The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.

I explain and motivate the shutdown problem: the problem of creating artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I then propose a solution: train agents to have incomplete preferences. Specifically, I propose that we train agents to lack a preference between every pair of different-length trajectories. I suggest a way to train such agents using (...) reinforcement learning: we give the agent lower reward for repeatedly choosing same-length trajectories. (shrink)

This paper addresses the phenomenon of incomplete preferences in disaster risk management. If an agent finds two options to be incomparable and thus has an incomplete preference ordering, i.e., neither prefers one option over the other nor finds them equally as good, it is not possible for the agent to perform a value tradeoff, necessary for an informed decision, between these two options. In this paper we suggest a way to model incomplete preference orderings by means (...) of probabilistic preferences, and how to reveal an agent’s incomplete preference ordering within a behaviorist framework. (shrink)

We study preferences over lotteries which do not necessarily satisfy completeness. We provide a characterization which generalizes Expected Utility theory. We show in particular that various sure-thing axioms are needed to guaranteee the representability in terms of utility intervals rather than numbers, and to provide a linear interval order representation which is very much in the spirit of Expected Utility theory.

The normative principle of description invariance presupposes that rational preferences must be complete. The completeness axiom is normatively dubious, however, and its rejection opens the door to rational framing effects. In this commentary, we suggest that Bermúdez's insightful challenge to the standard normative view of framing can be clarified and extended by situating it within a broader critique of completeness.

We propose an axiomatization of aversion to incomplete preferences. Some prevailing models of incomplete preferences rely on the hypothesis that incompleteness is temporary and that by keeping their opportunity set open individuals reveal a preference for flexibility. We consider that the maintenance of incomplete preference is also aversive. Our model allows us to show how incompleteness induces an aversive attitude in two different ways: intrinsic and instrumental. Intrinsic aversion holds when one instance of incomplete (...) preference in the set suffices to decrease its utility. Instrumental aversion holds only insofar dominating options are affected by incompleteness. Given two partially overlapping sets of axioms on the binary relation over sets we formalize their consistency with the two types of aversion to incompleteness. Finally, we relate our model to the classical Sen’s distinction between tentative and assertive incompleteness. The spelling out of this distinction in the terms of our approach uncovers to what extent aversion to incompleteness may be compatible with a preference for flexibility. (shrink)

Orthodox decision theory gives no advice to agents who hold two goods to be incommensurate in value because such agents will have incomplete preferences. According to standard treatments, rationality requires complete preferences, so such agents are irrational. Experience shows, however, that incomplete preferences are ubiquitous in ordinary life. In this paper, we aim to do two things: (1) show that there is a good case for revising decision theory so as to allow it to apply (...) non-vacuously to agents with incomplete preferences, and (2) to identify one substantive criterion that any such non-standard decision theory must obey. Our criterion, Competitiveness, is a weaker version of a dominance principle. Despite its modesty, Competitiveness is incompatible with prospectism, a recently developed decision theory for agents with incomplete preferences. We spend the final part of the paper showing why Competitiveness should be retained, and prospectism rejected. (shrink)

The quasi-cyclical preferences that Bermúdez ascribes to Agamemnon and others in analogous situations do not best represent them. I offer two alternative accounts. One works best if the preference ordering is taken to be the agent's personal betterness ordering of acts; the other works best if it is taken to provide a summary of the agent's dispositions to act.

This article revisits the standard results of demand theory when the preference relation is a continuous preorder that admits an equicontinuous multi-utility representation. We study the consumer problem as the constrained maximization of a continuous vector-valued utility mapping, and show how to rederive those results. In particular, we provide a link between the literature on vector optimization and the analysis of the consumer problem under incomplete preferences.

This paper introduces a new solution concept for games with incomplete preferences. The concept is based on rationalizability and it is more general than the existing ones based on Nash equilibrium. In rationalizable strategies, we assume that the players choose nondominated strategies given their beliefs of what strategies the other players may choose. Our solution concept can also be used, e.g., in ordinal games where the standard notion of rationalizability cannot be applied. We show that the sets of (...) rationalizable strategies are the maximal mutually nondominated sets. We also show that no new rationalizable strategies appear when the preferences are refined, i.e., when the information gets more precise. Moreover, noncooperative multicriteria games are suitable applications of incomplete preferences. We apply our framework to such games, where the outcomes are evaluated according to several criteria and the payoffs are vector valued. We use the sets of feasible weights to represent the relative importance of the criteria. We demonstrate the applicability of the new solution concept with an ordinal game and a bicriteria Cournot game. (shrink)

We generalize a previous result about dynamically consistent menu preferences to the case where preferences are not necessarily complete. We show that, as it is the case when preferences are complete, a subjective state space version of dynamic consistency is linked to a comparative theory of preference for flexibility. In words, an objective signal is interpreted as an event in the agent’s subjective state space and the agent acts in a dynamically consistent way after that if and (...) only if we can attribute all the differences between the agent’s preferences before and after the signal to the fact that the agent values flexibility more before the signal than after. (shrink)

This paper examines the incompleteness of collective preference. We provide a series of Arrovian impossibility theorems without completeness. First, we consider the notion of regularity introduced by Eliaz and Ok (2006, Games and Economic Behavior 56, 61–86); it is an appropriate richness property for strict preference when preference is allowed to be incomplete. We examine the implication of imposing regularity on collective preference. Second, we propose responsiveness, a variation of positive responsiveness. This axiom requires that some changes in individual (...) preferences make an alternative weakly better than another. Third, we consider coherency conditions for collective preferences; this conditionally requires the existence of comparable pairs in a certain manner. We prove an impossibility result for each condition using Arrovian axioms. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in (...) this setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, (...) the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927. (shrink)

Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...) changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating. (shrink)

This paper uses the idea of a proxy, which figures in discussions of bounded rationality, to construct an argument for a revisionary conclusion about ideal instrumental rationality. I consider how subjective responses can figure as proxies in heuristics and develop the following argument: (1) Proxies, even if relatively easy to recognize, can sometimes be messy, prompting incomplete or cyclic preferences. (2) From the point of view of ideal instrumental rationality, it is permissible for an agent to be concerned (...) with a proxy rather than with what it is a proxy for. And so, (3) although it is standardly assumed, as part of the prevailing conception of ideal instrumental rationality, that rational preferences are complete and acyclic, neither incomplete preferences nor cyclic preferences can be dismissed as invariably irrational from the point of view of ideal instrumental rationality. (shrink)

A new history of liberalism which argues that liberalism has been predicated on definite morality and should be viewed as an attempt to encompass both fear and hope. Liberalism, argues Alan Kahan, is the search for a society in which people need not be afraid. Freedom from fear is the most basic freedom. If we are afraid, we are not free. These insights, found in Montesquieu and Judith Shklar, are the foundation of liberalism. What liberals fear has changed over time (...) (revolution, reaction, totalitarianism, religious fanaticism, poverty, and now populism) but the great majority of liberal thinkers have relied on three pillars to ward off their fears and to limit the concentrated power that causes fear: freedom, markets, and morals, or, to put it another way, politics, economics, and religion or morality. Most liberal thinkers emphasize one or two pillars more than another, but it is typical of liberalism down to the Second World War to rely on all three, although there were always minority voices who preferred to stand on only one leg. After WWII, "thin" procedural/market liberals, who wanted to strip any moral or religious basis or purpose from liberalism, dominated "thick" liberal moralists, who thought liberalism needed a moral basis and/or goal. It is the political contention of this book that liberalism is most convincing as program, language, and social analysis when it relies on all three pillars, and that the relative weakness of liberalism at the end of the twentieth century had much to do with neglect of the moral pillar of liberalism. Its historical contention is that for much of the past two centuries it did rely on all three pillars. But Kahan also argues that liberalism is not only a party of fear. It is also a party of hope, or the party of progress. Many of the contradictions typical of liberalism derive from the seemingly contradictory effort to encompass both hope and fear. If in case of conflict fear often trumps hope for liberals (loss aversion applies in politics as much as in economics), and utopia is subject to indefinite postponement, progress in personal autonomy and development has always been at the heart of liberalism. Liberals typically support their hopes on the same three pillars of freedom, markets, and morals which they use to ward off their fears. Nevertheless, in one respect those historians and political theorists who identify liberalism with laissez-faire economics are not wrong. It is characteristic of liberalism then that it bases its hopes not on the state but on civil society, which for liberals is the common source of a free politics, a free market, and of morals. Alan S. Kahan is Professor of History at the Université de Versailles. His previous books include Tocqueville, Democracy, and Religion: Checks and Balances for Democratic Souls (Oxford 2015), Alexis de Tocqueville (Continuum Books) and Mind vs Money: The War Between Intellectuals and Capitalism (Transaction Publishing, 2010). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Thomas G. Pavel INCOMPLETE WORLDS, RITUAL EMOTIONS' IN recent years, the notion of "fictional world" has enjoyed a considerable rise in fortune. The expression, however, is not entirely new. To refer to the world of a literary work, of a novel or of a play, has always been a favorite way of speaking for literary critics and aestheticians. In most cases, these were informal worlds. A discussion of (...) the world of Balzac, Dostoyevsky, HenryJames, or Proust often amounts to a description of each author's preferences in die selection and rearrangement of his material. Such discussion primarily fits authors who purposefully attempt to build comprehensive representational artifacts. One speaks quite naturally about l'univers balzacien, or about the universe of Musil. But is one entitled to refer with equal ease to the world ofBenjamin Constant, meagerly perceptible in his Adolphe, a short novel built in the spirit of economy, displaying just a few characters and a minimum of worldly information? Perhaps density and comprehensiveness are not indispensable characteristics of literary worlds. Aestheticians and narratologists using the "fictional worlds" terminology seem to believe mat any kind of artistic text projects a world, be it rich or poor. Such worlds are imagined in the fashion of modern philosophy of logic as states of affairs, more or less comprehensive. Some writers believe that the states of affairs comprised in fictional worlds must be fairly sizable, since diey should include "not only what the author indicates, but also whatever is required (entailed) by that which he indicates." 1 The laws of nature which are not specifically contradicted by the text would belong to its world. Thus, a few notorious cases aside, there is no reason to doubt that every child born in fiction has been engendered by a human fadier as long as the text does not report an exception. And if it does? Then, assuming that the laws of logic still govern if not fiction itself at least our understanding of it, we may appeal to what "possible world" philosophers have called "small miracles." * Editor's note: This article, as well as the contributions by Gerald Prince, Peter van Inwagen, and Kendall Walton which follow it, grew out ofa symposium on "Styles ofFictionality," organized by Professor Pavel and held at Harvard University in 1981. The Fall, 1983 issue of PHILOSOPHY AND LITERATURE will contain additional papers presented at the symposium. 48 Thomas G. Pavel49 Imagine, for instance, the world in which Notre Dame de Paris would be covered with blue paint. While everything else would preserve the properties it possesses in the actual world, with the laws of nature and the caused chains maintained, a small local change, somewhat miraculous, would modify only the color of the venerable building. Similarly, the world of Balzac may be understood as the world of early and mid-nineteenth-century France, slightly modified by the addition of a few hundred imagined characters. That diese conform surprisingly well to the general laws of French society of the time is so much the goal of Balzac's successful project, that for the sociologically-minded reader die' actual nonexistence of Rastignac, Rubempré, Vautrin, or Birotteau may appear a mere accident. These characters, one may surmise, display every trait that actual counterparts of theirs would possess, except existence. Hence, why would Rastignac's or Vautrin's emergence in a world omerwise identical to nineteenth-century France amount to anydiing more than a "small miracle"? On the other hand, Balzac's world being blessed wim hundreds of such miracles, the very magnitude of the project vindicates the attribute of "visionary," ascribed to Balzac by Béguin, or, if metaphorically undercut, mat of"God the Father" given him by Thibaudet. For, would not such magnitude entail more than just local changes in an otherwise faithful representation of the "actual" nineteenthcentury France? Similarly, would we interpret a fictional world in which a child has been engendered not by a human father, but by a divinity, as identical in all respects to the actual world, except for the limited modification attributed to a small miracle? 2 If we grant for a moment the improbable assumption that nineteenth-century France was a given and that Balzac... (shrink)

Richard Bradley’s Bayesian model of preference kinematics is compared with Sven Ove Hansson’s AGM-style model of preference revision. Both seek to model the revision of preference orders as a consequence of retaining consistency when some preferences change. Both models are often interpreted normatively, as giving advice on how an agent should revise her preferences. I raise four criticisms of the Bayesian model: it is unrealistic; it neglects an important change mechanism; it disregards endogenous information relevant to preference change, (...) in particular about similarity and incompleteness; and its representational framework, when expanded with similarity comparisons, may give misleading advice. These criticisms are based on a principle of conservatism, and on two proposals of similarity metrics for the Bayesian model. The performance of the Bayesian model, with and without the similarity metrics, is then tested in three different cases of preference change, and compared to the performance of the AGM model. (shrink)

In this paper I aim to examine some problematic implications of the fact that individuals are prone to making systematic reasoning errors, for resource egalitarianism. I begin by disentangling the concepts of preferences, choices and ambitions, which are sometimes used interchangeably by egalitarians. Subsequently, I claim that the most plausible interpretation of resource egalitarianism takes preferences, not choices, as the site of responsibility. This distinction is salient, since preference-sensitive resource egalitarianism is faced with an important objection when applied (...) to situations in which the empirically reasonable assumption that individuals have different degrees of computational abilities is introduced. I first show that this objection can be raised in cases involving individuals who have incomplete information, but that it ultimately fails for such cases since we can appeal to higher order insurance markets in order to mitigate any initial concerns. I further claim, however, that the objection is much more powerful in cases involving individuals who have different reasoning skills, since the appeal to higher order insurance markets is no longer tenable. Consequently, the ideal principle of justice proposed by Dworkin is met with a new feasibility challenge. Finally, I claim that the problem of reasoning errors and various forms of cognitive biases also affect Dworkin’s non-ideal principle of justice, skewing the outputs of the hypothetical insurance mechanism in an unjustifiable manner. (shrink)

This paper is concerned with social choice without completeness of social preference. Completeness requires that pairs of alternatives are perfectly comparable. We introduce the concept of minimal comparability, which requires that for any profile, there is some comparable pair of distinct alternatives. Complete silence should be avoided according to this condition. We show that there exists no normatively desirable aggregation rule satisfying minimal comparability.

More philosophical effort is spent articulating evolutionary rationales for the development of belief-like capacities than for precursors of desires or preferences. Nobody, though, seriously expects naturally evolved minds to be disinterested epistemologists. We agree that world-representing states won’t pay their way without supporting capacities that prioritise from an organism’s available repertoire of activities in light of stored (and occurrent) information. Some concede that desire-like states would be one way of solving this problem. Taking preferences as my starting point (...) instead of belief-like states, I defend two conclusions. First, psychologically real preference states, which approximately token expected utilities, have a quite general evolutionary rationale. They are a solution to the problem of efficiently allocating capacities with incompatible uses. This argument is a version of the Environmental Complexity Thesis. Second, preferences can plausibly function and naturally evolve without belief-like states, even though the converse claim is incredible. Preferences, that is, can mediate between discriminations of occurrent states (‘internal’ or ‘external’) and the processes selecting activity without mediation by stored indicative representations. By tokening expected utilities of actions conditional on discriminated state, they can increase the rate at which the ‘right thing’ is done at appropriate times, and they can do this without the support of belief-like, world-representing states. Preferences, even incomplete and noisy sets of them, are a fuel for success that will tend to be favoured when environments are complex in ways that matter to an organism, and when the organisms have complex behavioural repertoires with heterogenous returns and costs. (shrink)

Modal fictionalists face a problem that arises due to their possible-world story being incomplete in the sense that certain relevant claims are neither true nor false according to it. It has recently been suggested that this incompleteness problem generalises to other brands of fictionalism, such as fictionalism about composite or mathematical objects. In this paper, I argue that these fictionalist positions are particularly threatened by a generalised incompleteness problem since they cannot emulate the modal fictionalists’ most attractive response. I (...) then defend mathematical and compositional fictionalism by showing that the reasons for which the incompleteness problem has been thought to affect them are mistaken. This leads to the question of whether there are other fictionalist positions to which the problem does in fact generalise. I give a general account of the features of a fictionalist position that generate the incompleteness problem and argue that whenever a fictionalist position does exemplify these features then the problem can be addressed in analogy to the modal fictionalists’ preferred response. (shrink)

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)

In an alleged counter-example to the completeness of rational preferences, a career as a clarinettist is compared with a career in law. It seems reasonable to neither want to judge that the law career is at least as preferred as the clarinet career nor want to judge that the clarinet career is at least as preferred as the law career. The two standard interpretations of examples of this kind are, first, that the examples show that preferences are rationally (...) permitted to be incomplete and, second, that the examples show that preferences are rationally permitted to be indeterminate. In this paper, I shall argue that the difference between these interpretations is crucial for the money-pump argument for transitivity, which is the standard argument that rational preferences are transitive. I shall argue that the money-pump argument for transitivity fails if preferences are rationally permitted to be incomplete but that it works if preferences are rationally permitted to be indeterminate and rationally required to be complete. (shrink)

According to Aristotle, the present is an indivisible instant, or now. Aristotle holds that present-tense movement claims are sometimes true, but he argues that nothing ‘kineitai’ (moves/is moving) in the now. He characterizes movement as something that is ‘incomplete’ while it is occurring. My paper is an attempt to understand this combination of views. I draw a contrast between Aristotle’s position and an alternative view (defended by certain modern philosophers, but also by Plotinus), on which a present-tense movement claim (...) is made true by the existence of something that is wholly present in the now. And I give some reasons for preferring Aristotle’s position. (shrink)

. Consistent valuation and societal prioritization of risks presupposes comparability among risks, that is, in order to rank risks in order of severity, and allocate risk preventative resources accordingly, we must be able to determine whether one risk is better or worse than another, and by how much. It is often claimed, however, that some risks are not amenable to this kind of comparison because they are incommensurable, which roughly means that they are not comparable with respect to a common (...) cardinal measure. The aim of this thesis is to i) consider what it means to say that two risks are incommensurable, ii) explore if incomparability - comparison failure with respect to a common ordinal scale - ever occurs, and how to model it if it does. Essay I is a critical examination of the most prominent argument for incomparability, the so-called small improvement argument. It is argued that the argument fails because it conflates incomparability and a kind of evaluative indeterminacy. Essay II outlines so-called margin of error principles for comparative value judgements. They are based on the idea that if a proposition concerning the value relation between two value-bearing options is true, but there are sufficiently similar cases in which it is false, it is not available to be known. The usefulness of these principles is demonstrated by utilizing them in an epistemological case against SIA. Essay III presents a novel account of incomplete preference orderings which acknowledges that incomparability can vary in degrees. This is achieved by means of a probabilistic analysis of preferences. (shrink)

An efficient method of value assessment of a set of exchangeable alternatives A = a1,a2, ? ,an is presented. It particularly applies to situations where certain preferences may be easily evaluated or are already known, while other binary comparisons may not at once be available. Further applications are to ranking partial tournaments and the emergence and the characterisation of organisational hierarchy. By sequentially performing transitively efficient assessments of uncompared pairs, an initial weakly acyclical preference structure in A is transformed (...) into an ordering of A in echelons. We call these nicely surveyable preference structures echelon orders. Theoretical properties of echelon orders are investigated, including a characterisation and a numerical representation. (shrink)

While very much in Sen's camp in rejecting revealed preference theory and emphasizing the complexity, incompleteness, and context dependence of preference and the intellectual costs of supposing that all the factors influencing choice can be captured by a single notion of preference, this essay contests his view that economists should recognize multiple notions of preference. It argues that Sen's concerns are better served by embracing a single conception of preference and insisting on the need for analysis of the multiple factors (...) that determine ‘preference’ so conceived. (shrink)

Most of the existing literature on social preferences either tests whether certain characteristics of the social context influence individual decisions, or tries to estimate parameters of social preference functions describing such behavior at the level of the entire population. In the present paper, we are concerned with measuring parameters of social preference functions at the individual level. We draw upon concepts developed for eliciting other types of utility functions, in particular the literature on decision making under incomplete information. (...) Our method derives parameters of social preference functions from indifference statements about the distribution of payoffs a group. We apply our method in a controlled social preference experiment to establish the external validity of estimated parameters. Our results show the expected relationships to some external factors and also a strong correspondence between parameter estimates and factors that, according to the subjects’ own descriptions, influenced their behavior. We also find that some concepts discussed in the literature on social preferences, in particular envy toward players receiving a larger payoff, have very diverse and complex effects at the individual level. (shrink)

Si l’apport d’Amartya Sen à la critique de la rationalité économique est reconnu, la relation entre sa contribution formelle et le raisonnement informel qu’elle sous-tend est parfois mal comprise. Dans cet article, nous proposons une analyse de la propre interprétation que donne Sen de ses travaux formels sur l’incomplétude des préférences. Cette réflexion sur les propriétés mathématiques de la relation de préférence en théorie du choix social met en évidence la volonté de Sen d’enrichir la représentation formelle des activités humaines (...) d’évaluation, de classement et de choix. En un sens, cela peut être compris comme une simple amélioration de cette représentation ; mais l’interprétation de l’incomplétude comme « incomplétude affirmée » montre que Sen vise également à enrichir la structure du cadre conceptuel welfariste afin de détacher ce dernier de l’interprétation utilitariste qui lui est généralement associée. (shrink)

In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (1968) proved two theorems about complete and transitive collective choice rules that satisfy strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s (1972) impossibility theorem is stronger (...) than Murakami’s impossibility theorem, both by virtue of replacing Murakami’s assumption of strict non-imposition with the assumptions of non-imposition and non-nullness. In this note, we first point out that these claims are incorrect: non-imposition and non-nullness are together equivalent to strict non-imposition for all transitive collective choice rules. We then generalize Murakami’s dichotomy and impossibility theorems to the setting of incomplete social preference. We prove that if one drops completeness from Murakami’s assumptions, his remaining assumptions imply (i) that a collective choice rule is either Paretian, anti-Paretian, or dis-Paretian (unanimous individual preference implies noncomparability) and (ii) that adding proposed constraints on noncomparability, such as the regularity axiom of Eliaz and Ok (2006), restores Murakami’s dictator-or-inverse-dictator result. (shrink)

This paper evaluates how Amartya Sen’s critique of revealed preference theory stands against the latter’s contemporary, ‘neo-Samuelsonian’ version. Neo- Samuelsonians have argued that Sen’s arguments against RPT are innocuous, in particular once it is acknowledged that RPT does not assume away the existence of motivations or other latent psychological or cognitive processes. Sen’s claims that preferences and choices need to be distinguished and that external factors need to be taken into account to analyze the act of choice then appear (...) to be irrelevant. However, while it is true that contemporary revealed preference theory partially evades Sen’s critique, I show that the latter is still relevant outside the restricted areas of consumer choice and market dynamics. In particular, Sen’s views regarding the importance of incomplete preferences and the multiplicity of levels of agency can hardly be integrated into the framework of CRPT. This is a significant limit, given the imperialistic claims of some of the proponents of the latter. (shrink)

We explore the computational complexity of justification, stability and relevance in incomplete argumentation frameworks (IAFs). IAFs are abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. These IAFs can be completed by deciding for each uncertain argument or attack whether it is present or absent. Such a completion is an abstract argumentation framework, for which it can be decided which arguments are acceptable under a given semantics. The justification status of an argument (...) in a completion then expresses whether the argument is accepted (in), not accepted because it is attacked by an accepted argument (out) or neither (undec). For a given IAF and certain argument, the justification status of that argument need not be the same in all completions. This is the issue of stability, where an argument is stable if its justification status is the same in all completions. For arguments that are not stable in an IAF, the relevance problem is of interest: which uncertain arguments or attacks should be investigated for the argument to become stable? In this paper, we define justification, stability and relevance for IAFs and provide a complexity analysis for these problems under grounded, complete, preferred and stable semantics. (shrink)

This article presents four analyses of an interaction between the middle-Bronze Age Pharaoh Nibmuarea and the Babylonian king Kadashman-Enlil as described in the Amarna letters (Moran [1992] The Amarna Letters, The Johns Hopkins Universiy Press, Baltimore, Maryland). Intent on denying the Pharaoh his daughter in marriage, the Babylonian king was faced with the choice of sending messengers who could (''dignitaries'') or could not identify (''non-dignitaries'') his missing sister in the Pharaoh's court. Intent on marrying the king's daughter, the Pharaoh was (...) faced with the choice of showing the sister or showing someone else. Based on the assumption of complete information (game 1), the analysis revealed a dominant-strategy equilibrium: Nibmuarea shows the sister and Kadashman-Enlil sends non-dignitaries. Based on the assumption of one-sided incomplete information (Pharaoh's misperception; game 2), the analysis revealed that the Pharaoh had a dominant strategy of showing the sister irrespective of whether the king is keen or reluctant to learn about his sister's fate. Based on the assumption of one-sided incomplete information (Kadashman-Enlil's misperception; game 3), the analysis revealed that if non-dignitaries are sent, the Pharaoh prefers showing someone other than his sister. Based on the assumption of two-sided incomplete information (game 4), the Pharaoh finds it more beneficial to present the sister irrespective of whether his intentions are genuine or feigned. With incomplete information, it is difficult to judge the other's intentions; the cost of being caught cheating by not showing the sister to knowledgeable messengers was quite high. These analyses highlight the strategic uncertainty that characterized this Bronze-Age interaction. (shrink)

This paper investigates behavior in finitely repeated simultaneous and sequential-move prisoner’s dilemma games when there is one-sided incomplete information and signaling about players’ concerns for fairness, specifically, their preferences regarding “inequity aversion.” In this environment, we show that only a pooling equilibrium can be sustained, in which a player type who is unconcerned about fairness initially cooperates in order to disguise himself as a player type who is concerned about fairness. This disguising strategy induces the uninformed player to (...) cooperate in all periods of the repeated game, including the final period, at which point the player type who is unconcerned about fairness takes the opportunity to defect, i.e., he “backstabs” the uninformed player. Despite such last-minute defection, our results show that the introduction of incomplete information can actually result in a Pareto improvement under certain conditions. We connect the predictions of this “backstabbing” equilibrium with the frequently observed decline in cooperative behavior in the final period of finitely repeated experimental games. (shrink)

Cosmopolitanism is a form of egalitarianism about global justice. Egalitarians hold that economic inequalities are justifiable only under limited conditions. Cosmopolitans, like Brock, embrace basic principles of distributive justice that apply to all human beings. Their opponents, sometimes called liberal nationalists, are also egalitarians but limit the scope of egalitarian justice to cooperating members of a society. Outsiders are owed help to lead minimally decent lives but these are humanitarians obligations, not obligations of distributive justice. Brock’s defense of cosmopolitanism is (...) thoughtful and sensitive but appears to be too weak. Her basic principle of distributive justice appears to allow more inequality than cosmopolitans can accept. Liberal nationalists defend preference for fellow citizens and Brock seems not to have done a fully adequate job answering their arguments, especially their appeal to reciprocity among citizens. It’s therefore difficult to know where Brock stands on some of the crucial issues about global justice. (shrink)

In the homogeneous case of one-dimensional objects, we show that any relation that is positive and homothetic can be represented by a ratio-scale and a unique and constant biasing factor. This factor may favor or disfavor the preference for an object over another. In the first case, preferences are complete but not transitive and an object may be preferred even when its value is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and (...) it may not be sufficient for an object to have a greater value to be preferred. In this manner, the biasing factor reflects the extent to which preferences may depart from a maximization process. (shrink)

I argue that any plausible decision theory for agents with incomplete preferences which obeys the Never Worse Principle will violate Transitivity. The Never Worse Principle says that if one option never does worse than another, you shouldn’t disprefer it. Transitivity says that if you prefer X to Y and you prefer Y to Z, then you should prefer X to Z. Violating Transitivity allows one to be money pumped. Although agents with incomplete preferences are already, in (...) virtue of having incomplete preferences, vulnerable to being money pumped, I argue that the money pump argument for Transitivity is more serious than the one for Completeness. (shrink)

A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences.

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule (...) called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons. (shrink)

Incomplete preferences displaying ‘mildly sweetened’ structure are common, yet theoretically problematic. This paper examines the properties of the rankings induced by the set of all coherent completions of the mildly sweetened partial preference structure. Building on these properties, I propose an ensemble-based refinement of Hare’s prospectism criterion for rational choice when preferences are incomplete. Importantly, this ensemble-based refinement is immune to Peterson’s weak money pump argument. Hence, ensemble prospectism ensures outcome rationality. Furthermore, by recognizing the structural (...) isomorphism between mildly sweetened preference structures and Cover’s splitting rule in Blackwell’s Pick the Largest Number problem, ensemble prospectism can be shown to yield better-than-even odds of selecting the ex-post higher utility option—despite the absence of all-things-considered preferences ex ante. (shrink)

Nudges are small changes in the presentation of options that make a predictable impact on people's decisions. Proponents of nudges often claim that they are justified as paternalistic interventions that respect autonomy: they lead people to make better choices, while still letting them choose for themselves. However, existing work on nudges ignores the possibility of “hard choices”: cases where a person prefers one option in some respects, and another in other respects, but has no all‐things‐considered preference between the two. In (...) this paper, I argue that many significant medical decisions are hard choices that provide patients with an opportunity to exercise a distinctive sort of “formative autonomy” by settling their preferences and committing themselves to weigh their values in a particular way. Since nudges risk infringing formative autonomy by depriving patients of this opportunity, their use in medical contexts should be sensitive to this risk. (shrink)

Let’s say that you regard two things as on a par when you don’t prefer one to other and aren’t indifferent between them. What does rationality require of you when choosing between risky options whose outcomes you regard as on a par? According to Prospectism, you are required to choose the option with the best prospects, where an option’s prospects is a probability-distribution over its potential outcomes. In this paper, I argue that Prospectism violates a dominance principle—which I call The (...) Principle of Predominance—because it sometimes requires you to do something that’s no better than the alternatives and might be worse. I argue that this undermines the strongest argument that’s been given in favor of Prospectism. (shrink)