Preference orderings assigned by coherent lower and upper conditional previsions are defined and they are considered to define maximal random variables and Bayes random variables. Sufficient conditions are given such that a random variable is maximal if and only if it is a Bayes random variable. In a metric space preference orderings represented by coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures are given.

This article discusses approaches to the problem of the number of preference orderings that can be constructed from a given set of alternatives. After briefly reviewing the prevalent approach to this problem, which involves determining a partitioning of the alternatives and then a permutation of the partitions, this article explains a recursive approach and shows it to have certain advantages over the partitioning one.

In a recent article published in this journal (van Deemter, Gatt, van der Sluis, & Power, 2012), the authors criticize the Incremental Algorithm (a well-known algorithm for the generation of referring expressions due to Dale & Reiter, 1995, also in this journal) because of its strong reliance on a pre-determined, domain-dependent Preference Order. The authors argue that there are potentially many different Preference Orders that could be considered, while often no evidence is available to determine which is a (...) good one. In this brief note, however, we suggest (based on a learning curve experiment) that finding a Preference Order for a new domain may not be so difficult after all, as long as one has access to a handful of human-produced descriptions collected in a semantically transparent way. We argue that this is due to the fact that it is both more important and less difficult to get a good ordering of the head than of the tail of a Preference Order. (shrink)

A second-order preference is a preference over preferences. This paper addresses the role that second-order preferences play in a theory of instrumental rationality. I argue that second-order preferences have no role to play in the prescription or evaluation of actions aimed at ordinary ends. Instead, second-order preferences are relevant to prescribing or evaluating actions only insofar as those actions have a role in changing or maintaining first-order preferences. I establish these claims by examining and rejecting the view that (...) second-order preferences trump first-order preferences. I also examine and reject the view that second-order preferences give additional normative force to an agent’s preferred first-order preferences. I conclude by arguing that second-order preferences should be integrated into an agent’s object-level preference ordering, and by explaining how best to make sense of this integration. (shrink)

In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete (...) axiomatisation for this class, without having the number of individuals or alternatives specified in the language. We are able to express classical axiomatic requirements in our first-order language, giving formal axioms for three classical theorems of preference aggregation by Arrow, by Sen, and by Kirman and Sondermann. We explore to what extent such theorems can be formally derived from our axiomatisations, obtaining positive results for Sen’s Theorem and the Kirman-Sondermann Theorem. For the case of Arrow’s Theorem, which does not apply in the case of infinite societies, we have to resort to fixing the number of individuals with an additional axiom. In the long run, we hope that our approach to formalisation can serve as the basis for a fully automated proof of classical and new theorems in social choice theory. (shrink)

The cognitive critique of the goals and desires that are input into the implicit calculations that result in instrumental rationality is one aspect of what has been termed broad rationality (Elster, 1983). This cognitive critique involves, among other things, the search for rational integration (Nozick, 1993)—that is, consistency between first-order and second-order preferences. Forming a second-order preference involves metarepresentational abilities made possible by mental decoupling operations. However, these decoupling abilities are separable from the motive that initiates the cognitive critique (...) itself. I argue that Velleman (1992) has identified that motive (“the desire to act in accordance with reasons”), and that it might be operationalisable as a thinking disposition at a very superordinate cognitive level. This thinking disposition, the Master Rationality Motive, is likely to be of particular importance in explaining individual differences in the tendency to seek rational integration. Preliminary research on related constructs suggests that this construct is measurable. (shrink)

It seems natural to think of an unwilling addict as having a pattern of preferences that she does not endorse—preferences that, in some sense, she does not ‘identify’ with. Following Frankfurt (1971), Jeffrey (1974) proposed a way of modeling those features of an agent’s preferences by appealing to preferences among preferences.Th„e addict’s preferences are preferences she does not prefer to have. I argue that this modeling suggestion will not do, for it follows from plausible assumptions that a minimally rational agent (...) must prefer those first-order preferences she actually has. I close by considering two different but related ways to think about the initial phenomenon. (shrink)

Axiomatizations of ordered preference differences typically assume that preferences are ordered. However, the mere assumption that preference differences can be ordered says nothing about whether preferences themselves are ordered. Utility representations for ordered differences without ordered preferences are investigated.

A method is presented for collecting data which yield a scale on which the entities are ranked in preference and all combinations of value distances are ranked. The method is based on the concept of secondary preference, i.e. preference among preferences. This method is compared with a classical method based on 50–50 game comparison. Two empirical studies are presented. The first examines whether both methods yield the same ordering of value distances. The second involves empirical derivation of (...) a higher-ordered metric scale. (shrink)

Recently, Jardas _et al_ have convincingly defended the patient preference predictor (PPP) against a range of autonomy-based objections. In this response, I propose a new autonomy-based objection to the PPP that is not explicitly discussed by Jardas _et al_. I call it the ‘objection from higher-order preferences’. Even if this objection is not sufficient reason to reject the PPP, the objection constitutes a pro tanto reason that is at least as powerful as the ones discussed by Jardas _et al._.

Normative theories suggest that inconsistencies be pointed out to the Decision Maker who is thus given the chance to modify his/her judgments. In this paper, we suggest that the inconsistencies problem be transferred from the Decision Maker to the Analyst. With the Mixture of Maximal Quasi Orders, rather than pointing out incoherences for the Decision Maker to change, these inconsistencies may be used as new source of information to model his/her preferences.

This article presents a characterization of higher-order risk preferences such as prudence or temperance in terms of statistical moments. Our results, which are generalizations of Roger :27–44, 2011) and Ekern, 329–333, 1980), give a better understanding of how higher-order risk preferences relate to skewness preference and kurtosis aversion. While they are not based on expected utility theory, an implication within that theory is that all commonly used utility functions exhibit skewness preference and kurtosis aversion.

To advertise or estimate demand, many pre-order items appear on crowdfunding platforms. Few studies have explored backers’ preferences between crowdfunding projects and pre-order items. To analyze backers’ preferences, 1,800 technology and innovation campaigns were collected from the Indiegogo crowdfunding platform. Using the product stage badge, the campaigns in the concept and prototype stages were treated as crowdfunding projects, while those in the production and shipping stages were labeled pre-order items, resulting in 1,305 crowdfunding projects and 495 pre-order items, respectively. Propensity (...) score matching was leveraged to investigate differences in fundraising outcomes between crowdfunding projects and pre-order items. The results indicate that pre-order items have better fundraising outcomes than crowdfunding projects, suggesting that backers are risk-averse on the crowdfunding platform. (shrink)

Abstracts These are abstracts of the papers that receive a reply, not of the replies themselves. The abstracts appear in the alphabetical order of the authors' names; for the contributions to the ...

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

We consider the role of preferences in the assessment of an agent's freedom, visualized as the opportunity for choice. After discussing several possible intuitive approaches to the problem, we explore an approach based on the notion of preference orderings that a reasonable person may possibly have. Using different sets of axioms, we characterize the rules for ranking opportunity sets in terms of freedom. We also show that certain axioms for ranking opportunity sets are incompatible.

A much discussed topic in the theory of choice is how a preference order among options can be derived from the assumption that the notion of ' choice' is primitive. Assuming a choice function that selects elements from each finite set of options, Arrow (Económica 26: 121-127,1959) already showed how we can generate a weak ordering by putting constraints on the behavior of such a function such that it reflects utility maximization. Arrow proposed that rational agents can be modeled (...) by such choice functions. Arrow's standard model of rationality has been criticized in economics and gave rise to approaches of bounded rationality. Two standard assumptions of rationality will be given up in this paper. First, the idea that agents are utility optimizers (Simon). Second, the idea that the relation of ' indifference' gives rise to an equivalence relation. To account for the latter, Luce (Econometrica 24: 178-191, 1956) introduced semi-orders. Extending some ideas of Van Benthem (Pac Philos Q 63: 193-203, 1982), we will show how to derive semi-orders (and so-called interval orders) based on the idea that agents are utility satisficers rather than utility optimizers. (shrink)

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief (...) revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation. (shrink)

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference logic (...) (cf. Hansson [10]) studies formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can “deconstruct” standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power.. (shrink)

In general, the technical apparatus of decision theory is well developed. It has loads of theorems, and they can be proved from axioms. Many of the theorems are interesting, and useful both from a philosophical and a practical perspective. But decision theory does not have a well agreed upon interpretation. Its technical terms, in particular, ‘utility’ and ‘preference’ do not have a single clear and uncontroversial meaning. How to interpret these terms depends, of course, on what purposes in pursuit (...) of which one wants to put decision theory to use. One might want to use it as a model of economic decision-making, in order to predict the behavior of corporations or of the stock market. In that case, it might be useful to interpret the technical term ‘utility’ as meaning money profit. Decision theory would then be an empirical theory. I want to look into the question of what ‘utility’ could mean, if we want decision theory to function as a theory of practical rationality. I want to know whether it makes good sense to think of practical rationality as fully or even partly accounted for by decision theory. I shall lay my cards on the table: I hope it does make good sense to think of it that way. For, I think, if Humeans are right about practical rationality, then decision theory must play a very large part in their account. And I think Humeanism has very strong attractions. (shrink)

We consider the role of preferences in the assessment of an agent's freedom, visualized as the opportunity for choice. After discussing several possible intuitive approaches to the problem, we explore an approach based on the notion of preference orderings that a reasonable person may possibly have. Using different sets of axioms, we characterize the rules for ranking opportunity sets in terms of freedom. We also show that certain axioms for ranking opportunity sets are incompatible.

Cognitive Science, Volume 46, Issue 10, October 2022.

The illness immersion condition prevents patients from enjoying everything worth living life for. In any case, according to Frank, this condition could represent one of the most insightful experiences towards understanding the meaning of life. Using the metaphor of phoenix taken from May, Frank identified four kinds of embodiments through which the phoenix can reveal itself in a patient after an illness immersion experience: the phoenix that could ever be and the phoenix that might have been; the recurrent and cumulative (...) phoenix and the reluctant phoenix. Based on these considerations, a qualitative study was conducted in order to give voice to the different phoenix embodiments focusing on several autobiographies of patients afflicted with severe or terminal illness. The analysis highlights several similarities that the different phoenixes shared ; however, a deep difference emerged in their worldview which proves able to lead them towards different epiphanies. These evidences reveal that every sick person should be understood, stimulated and accompanied throughout his lived experience of illness by an expressly designed and dedicated care. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the (...) status quo, then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status quo and the (...) lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence. (shrink)

In this rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.

Accounts of adaptive preferences are of two kinds: well-being accounts fully theorized for their own sake and political accounts theorized to facilitate the political project of reducing oppression and marginalization. Given their practical role, the latter are often less fully theorized, and are therefore less robust to theoretical criticism. In this paper, I first draw on well-being accounts to identify the well-theorized elements that political accounts should want to adopt in order to strengthen their project and avoid common criticisms. Second, (...) I appeal to the political project to show the shortcomings of the well-being accounts on which I draw. (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 (...) class='Hi'>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 rather technical paper we establish a useful combination of belief revision and verisimilitude according to which better theories provide better predictions, and revising with more verisimilar data results in theories that are closer to the truth. Moreover, this paper presents two alternative definitions of refined verisimilitude, which are more perspicuous than the algebraic version used in previous publications.

This paper examines an extended framework of Arrovian social choice theory. We consider two classes of values: consequential values and non-consequential values. Each individual has a comprehensive preference based on the two. Non-consequential values are assumed to be homogeneous among individuals. It is shown that a social ordering function satisfying Arrovian conditions must be non-consequential: a social comprehensive preference gives unequivocal priority to non-consequential values. We clarify the role of common preferences over non-consequential features.

Seidenfeld (Seidenfeld, T. [1988a], Decision theory without 'Independence' or without 'Ordering', Economics and Philosophy 4: 267-290) gave an argument for Independence based on a supposition that admissibility of a sequential option is preserved under substitution of indifferents at choice nodes (S). To avoid a natural complaint that (S) begs the question against a critic of Independence, he provided an independent proof of (S) in his (Seidenfeld, T. [1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy 4: 309-315). In reply to (...) my (Rabinowicz, W. [1995], To have one's cake and eat it too: Sequential choice and expected-utility violations, The Journal of Philosophy 92: 586-620), in which I argue that the proof is invalid, Seidenfeld (Seidenfeld, T. [2000], Substitution of indifferent options at choice nodes and admissibility: A reply to Rabinowicz, Theory and Decision 48: 305–310 this issue) submits that I fail to give due consideration to one of the underlying assumptions of his derivation: it is meant to apply only to those cases in which the agent's preferences are stable throughout the sequential decision process. The purpose of this note is to clarify the notion of preference stability so as meet this objection. (shrink)

To the normal reasons that we think can justify one in preferring something, x (namely, that x has objectively preferable properties, or has properties that one prefers things to have, or that x's obtaining would advance one's preferences), I argue that it can be a justifying reason to prefer x that one's very preferring of x would advance one's preferences. Here, one prefers x not because of the properties of x, but because of the properties of one's having the (...) class='Hi'>preference for x. So-revising one's preferences is rational in paradoxical choice situations like Kavka's Deterrence Paradox. I then try to meet the following objections: that this is stoicist, incoherent, bad faith; that it conflates instrumental and intrinsic value, gives wrong solutions to the problems presented by paradoxical choice situations, entails vicious regresses of value justification, falsifies value realism, makes valuing x unresponsive to x's properties, causes value conflict, conflicts with other standards of rationality, violates decision theory, counsels immorality, makes moral paradox, treats value change as voluntary, conflates first- and second-order values, is psychologically unrealistic, and wrongly presumes that paradoxical choice situations can even occur. (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)

This paper focuses on a specific challenge for welfarist theories of intergenerational justice. Subjective welfarism permits and even requires that a generation, G1, inculcates cheap preferences in the next generation, G2. This would allow G1 to deplete resources instead of saving them, which seems to contradict the ideal of sustainability. The aim of the paper is to show that, even if subjective welfarism requires the cultivation of cheap preferences among future generations, it can accommodate two major objections to cheap preferences (...) engineering, the Autonomy Objection and the Fairness Objection. The paper argues that teaching autonomy-related abilities is compatible with cheap preferences engineering insofar as autonomy is understood as an end-state and not as a precondition. Furthermore, teaching autonomy-related abilities could even be required in order to improve G2’s prospects for well-being. However, since being autonomous renders G2 able to revise their initially cheap preferences, G1 should also save enough resources to enable members of G2 to do so. Therefore, cultivating cheap preferences among G2 does not allow G1 to deplete the available resources. (shrink)

According to normative decision theory there exists a principle of procedure invariance which states that a decision maker's preference order should remain the same, independently of which response mode is used. For example, the decision maker should express the same preference independently of whether he or she has to judge or decide. Nevertheless, previous research in behavioral decision making has suggested that judgments and choices yield different preference orders in both the risky and the riskless domain. In (...) the latter, the prominence effect has been demonstrated. The main purpose of the present series of experiments was to test cognitive explanations which account for the prominence effect. One of the explanations provided a psychological account based primarily on decision-strategy compatibility. Two other explanations built on information structuring approaches. In the first one, the general idea was that decision makers differentiate between alternatives by value and belief restructuring. In the second approach, violations of invariance were assumed to be attributed to the information structure of the task which in many cases demand problem simplification. A prominence effect was in most experiments found for both choices and preference ratings. This finding spöke against the strategy compatibility explanation. Instead, the different forms of cognitive restructuring provided a better account. However, none of these provided a single explanation. Yet, the structure compatibility explanation appeared to be the more viable one, in particular of the relation between experimentäl manipulations and response mode outcomes. The predictions of the value-belief restructuring explanation, on the other hand, seemed to be more valid for the prominence effect found in choice than for preference ratings. (shrink)

Philosophers have advocated different kinds of freedom, but each has value and none should be neglected in a complete theory of freedom and responsibility. There are three kinds of freedom of preference and action that should be distinguished. A person S may fully prefer to do A at every level, and that is one kind of freedom. A person S may autonomously prefer to do A when S has the preference structure concerning doing A because S prefers to (...) have that very preference structure, and that is a second kind of freedom. A person S may prefer to do A when S could have preferred otherwise, and that is a third kind of freedom. These forms of freedom may be combined, but they are valuable and essentially independent. They all involve the metamental ascendence of preference over desire, but it is autonomous preference that makes a person the author of his or her preference. The responsibility a person has for what he or she does out of a preference for doing it depends on the kinds of freedom of preference the person has and must be ranked in terms of them. (shrink)

The presented contribution stresses the role of preference ordering and of the logical culture in many spheres of human rational activities, especially in the domains connected with evaluating and decision-making tasks. Since preference relation is conceived as a relation of proposition-like-entities , any construction of preference ordering pre_- supposes the application of comparability principles. Preference expressions can be considered as a special form of propositional attitudes and the concept of preference itsself as an intensional operator.

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group (...) R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

When discussing the general inertia in climate change mitigation, it is common to approach the analysis either in terms of epistemic obstacles (climate change is too scientifically complex to be fully understood by all in its dramatic nature and/or to find space in the media) and/or moral obstacles (the causal link between polluting actions and social damage is too loose, both geographically and temporally, to allow individuals to understand the consequences of their emissions). In this chapter I maintain that both (...) categories of obstacles now play a secondary role: many people have a clear understanding of the physical and social dynamics involved in climate change. The main reason why so few manage to reduce their ecological footprint is an ethical short-circuit that does not allow most people to reveal their “true” climate-related preferences in their daily choices. This short-circuit manifests itself in two phenomena that can be analysed through the lens of moral psychology. First, as the possibility of anticipated utility approaches, individuals further discount expected future utility and may even reverse their preferences (due to the so-called immediacy multiplier, in addition to the better known and discussed future utility discounting). Second, individuals struggle to order their preferences transitively when presented with the opportunity to obtain small net marginal utilities in the short run. The intertemporal and collective structure of the climate problem creates fertile ground for both phenomena, which means that even those who are sincerely convinced of the need to contribute to climate change mitigation end up trapped in loops of procrastination, both first and second level. If, however, we can understand the origin of these phenomena, then we will be able to devise counteracting solutions that will speed up individual mitigation efforts. I will therefore briefly propose three ethical/public strategies to break the procrastination loop: pre-commitment; increasing the costs of marginal postponements; reducing the disutility of action that is likely to be postponed. (shrink)