Choice Functions with States of Mind

An agent is rational by dominance then states of mind (DSM) if he makes his decisions by, first, preselecting the alternatives that are not dominated by any other alternative in the choice set, and second, by choosing the preselected alternative corresponding to his state of mind. This state of mind is dependent on the previous choices he made. An agent is rational by states of mind then dominance (SMD) if he makes his decisions by, first, preselecting the alternatives corresponding to his state of mind and second, choosing the alternative that is not dominated. We give axiomatizations for SMD-rational or DSM-rational choice functions.      

Varieties of failure of monotonicity and participation under five voting methods

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can occur. Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity.     

Reflective coherence and Newcomb problems: A simple solution

Assignments of greater expected value to dominated options in Newcomb problems are analyzed as manifestations of reflective incoherence. The prospect of a greater reward by choosing a dominated option is illusory, since any ill gotten, i.e. irrational, gains can be leeched away by submitting the agent to a dynamic Dutch Book. In the Appendix, a proof is given which shows that if the agent is to avoid the Dutch Book in Newcomb situations, his degrees of belief are reflectively coherent if and only if his desirabilities at the time of choice align with his desirabilities at the time of action.     

On Hobbes’s state of nature and game theory

Hobbes’s state of nature is often analyzed in two-person two-action non-cooperative games. By definition, this literature only focuses on duels. Yet, if we consider general games, i.e., with more than two agents, analyzing Hobbes’s state of nature in terms of duel is not completely satisfactory, since it is a very specific interpretation of the war of all against all. Therefore, we propose a definition of the state of nature for games with an arbitrary number of players. We show that this definition coincides with the strategy profile considered as the state of nature in two-person games. Furthermore, we study what we call rational states of nature (that is, strategy profiles which are both states of nature and Nash equilibria). We show that in rational states of nature, the utility level of any agent is equal to his maximin payoff. We also show that rational states of nature always exist in inessential games. Finally, we prove the existence of states of nature in a class of (not necessarily inessential) symmetric games.     

Negotiation and Defeasible Decision Making

In economically meaningful interactions negotiations are particularly important because they allow agents to improve their information about the environment and even to change accordingly their own characteristics. In each step of a negotiation an agent has to emit a message. This message conveys information about her preferences and endowments. Given that the information she uses to decide which message to emit comes from beliefs generated in previous stages of the negotiation, she has to cope with the uncertainty associated with them. The assessment of the states of the world also evolves during the negotiation. In this paper we analyze the intertwined dynamics of beliefs and decision, in order to determine conditions on the agents that allow them to reach agreements. The framework for decision making we consider here is based on defeasible evaluation of possibilities: an argument for a choice defeats another one if it is based on a computation that better uses all the available information.     

Is the Disposition of Constrained Maximization Chosen Rationally?

One of the most important issues in moral philosophy is whether morality can be justified by rationality. The purpose of this study is to examine Gauthier’s moral theory, focusing on the disposition of constrained maximization, which is the main thrust of his project to justify morality rationally. First of all, I shall investigate Gauthier’s assumption and condition for the rationality of the disposition of constrained maximization so as to disclose that the disposition of constrained maximization is not necessarily chosen by rational agents. Then I shall explore his other arguments including ones for the reinterpretation of rationality and the self-critical reflection of rational beings, which can be considered as his further efforts to make the disposition of constrained maximization a rational choice. By exploring them, I shall attempt to indicate that those arguments are not valid so long as he clings to the maximizing conception of rationality and thereby this conception of rationality itself is not enough to provide morality with a basis.     

A note on Savage's theorem with a finite number of states

This article gives a preference-based characterization of subjective expected utility for the general equilibrium model with a finite number of states. The characterization follows Savage (1954) as closely as possible but has to abandon his axiom (P6), atomlessness of events, since this requires an infinite state space. To introduce continuity we replace (P6) with a continuity assumption on the set of consequences and assume the preferences are smooth. Then we apply Savage's sure-thing principle and his state-independence axiom to get an additively separable utility representation. Finally, to separate subjective probabilities from basic tastes, we apply a new axiom, which states that for each pair of states the marginal rate of substitution is constant along the certainty line.     

Divide-the-Dollar Game Revisited

In the Divide-the-Dollar (DD) game, two players simultaneously make demands to divide a dollar. Each player receives his demand if the sum of the demands does not exceed one, a payoff of zero otherwise. Note that, in the latter case, both parties are punished severely. A major setback of DD is that each division of the dollar is a Nash equilibrium outcome. Observe that, when the sum of the two demands x and y exceeds one, it is as if Player 1's demand x (or his offer (1−x) to Player 2) suggests that Player 2 agrees to λ_x < 1 times his demand y so that Player 1's demand and Player 2's modified demand add up to exactly one; similarly, Player 2's demand y (or his offer (1−y) to Player 1) suggests that Player 1 agrees to λ_yx so that λ_yx+y = 1. Considering this fact, we change DD's payoff assignment rule when the sum of the demands exceeds one; here in this case, each player's payoff becomes his demand times his λ; i.e., each player has to make the sacrifice that he asks his opponent to make. We show that this modified version of DD has an iterated strict dominant strategy equilibrium in which each player makes the egalitarian demand 1/2. We also provide a natural N-person generalization of this procedure. This revised version was published online in June 2006 with corrections to the Cover Date.     

Is diversity in capabilities desirable when adding decision makers?

When the benefit of making a correct decision is sufficiently high, even a slight increase in the probability of making such a decision justifies an increase in the number of decision makers. Applying a standard uncertain dichotomous choice benchmark setting, this study focuses on the relative desirability of two alternatives: adding individuals with capabilities identical to the existing ones and adding identical individuals with mean-preserving capabilities that depend on the states of nature. Our main result establishes that when the group applies the simple majority rule, variability in the capabilities of the new decision makers under the two states of nature, which is commonly observed in various decision-making settings, is less desirable in terms of the probability of making the correct decision.     

Can Choice in Welfare States Be Equitable?

Whether choice is fine or dire for the welfare state is a question that cannot be answered theoretically. That is the conclusion of this article, which discusses conditions that must be fulfilled if choice or increased choice are not to be reflected in increased inequality in access to welfare services. The consequences of non-decision and stress in relation to choice are touched upon. The implication of the analysis is that concrete, empirical analysis is important in order to ascertain whether the conditions for ensuring an informed choice without negative impact on equity in modern welfare states can be fulfilled.     

On Seidenfeld‘s Criticism of Sophisticated Violations of the Independence Axiom 1

An agent who violates independence can avoid dynamic inconsistency in sequential choice if he is sophisticated enough to make use of backward induction in planning. However, Seidenfeld has demonstrated that such a sophisticated agent with dependent preferences is bound to violate the principle of dynamic substitution, according to which admissibility of a plan is preserved under substitution of indifferent options at various choice nodes in the decision tree. Since Seidenfeld considers dynamic substitution to be a coherence condition on dynamic choice, he concludes that sophistication cannot save a violator of independence from incoherence. In response to McClennens objection that relying on dynamic substitution when independence is at stake must be question-begging, Seidenfeld undertakes to prove that dynamic substitution follows from the principle of backward induction alone, provided we assume that the agents admissible choices from different sets of feasible plans are all based on a fixed underlying preference ordering of plans. This paper shows that Seidenfelds proof fails: depending on the interpretation, it is either invalid or based on an unacceptable assumption.     

通过“合意”建构的三元行动理论:重探韦伯的《关于理解社会学的一些范畴》

韦伯的《关于理解社会学的一些范畴》（下文简称《范畴》）对于发展社会行动具有关键作用，却由于诸多因素让位于《社会学的基本概念》。本文从《范畴》内部的论述结构与外部的参照比较出发，进行相关脉络的梳理，以证明该文具有独特的理论内涵，然后指出“合意”在社会行动与社会关系上的双元角色以及通过“合意”所建构的“共同体行动/合意行动/社会体行动”三元行动类型。综观之，《范畴》的理论意涵值得我们反思“从行动到秩序”之间的另一种可能性。     

Analysis of Intertemporal Choice: A New Framework and Experimental Results

This paper reports the results of a series of experiments examining intertemporal choice. The paper makes three contributions: First, it presents a new analytic device, the intertemporal choice triangle, which is analogous to the Marschak--Machina choice triangle used in the analysis of choice under risk. Second, we have developed a new experimental design based on the intertemporal choice triangle which allows subjects greater flexibility in making choices, and which allows the researcher to make more subtle inferences, than are possible with designs previously employed. Subjects are able to create their most-preferred outcome in each choice situation by choosing a constrained linear combination of two extreme options. Third, our results show that while subjects do not typically maximize present value, they are significantly influenced break by present value considerations. We refer to this finding as it present value-seeking behavior. We find only weak evidence of several previously documented intertemporal choice anomalies in our framework.     

Weighted averaging,Jeffrey conditioning and invariance

Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent’s priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging (for the events whose probability the other agent reveals) and Jeffrey conditioning (for the events whose probability the other agent does not reveal) is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed.     

Stranger Danger: Redistricting,Incumbent Recognition,and Vote Choice*

Objectives. We take a step forward in examining the electoral effects of redistricting by: (1) demonstrating that voters with a new incumbent because of redistricting are less likely to recognize their representative, and (2) voters are less likely to vote for their representative if they fail to recognize him or her. Methods. Our data come from a survey of white respondents who resided in the redrawn Eighth District of Georgia for the 2006 U.S. House elections. We use probit regressions to first measure the effect of redistricting on incumbent recognition. Then, we assess the likelihood of voting for the incumbent depending on whether a respondent was redrawn or has the same incumbent after redistricting, and whether or not the respondent could recognize his or her representative. Results. Our analyses make it clear that redrawn voters were much less likely to recognize their incumbent and it is the inability to recognize one's incumbent, irrespective of whether the representative has changed due to redistricting, which accounts for a reduced likelihood of voting for the incumbent. Conclusions. Other scholars have examined the relationship between redistricting and incumbent recognition. Likewise, many have evaluated the effects of redistricting on vote choice. This article, however, is the first to merge these two relationships. We find that redrawn constituents are less likely to know who their representative is, and it is indeed a lack of familiarity that reduces an incumbent's vote share. Thus, we have shown empirically that the absence of a personal vote, which is exacerbated by redistricting, proves electorally harmful to the incumbent.     

Updating beliefs with imperfect signals: Experimental evidence

We conduct an experiment on individual choice under risk in which we study belief updating when an agent receives a signal that restricts the number of possible states of the world. Subjects observe a sample drawn from an urn and form initial beliefs about the urn??s composition. We then elicit how beliefs are modified after subjects receive a signal that restricts the set of the possible urns from which the observed sample could have been drawn. We find that this type of signal increases the frequency of correct assessments and that prediction accuracy is higher for lower levels of risk. We also show that prediction accuracy is higher after invalidating signals (i.e. signals that contradict the initial belief). This pattern is explained by the lower level of risk associated with invalidating signals. Finally, we find evidence for a lack of persistence of choices under high risk.     

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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Accepting and Negotiating Service Users' Choices in Mental Health Transition Meetings

Across Western welfare regimes, policies emphasize that service users should have more choices regarding their services. This article examines how service choices are presented, responded to and decided in interactions between service users and professionals in mental health transition meetings. Choice is often associated with consumerist user involvement ideas, but in mental health choice also relates to the democratic user involvement approach and to shared decision making between professionals and service users. The results of the study show that professionals construct service users as consumers by offering service options in choice making sequences, expecting users to make appropriate choices. Service users mostly act like consumers by responding to these choice options. However, the study also demonstrates that the professionals do not always accept the user's first choice but respond to them as non‐preferred. Sometimes, they also suggest choices on behalf of the users. In these ‘non‐accepting’ sequences, choices are negotiated in interaction between the parties, rather than users acting as autonomous choice makers. The sequences are based on two kinds of professional reasoning: first, the professional‐led needs assessment and, second, the structure of the service package that the user is being offered. This negotiation has elements of shared decision making and the ‘logic of care’. But it also has elements of paternalist control which challenge both consumerist and democratic service user involvement and suggests consideration of more collectively oriented service user actions.