imply support for quasi‐markets overall and is not considered alongside possible competing values that people may hold at the same time as they value choice. Additionally, views of parents are often examined without considering possible differences in views between parents and non‐parents. Contributing to debates about how far a public desire exists for quasi‐markets in education, this article draws on data from newly designed questions fielded as part of the 2010 British Social Attitudes survey. The article finds that while choice ‘in the abstract’ is supported widely by both parents and non‐parents (albeit slightly more so by parents), a valuing of choice among the British public appears to be more instrumental than intrinsic – potentially problematic given evidence on the extrinsic benefits of quasi‐markets is mixed. Support for choice is tempered among parents and non‐parents by clear opposition to vouchers, school diversity, government spending on transport costs to facilitate choice and by strong support for the idea of sending children to the ‘nearest state school’.     

Rationality from a computational standpoint

A computationally viable choice function possesses, in addition to other important properties, adaptability - as new alternatives become feasible the set of best alternatives corresponding to the new feasible set can be located without having to reconsider previously rejected alternatives. Adaptability is shown to be closely related to, in fact characteristic of, the standard notions of rationality (expressed in terms of transitivity properties). Adaptability provides a generalization of conventional rationality and in addition leads to the choice function proposed by Schwartz, albeit from an entirely different route, that of computational viability.     

应对当下金融危机的财政政策效应及选择

财政政策是应对当下金融危机重要的政策手段,如何针对财政政策发挥功能的特性来选择有效的财政政策加以实施,是目前急需研究的议题。为此,以当下金融危机的特点及对中国经济影响的特征来确定财政政策的功能和取向,进而对具体实施的财政政策加以选择,是研究财政政策应对金融危机必须涉及的几项关键性内容。     

Revealed preference and linear utility

We study a Linear Axiom of Revealed Preference (LARP) that characterizes the consistency of a choice function with respect to a preference order satisfying the independence axiom. In addition, LARP characterizes lexicographic linear utility rationality when the choice space is a convex subset of a finite-dimensional real vector space, and LARP characterizes linear utility rationality when the choice space corresponds to a finite choice experiment.     

Even Risk-Averters may Love Risk

A decision maker bets on the outcomes of a sequence of coin-tossings. At the beginning of the game the decision maker can choose one of two coins to play the game. This initial choice is irreversible. The coins can be biased and the player is uncertain about the nature of one (or possibly both) coin(s). If the player is an expected-utility maximizer, her choice of the coin will depend on different elements: the nature of the game (namely, whether she can observe the outcomes of the previous tosses before making her next decision), her utility function, the prior distribution on the bias of the coin. We will show that even a risk averter might optimally choose a riskier coin when learning is allowed. We will express most of our results in the language of stochastic orderings, allowing comparisons that are valid for large classes of utility functions.