Invoking a Cartesian product structure on social states

The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard’s and Sen’s paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. We then apply these notions to Gibbard’s paradox and to Sen’s impossibility of a Paretian liberal. Finally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems.     

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.

---

     

Postulates and paradoxes of relative voting power — A critical re-appraisal

This paper re-evaluates the problem of measuring thea priori relative voting power of a voter in an assembly. We propose several new intuitively compelling postualtes that any reasonable index of voting power ought to satisfy. At the same time we argue that most of the paradoxes of voting power discussed in the literature are paradoxical only in a weak sense, if at all. This leaves three crippling paradoxes — the well-known paradox ofweighted voting, and two new ones presented here: thebloc anddonation paradoxes. We evaluate the four main relative power indices discussed in the literature with respect to these three severe paradoxes. The Shapley-Shubik index is seen to be immune to all three paradoxes, while the Deegan-Packel index is vulnerable to all three. The Banzhaf and the Johnston indices are demonstrably immune to the paradox of weighted voting. However, they are shown to suffer from both the bloc and the donation paradoxes. We argue that this seriously undermines these indices in a hitherto unsuspected way. Several other theoretical issues relating to voting power are discussed.     

The conflict between naive and sophisticated choice as a form of the ‘liberal paradox’

Pareto-inefficient perfect equilibria can be represented by the liberal paradox approach of Sen, appropriately reconfigured to model intertemporal decision-making by an individual. We show that the preference profile used by Grout (1982) to construct a case in which naive choice Pareto-dominates sophisticated choice can be so represented, if tastes change and if the individual can make decisions at time t, which restrict or determine opportunities available in period t + 1 and beyond. This ability to make a decision that binds oneself in the future is a form of rights assignment. We also show how two resolutions of the liberal paradox work out in the individual decision framework.     

A “Pseudo-endowment” effect,and its implications for some recent nonexpected utility models

This article describes a modification of the Allais paradox that induces preferences inconsistent with two conditions weaker than the independence axiom, namely quasi-convexity (a special case of which is the betweenness axom), and Hypothesis II of Machina (also called fanning-out). These violations can be formally derived from prospect theory by invoking a nonliner transformation of probability into decision weight.I would like to thank David Bell, Vijay Krishna, John Pratt, and especially Colin Camerer for helpful comments and criticism.     

走向法庭还是走上街头：超越维权困境的一条行动路径

制度外抗争与制度内法律维权有着显著不同的结果和制度逻辑。现有文献中的“依法抗争”或“以法抗争”可以通过制度外或者制度边缘的集体行动获得政府及时的反应,但却有着多重困境：机会困境、风险困境、组织困境、制度困境。制度内法律维权可以很大程度上破解这些困境,但也有着该模式下独特的结果困境：费时费力而又缺乏即时直接的回报困扰或者阻碍制度内法律维权者去为了获得长期的有益于整个群体的普遍性制度化后果采取行动。但本研究中的业主维权行动在一定程度上破解了这一困境。他们的制度内维权行动让法律在实践中最大可能地运转了起来,从而超越了传统维权的困境。独特的政治机会结构和制度内维权本身所具有的特征,促进一些群体走向法庭,而非走上街头。     

Nozick on Sen: A misunderstanding

This discussion examines Robert Nozick's claim inAnarchy, State, and Utopia (New York 1974) that his entitlement theory of justice avoids the paradox of collective choice shown by A. K. Sen inCollective Choice and Social Welfare (San Francisco 1970). Nozick argues his system is a stable principle of distributive justice. The author shows Nozick's principle of justice in transfer qualifies as a social decision function in Sen's sense because it is a collective choice rule and meets necessary and sufficient conditions for the existence of a choice function. Next the author demonstrates Nozick's principle of justice in transfer requkes Sen's conditions of unrestricted domain, the Pareto principle, and liberalism which are the conditions of the Sen paradox Nozick claims to avoid. Thus, Nozick's principle of justice in transfer is shown not to be a stable principle of distributive justice.     

The doctrinal paradox, the discursive dilemma, and logical aggregation theory

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager??s doctrinal paradox and List and Pettit??s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ??general logic?? built in this framework.     

Ordinal independence in nonlinear utility theory

Individual behavior under uncertainty is characterized using a new axiom, ordinal independence, which is a weakened form of the von Neumann-Morgenstern independence axiom It states that if two distributions share a tail in common, then this tail can be modified without altering the individual's preference between these distributions. Preference is determined by the tail on which the distributions differ. This axiom implies an appealing and simple functional form for a numerical representation of preferences. It generalizes the form of anticipated utility, and it explains some well-known forms of behavior, such as the Friedman-Savage paradox, that anticipated utility cannot.     

Rules, Social Ontology and Collective Identity

Mainstream game theory explains cooperation as the outcome of the interaction of agents who permanently pursue their individual goals. Amartya Sen argues instead that cooperation can only be understood by positing a type of rule-following behaviour that can be (and often is) out of phase with the pursuit of individual goals, due to the existence of a collective identity. However, Sen does not clarify the ontological preconditions for the type of social behaviour he describes. I will argue that Sen's account of collective identity can be best interpreted in the light of John Searle's notion of collective intentionality, while Sen's explanation of rule-following behavior and agency is best understood using the critical realist transformational model of social activity.     

Resolving Rabin’s paradox

We present a theoretical model of Rabin’s famous calibration paradox that resolves confusions in the literature and that makes it possible to identify the causes of the paradox. Using suitable experimental stimuli, we show that the paradox truly violates expected utility and that it is caused by reference dependence. Rabin already showed that utility curvature alone cannot explain his paradox. We, more strongly, do not find any contribution of utility curvature to the explanation of the paradox. We find no contribution of probability weighting either. We conclude that Rabin’s paradox underscores the importance of reference dependence.

     

. . .and why there is no simple solution, but reasons for optimism

This article has three objectives. First, to apply the debate concerning deliberative or discursive democracy to the subject of social policy in order to renew and update the long-standing attempt to go beyond the paradigm of welfare-state capitalism. The 'crisis of universalism' is outlined and this is then explained in terms of the traditional welfare state's 'democratic deficit'. Second, to suggest that applying these debates reveals two paradoxes that bear implications not only for social policy but also for the entire project of discursive democracy. The first paradox refers to the need to combine proceduralist and pluralist theories of deliberative democracy, despite the ultimate irreconcilability of these philosophies. The second refers to the problem of social transition and the fact that democratisation and social equalisation require one other. The third objective is therefore to suggest that welfare traditionalists have nothing to fear from what are here called 'post-universalist' critiques.     

当代中国法治化进程中的五大矛盾辨思

在当代中国法治化的进程中 ,存在着法律与立法、控权与维权、确定性法律与解释性法律、新道德与旧道德、法律普通化与特殊化等五大矛盾。正确认识这些矛盾 ,将有助于我们完成法治本土化的历史使命。     

Time,bounded utility,and the St. Petersburg paradox

The assumption of bounded utility function resolves the St. Petersburg paradox. The justification for such a bound is provided by Brito, who argues that limited time will bound the utility function. However, a reformulated St. Petersburg game, which is played for both money and time, effectively circumvents Brito's justification for a bound. Hence, no convincing justification for bounding the utility function yet exists.     

Peace building: a conceptual framework

An interdisciplinary legal and social work framework for peace building is presented. Inequality and its eradication are identified as linking factors transforming conflict into coexistence. Peace building is determined to entail participation in the struggle for social justice. Three conditions are identified as central to the peace building process. The first necessitates the establishment of inclusive, autonomous communities, each free to express religious, cultural and national aspirations and identity. The second requires the recognition of the legitimacy of each community to assert rights and claims without denying those of the other . This premise supports the view of the individual in relation and notes that coexistence can only be advanced through the building of mutual relationships. Finally, peace building requires recognition of human rights as a tool to promote relationships both within and between societies.     

The impossibility of the Paretian liberal and its relevance to welfare economics

The purpose of this study is to analyse the implications of Sen's impossibility result, the liberal paradox, for orthodox welfare economics. Because the rather special format of social choice theory makes it a little difficult to be sure of the relevance of this result, the whole dilemma is posed here in terms of a rather informal analysis of information al patterns.On the one hand, it is argued that the traditional approach to welfare economics, including both utilitarianism and Paretian ordinalism, contains severe informational constraints eliminating the use of all kinds of independent non-utility information in the social evaluation process. This property, called welfarism, is also present in the weak Pareto principle, which conflicts with even minimal requirements of personal liberty according to Sen's result.On the other hand, it is argued that there is in fact little to be resolved in this problem in spite of several attempts to circumvent the conflict. These studies are argued to be mainly ad hoc solutions to the formal problem and relevant only to the extent they indicate how severe restrictions are needed to avoid the paradox. The analogy with the prisoner's dilemma does not work either. Since liberal values are intrinsically non-welfaristic, the liberal paradox can be interpreted as only one, but a rather powerful, example of the informational deficiency of the orthodox approach.Finally, it is argued that the liberal paradox has striking implications for both the concept of preference and social optimum as well as empirical research on social welfare. This means that if the impossibility is to be taken seriously we need to revalue both the status of utility information and the role of the Pareto principle in social welfare analysis.The author is grateful to Professor Amartya Sen and Matti Tuomala for helpful comments and suggestions.     

Liberalism,non-binary choice and Pareto principle

It is shown in this paper that a very mild form of Pareto principle is compatible with a set of restrictive conditions. Deriving a choice set identical with the set of alternatives in the case of paradox of voting amounts to begging the problem. If we restrict that the choice set should be a proper sub-set of the original set, the paradox will be revived. In the realistic sense liberalism may well be treated as an outcome of the choice rather than as a basic value judgement. Choice of Rules of the Game ought to be the first step and then only society can seek the optimal situation under those Rules.I am very grateful to P. K. Pattanaik for helpful discussions and valuable comments on the first draft. I am also grateful to Prof. Amartya Sen whose lectures at the Delhi School of Economics introduced me to the theory of social choice.     

Nozick on Sen: A reply to Perelli-Minetti

Perelli-Minetti argues that Nozick's principle of justice in transfer requires, inter alia, Sen's liberalism condition (L) and is subject to Sen's paradox. It is shown here that a weaker liberalism condition L _W is sufficient for justice in transfer and consistent with Sen's other conditions on the social decision function. The conjunction of conditions L _W, I _P, and N is equivalent to L. It is implausible and perhaps illogical that a society applying Nozick's entitlement theory will impose both I _P and N, and if it does not, then Sen's paradox does not affect Nozick's theory of justice in transfer.     

Security level,potential level,expected utility: A three-criteria decision model under risk

Among the violations of expected utility (E.U.) theory which have been observed by experimenters, the violations of its independence axiom is, by far, the most common. It seems that, in many cases, these inconsistencies can be ascribed to the desire for security - called the security factor by L. Lopes (1986) - which makes people attach special importance to the worst outcomes of risky decisions as well as to the sole outcomes of riskless decisions (certainty effect). J.-Y. Jaffray (1988) has proposed a model which generalizes E.U. theory by taking into account this factor and is then able to account for certain violations. However, especially in experiments on choice involving prospective losses, violations of the von Neumann-Morgenstern independence axiom cannot be explained by the security factor alone and have to be partially ascribed to the potential factor (L. Lopes, 1986) which reflects heightened attention to the best outcomes of decisions, especially when the best outcome is the status quo. In this paper, we construct an axiomatic model for subjects taking into account simultaneously or alternatively the security factor and the potential factor. For this, as in Jaffray's model, it has been necessary to weaken not only the standard independence axiom but also the continuity axiom and, in the same time, to reinforce the dominance axiom. In the resulting model, choices are partially determined by the mere comparison of the (security level, potential level) (i.e. the (worst outcome, best outcome)) pairs offered, and completed by the maximization of an affine function of the expected utility, the coefficients of which depend on both the security level and potential level.In this model, a decision maker who (i) has constant marginal utility for money, (ii) is sensitive to the security factor alone in the domain of gains, (iii) is sensitive to the potential factor alone in the domain of losses, behaves as a risk averter for gains and a risk seeker for losses.     

An additive representation on the product of complete,continuous extensive structures

This article develops an axiom system to justify an additive representation for a preference relation \({\succsim}\) on the product \({\prod_{i=1}^{n}A_{i}}\) of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor A _i makes it possible to yield a special type of restricted solvability, i.e., additive solvability and the usual cancellation on \({\prod_{i=1}^{n}A_{i}}\). In addition, the assumption of continuity and completeness for A _i implies a stronger type of solvability on A _i . The additive solvability, cancellation, and stronger solvability axioms allow the weakened independence to be effective enough in constructing the additive representation.