We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets (...) of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

In order to vindicate rational-choice theory as a mode of explaining social patterns in general - social patterns beyond the narrow range of economic behaviour - we have to recognize the legitimacy of explaining the resilience of certain patterns of behaviour: that is, explaining, not necessarily why they emerged or have been sustained, but why they are robust and reliable. And once we allow the legitimacy of explaining resilience, then we can see how functionalist theory may also serve us (...) well in social science; we lose the basis - the empty black box argumenton which the rational-choice critique of the theory has mostly been grounded. (shrink)

A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum of (...) order-types, each of which either has finitely many blocks, or has order-type n · η for some integer n. (shrink)

On analyzing the problem that arises whenever the set of maximal elements is large, and a selection is then required (see Peris & Subiza 1998), we realize that logical ways of selecting among maximals violate the classical notion and axioms of rationality. We arrive at the same conclusion if we analyze solutions to the problem of choosing from a tournament (where maximal elements do not necessarily exist). So, in our opinion the notion of rationality must be discussed, not only in (...) the traditional sense of external conditions (Sen 1993), but in terms of the internal information provided by the binary relation. (shrink)

We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.

A hard choice is a situation in which an agent is unable to make a justifiable choice from a given menu of alternatives. Our objective is to present a systematic treatment of the axiomatic structure of such situations. To do so, we draw on and contribute to the study of choice functions that can be indecisive, i.e., that may fail to select a non-empty set for some menus. In this more general framework, we present new characterizations of (...) two well-known choice rules, the maximally dominant choice rule and the top-cycle choice rule. Together with existing results, this yields an understanding of the circumstances in which hard choices arise. (shrink)

Recently, null arguments have been treated as an ellipsis phenomenon, derived by PF-deletion or LF-copy under some kind of identity requirements. Focusing on Japanese null arguments, this paper argues that they are base-generated empty nominals which are interpreted via choice functions. The functional approach is supported by cases involving intermediate scope readings, missing antecedents, and implicational bridging. A less standard case of Japanese null arguments anteceded by QPs is also discussed and shown to be amenable to the choice (...) functional analysis supplemented by a general requirement of structural parallelism. (shrink)

A recent popular analysis of English indefinites isthat they involve a choice function mechanism in their semantic interpretation. However,there are diversified views regarding how intermediate scope readings should be dealt withand which level(s) existential closure should apply to. This paper attempts to make acontribution to this debate by examining existential polarity wh-phrases in Chinese. I showthat unlike the behaviors of polarity indefinites in St''át''imcets reported by Matthewson(1999), intermediate scope readings are possible for polarity wh-phrases in Chinese but aresubject (...) to some locality conditions. I suggest that implicit arguments of choice functionsmight have a parametric value the choice of which affects availability of intermediate readings.The findings in this paper thus revive the possibility, rejected by Matthewson (1999), that thechoice function mechanism may vary from language to language or from indefinite NPs in onelanguage to indefinite NPs in another language or even from one type of indefiniteNP to another type of indefinite NP within the same language. (shrink)

The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with parameters)? A natural dichotomy arises where the trees that fall in the first class don't have a definable choice function and the trees in the second class have even a definable well ordering of their elements. This has (...) a close connection to the uniformization problem. (shrink)

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. (shrink)

We introduce an independence notion for choice functions, which we call ‘epistemic independence’ following the work by De Cooman et al. [17] for lower previsions, and study it in a multivariate setting. This work is a continuation of earlier work of one of the authors [29], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [11]. We obtain the many-to-one independent natural extension (...) in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less expressive imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [28], which De Bock and De Cooman [2] have called S-independence. We show that neither is more general than the other. (shrink)

The Nash axiom is a basic property of consistency in choice. This paper proposes weaker versions of the axiom and examines their logical implications. In particular, we demonstrate that weak Nash axioms are useful to understand the relationship between the Nash axiom and the path independence axiom. We provide an application of weak Nash axioms to the no-envy approach. We present a possibility result and an impossibility result.

There are two main approaches to the scopal properties of the N’-restrictors of which-phrases. One line attributes widest scope within the interrogative clause to the entire which-phrase, outside the question formation operator, often assumed to reside in C0. The result is Karttunen ’s question denotation --exemplified in --,1 whose distinctive feature is that the semantic contribution of the N’- restrictor of the which-phrase is represented outside the so-called question nucleus, i.e., outside the subformula “p=…”. The second main avenue interprets the (...) N’-restrictor of which-phrases somewhere inside the question nucleus, that is, under the scope of the question formation operator and possibly under other, further embedded operators. The outcome is Hamblin’s --or unselective binding—question meaning, as in. This paper will be concerned with this second line, which I will refer to as the base position line. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one (...) we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic (...) is decidable, and give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

Set-valued choice functions provide a framework that is general enough to encompass a wide variety of theories that are significant to the study of rationality but, at the same time, offer enough structure to articulate consistency conditions that can be used to characterize some of the theories within this encompassed variety. Nonetheless, two-tiered choice functions, such as those advocated by Isaac Levi, are not easily characterized within the framework of set-valued choice functions. The present work proposes conditional (...) choice functions as the proper carriers of synchronic rationality. The resulting framework generalizes the familiar one mentioned above without emptying it and, moreover, provides a natural setting for two-tiered choice rules. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic (...) is decidable, and give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

There is a longstanding discussion whether wide-scope indefinites denote choice functions that are existentially bound or remain free. Data from Ga, an under-researched language spoken in Ghana, show that there are wide-scope indefinites denoting existentially bound skolemized choice functions whose parameter is bound by a higher quantificational NP, free skolemized choice functions with the speaker or a higher quantificational NP as a parameter, and narrow scope quantificational indefinites. Thus the data show that both existentially bound and free (...) skolemized choice functions are attested in natural language shedding new light on the semantics of indefinites. (shrink)

Kratzer 1998 proposes that certain indefinite determiners (at least in some of their uses) might be variables for (Skolemized) choice functions that receive a value from the utterance context. What does it mean for a choice function variable to receive a value from the context of utterance? How can a context provide such a function? To sharpen intuitions, here is an example describing a custom from my home town Mindelheim. After every funeral, all the mourners gathered (...) around the still open grave say a prayer that starts with the words: “And now let us pray for the person among us who will die next.” Suppose an anthropologist attended one or more funerals in Mindelheim, and reports on what she found out in a lecture using (1), or the more general (2). (shrink)

Over the last two decades, semantic theory has been marked by a continuing shift from a static view of meaning to a dynamic one. The increasing interest in extending semantic analysis from isolated sentences to larger units of discourse has fostered the intensive study of anaphora and coreference, and this has engendered a shift from viewing meaning as truth conditions to viewing it as the potential to change the "informational context".

It is well known that indefinite phrases are more liberal in taking scope than other quantifying phrases. In general, the scope of indefinites is not limited by the finite clause in which they occur, although the scope of universal quantifiers is. Wh-phrases behave very much like indefinites: in languages with wh in situ, their scope need not be restricted by anything like clause boundedness.

Although choice and preference are distinct categories, it may in some contexts be a useful idealization to treat choices as fully determined by preferences. In order to construct a general model of such preference-based choice, a method to derive choices from preferences is needed that yields reasonable outcomes for all preference relations, even those that are incomplete and contain cycles. A generalized choice function is introduced for this purpose. It is axiomatically characterized and is shown to (...) compare favourably with alternative constructions. (shrink)

The present paper discusses two interesting phenomena concerning phi-features on plural pronouns: plural pronouns that denote atomic individuals, and plural pronouns with more than one binder. A novel account of these two phenomena is proposed, according to which all occurrences of phi-features are both semantically and morphologically relevant. For such a ‘uniformly semantic account’ of phi-features, dependent plural pronouns constitute a theoretical challenge, while partial binding is more or less straightforwardly accounted for. In order to make sense of the semantic (...) effects of the phi-features on dependent plural pronouns, the following idea is pursued: the phi-features on a dependent plural pronoun reflect the range of values that the pronoun takes, rather than the particular value it denotes at a time. This idea is implemented in a compositional semantics by making use of choice functions. An appealing feature of the present account is that, unlike its predecessors, it accounts for dependent plural pronouns without c-commanding antecedents in essentially the same way as for those with c-commanding antecedents. It is also shown how this account of dependent plural pronouns can straightforwardly be augmented with set indices to account for partial binding. (shrink)

The idea of confining the idea of ‘rationality’ with that of the ‘choice of best elements’ unnecessarily limits the sense and scope of ‘rationality’. The existing internal consistency conditions that are popularly used in the social choice theory to assess a choice function are insufficient to analyse several choice patterns. The paper tries to address that problem by accepting a broader definition of rationality and characterizes choice behaviours where an individual chooses a k-th best (...) element from set of alternatives, where k is an integer. (shrink)

Two scenarios illustrate uses of von Neumann–Morgenstern stable sets in the construction of choice functions. A comparison is made to the construction of choice functions by the selection of maximal elements. A characterization is given of choice functions that are von Neumann–Morgenstern stable set rationalizable by acyclic, asymmetric binary relations. Two examples illustrate the use of the characterization.

We shall investigate certain statements concerning the rigidity of unary functions which have connections with forms of the axiom of choice.

It has been claimed that beneath the government rhetoric of patient choice, no real choice exists either in law or in National Health Service policy. Thus, choice is considered to be a fallacy in that patients are not able to demand specific treatment, but are only able to express preferences amongst the available options. This article argues that, rather than considering choice only in terms of patient autonomy or consumer rights, choice ought to be seen (...) as serving other functions: Choice serves as a mechanism of destabilisation, i.e., as a lever for change. This is apparent at the level of patient and doctor, and at the level of patient and health authority, but even more so, at the level of government. Patient choice, rather than benefiting the individual, can have effects on a wider scale. It encourages change and reform in healthcare practices and in the NHS institutions. (shrink)

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between metric spaces, and the second declares that sequentially compact pseudometric spaces are \—meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous.

This book represents a considerable revision and expansion of Public Choice II. Six new chapters have been added, and several chapters from the previous edition have been extensively revised. The discussion of empirical work in public choice has been greatly expanded. As in the previous editions, all of the major topics of public choice are covered. These include: why the state exists, voting rules, federalism, the theory of clubs, two-party and multiparty electoral systems, rent seeking, bureaucracy, interest (...) groups, dictatorship, the size of government, voter participation, and political business cycles. Normative issues in public choice are also examined including a normative analysis of the simple majority rule, Bergson–Samuelson social welfare functions, the Arrow and Sen impossibility theorems, Rawls's social contract theory and the constitutional political economy of Buchanan and Tullock. (shrink)

Due to the rise of functional foods,the distinction between foods and medicines hasbecome increasingly blurred. A new EUregulation covering health claims and otherclaims on food and drink products is on thedocks. A basic motive of legal regulation oflabeling and advertising is to inform andprotect the consumer. Promotion of informedchoice and consumer protection may, however, beconflicting objectives. A further problemsprings from the fact that choice, likeconsent, is a propositional attitude andtherefore opaque. Thus it is extremelydifficult for regulators to fasten onparticular (...) formulations of claims. Despite theprofessed respect for the autonomy of theconsumer, paternalism is never far away andeasily enters in various guises. (shrink)

Although previous work has linked parent autonomy support to the development of children’s executive function skills, the role of specific autonomy-supportive behaviors has not been thoroughly investigated. We compiled data from four preschool-age samples in the Midwestern United States to examine three relevant autonomy-supportive behaviors and their associations with child EF. We coded parent autonomy-supportive behaviors from a 10-min interaction between parent and child dyads working on challenging jigsaw puzzles together. Children completed a battery of EF. Overall, child EF (...) was most consistently correlated with the offering choice subscale. Additionally, only the offering choice subscale predicted child EF while controlling for the other autonomy support subscales and child age. These results suggest that parent provision of choice is an especially relevant aspect of autonomy-supportive parenting and may be important to the development of EF in early childhood. Future research should directly measure children’s experience with choice and how it relates to emerging EF. (shrink)

To avoid post-neurosurgical language deficits, intraoperative mapping of the language function in the brain can be complemented with preoperative mapping with functional magnetic resonance imaging. The validity of an fMRI “language localizer” paradigm crucially depends on the choice of an optimal language task and baseline condition. This study presents a new fMRI “language localizer” in Russian using overt sentence completion, a task that comprehensively engages the language function by involving both production and comprehension at the word and (...) sentence level. The paradigm was validated in 18 neurologically healthy volunteers who participated in two scanning sessions, for estimating test–retest reliability. For the first time, two baseline conditions for the sentence completion task were compared. At the group level, the paradigm significantly activated both anterior and posterior language-related regions. Individual-level analysis showed that activation was elicited most consistently in the inferior frontal regions, followed by posterior temporal regions and the angular gyrus. Test–retest reliability of activation location, as measured by Dice coefficients, was moderate and thus comparable to previous studies. Test–retest reliability was higher in the frontal than temporo-parietal region and with the most liberal statistical thresholding compared to two more conservative thresholding methods. Lateralization indices were expectedly left-hemispheric, with greater lateralization in the frontal than temporo-parietal region, and showed moderate test-retest reliability. Finally, the pseudoword baseline elicited more extensive and more reliable activation, although the syllable baseline appears more feasible for future clinical use. Overall, the study demonstrated the validity and reliability of the sentence completion task for mapping the language function in the brain. The paradigm needs further validation in a clinical sample of neurosurgical patients. Additionally, the study contributes to general evidence on test–retest reliability of fMRI. (shrink)