An expected utility model of individual choice is formulated which allows the decision maker to specify his available actions in the form of controls (partial contingency plans) and to simultaneously choose goals and controls in end-mean pairs. It is shown that the Savage expected utility model, the Marschak- Radner team model, the Bayesian statistical decision model, and the standard optimal control model can be viewed as special cases of this goal-control expected utility model.

The Borel–Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. (...) The conditional probabilities on probability zero events in the Borel–Kolmogorov Paradox also can be calculated using conditional expectations. The alleged clash arising from the fact that one obtains different values for the conditional probabilities on probability zero events depending on what conditional expectation one uses to calculate them is resolved by showing that the different conditional probabilities obtained using different conditional expectations cannot be interpreted as calculating in different parametrizations of the conditional probabilities of the same event with respect to the same conditioning conditions. We conclude that there is no clash between the correct intuition about what the conditional probabilities with respect to probability zero events are and the technically proper concept of conditionalization via conditional expectations—the Borel–Kolmogorov Paradox is just a pseudo-paradox. (shrink)

The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.

This paper is devoted to fill the gap in studying logics for biprobability structures. We introduce the logic equation image with two conditional expectation operators and prove the completeness theorem. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Reflection and martingale principles are central to models of rational learning. They can be justified in a variety of ways. In what follows we study martingale and reflection principles in the con...

We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the (...) probability measure. If a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric and non-transitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes’ rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization. (shrink)

Sequel to Armendt 1986, ‘A Foundation for Causal Decision Theory.’ The representation theorem for causal decision theory is slightly revised, with the addition of a new restriction on lotteries and a new axiom (A7). The discussion gives some emphasis to the way in which appropriate K-partitions are characterized by relations found among the agent’s conditional preferences. The intended interpretation of conditional preference is one that embodies a sensitivity to the agent’s causal beliefs.

Several fallacies of conditionalization are illustrated, using the two-envelope problem as a case in point.

Davey suggests that increased resistance to extinction of CRs conditioned to fear-relevant stimuli may be due to more persistent expectancies of the UCS following these stimuli. However, this viewpoint is contradicted by existing empirical evidence that fear-relevant CRs survive an extinction trials series producing extinction of expectancies whereas CRs conditioned to non-fear-relevant CSs do not.

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty (...) about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

As a rapidly growing emerging capital market, China has attracted the attention of both investors and scholars. To alleviate the expectation of external users of listed companies’ financial statements to “discount” items in levels 2 and 3 of the fair value measurement, listed companies will treat these items as conditional conservatism. It refers to the conservatism of companies when confirming bad news of unrealized gains and losses sooner than confirming good news. A sample was selected for empirical analysis (...) to verify the existence of this relationship. The results are as follows: the higher the proportion of levels 2 and 3 fair value measurements, the stronger the conditional conservatism of the company’s profit and loss; the higher the proportion of cash holding of operating activities in a company’s operating profit and the higher the audit quality, the higher the proportion of levels 2 and 3 fair value hierarchy measurements, and the stronger the conditional conservatism of the company’s profit and loss; and the lesser the internal control defects in a company, the higher the proportion of levels 2 and 3 fair value hierarchy measurements, and the stronger the conditional conservatism of its profit and loss. The findings provide empirical evidence to identify listed companies adopting conditional conservatism to alleviate discounting expectations of fair value items of financial statements’ external users and provide a reference for improving the standards and regulation of listed companies. (shrink)

During evaluative conditioning, a neutral conditional stimulus becomes pleasant or unpleasant after pairings with a positive/negative unconditional stimulus. Measures of US expectancy are...

Engineering and scientific education conditions us to expect everything, including intelligence, to have a simple, compact explanation. Accordingly, when people new to AI ask "What's AI all about," they seem to expect an answer that defines AI in terms of a few basic mathematical laws.

While the contemporary philosophical literature is replete with discussion of the control or freedom required for moral responsibility, only more recently has substantial attention been devoted to the knowledge or awareness required, otherwise called the epistemic condition. This area of inquiry is rapidly expanding, as are the various positions within it. This chapter introduces two major positions: the reasonable expectation view and the quality of will view. The chapter then explores two dimensions of the epistemic condition that serve as (...) fault lines along which these two views diverge. The first dimension concerns different kinds of ignorance. The second concerns what agents can be directly blameworthy for. The chapter closes by sketching a novel approach that incorporates advantages of opposing positions on this topic. (shrink)

Legitimate expectations should be considered in the transition to a low-carbon society. After explaining under what conditions and circumstances expectations are legitimate, this paper shows that those expectations whose frustration undermines the ability to plan, infringes basic moral rights, or is extremely costly for its bearer might justify a deviation in the baseline of justice in favour of the expectation holder. People should be notified about the likely frustration of their expectations so that they can avoid the frustration of (...) their expectations, adapt their life plans and minimise costs. Since the frustration of legitimate expectations seems unavoidable in the transformation to a low-carbon society, priority should be given to the protection of the expectations of those who cannot be materially compensated. Still, if two groups are eligible for material compensation, we should give priority to protecting the expectation of those who cannot continue with the same life plan as before if their expectations are frustrated. (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

I consider difficult data involving the interaction of attitudes and conditionals, specifically non-doxastic attitude expressions like 'regret'. I first show that felicitous attitude conditionals in "ignorance contexts", where the relevant person doesn't know the antecedent is true, give rise to a number of difficult problems given widely held assumptions in semantics. I then argue that, even so, we should expect these conditionals to be true and reasonable to utter in ignorance contexts, given certain other kinds of attitude construction that tend (...) to involve free relatives like `whatever'. I then use that observation to explain many of the more puzzling aspects of these conditionals, and to show that we should treat felicitous doxastic attitude conditionals differently from felicitous non-doxastic ones. I leave explaining felicitous doxastic attitude conditionals for future work, but offer constraints on a satisfying explanation of them. (shrink)

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should (...) be careful to distinguish diachronic update principles from related synchronic principles for conditional probability. (shrink)

Climate change increases the frequency and intensity of certain kinds of natural hazard events in alpine areas. This interdisciplinary study addresses the hypothetical possibility of relocating the residents of three alpine areas in Austria: the Sölk valleys, the Johnsbach valley, and the St. Lorenzen/Schwarzenbach valleys. Our particular focus is on these residents’ expectations about such relocations. We find that (1) many residents expect that in the next decades the state will provide them with a level of natural hazards protection, aid, (...) and relief that allows them to continue to live in these valleys; (2) this expectation receives some legal protection but only when it is associated with fundamental rights; and (3) the expectation is morally significant, i.e., it ought to be considered in assessing the moral rightness or justness of relocation policies. These results suggest legal changes and likely extend to many other (Austrian) alpine areas as well. (shrink)

Many philosophers think that a necessary condition on moral blameworthiness is that the wrongdoer can reasonably be expected to avoid the action for which she is blamed. Those who think so assume as a matter of course that the expectations at issue here are normative expectations that contrast with the non-normative or predictive expectations we form concerning the probable conduct of others, and they believe, or at least assume, that there is a clear-cut distinction between the two. In this paper (...) I put this widespread assumption under scrutiny and argue that it’s mistaken: although predictive and normative expectations are indeed distinct, there is no sharp separation between them. On the contrary, predictive expectations can have a substantial bearing on normative expectations in two related ways: they can recalibrate what is reasonable to expect of agents when responsibility attributions are at stake and they can help to uncover previously undetected excusing conditions. I illustrate my claims with the famous bystander effect from social psychology and show that it yields predictive expectations that affect normative expectations in these two ways. (shrink)

I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not (...) require the binary relation reflecting an agent’s comparative judgments to be reflexive, complete or even transitive, and it applies to an absolutely arbitrary collection of gambles, free of structural conditions (e.g., closure, measurability, etc.). Moreover, unlike de Finetti’s criterion of coherence, the qualitative criterion respects the principle of weak dominance, a standard of rational decision making that obliges an agent to reject a gamble that is possibly worse and certainly no better than another gamble available for choice. Despite these weak assumptions, I establish a qualitative analogue of de Finetti’s Fundamental Theorem of Prevision, from which it follows that any coherent system of comparative expectations can be extended to a weakly ordered coherent system of comparative expectations over any collection of gambles containing the initial set of gambles of interest. The extended weakly ordered coherent system of comparative expectations satisfies familiar additivity and scale invariance postulates (i.e., independence) when the extended collection forms a linear space. In the course of these developments, I recast de Finetti’s quantitative account of coherent prevision in the qualitative framework adopted in this article. I show that comparative previsions satisfy qualitative analogues of de Finetti’s famous bookmaking theorem and his Fundamental Theorem of Prevision.The results of this article complement those of another article (Pedersen, Strictly coherent preferences, no holds barred, Manuscript, 2013). I explain how those results entail that any coherent weakly ordered system of comparative expectations over a unital linear space can be represented by an expectation function taking values in a (possibly non-Archimedean) totally ordered field extension of the system of real numbers. The ordered field extension consists of formal power series in a single infinitesimal, a natural and economical representation that provides a relief map tracing numerical non-Archimedean features to qualitative non-Archimedean features. (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as (...) we want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

This paper is concerned with how we ought to think about legitimate expectations in the non-ideal, ‘real’ world. In one (dominant) strand of contemporary theories of justice, justice requires not that each gets what she deserves, but that each gets that to which she is entitled in accordance with what Rawls calls ‘the public rules that specify the scheme of cooperation’. However, that is true only if those public rules are part of a fully just scheme and it is plausibly (...) the case that no such scheme obtains in the real world. Given that, and given the centrality of legitimate expectations to theories of justice, it is vital to think about the status of such expectations in non-ideal circumstances. Having explained the sense in which legitimate expectations have come to play a role often previously associated with desert, a brief argument in favour of an ‘expectations’ view of punishment is considered to show that the system to public rules that generates expectations must itself be (in some sense) just. This argument is illustrated by appeal to just punishment and the relevance of thinking about punishment and not merely distributive justice is defended. In the absence of justice, one possibility would be simply to declare that there are no legitimate expectations and so theories of justice provide no guidance as to who should get what in non-ideal conditions. However, this would be to render such theories more-or-less useless in practice. Through discussion of a series of vignettes, the paper offers an account of how we might think about the demands such expectations place on the systems that give rise to them even in cases where the system is unjust. (shrink)

Life history theory predicts that greater extrinsic mortality will lead to earlier and higher fertility. To test this prediction, I examine the relationship between life expectancy at birth and several proxies for life history traits (ages at first sex and first marriage, total fertility rate, and ideal number of children), measured for both men and women. Data on sexual behaviors come from the Demographic and Health Surveys (DHS). Two separate samples are analyzed: a cross-sectional sample of 62 countries and a (...) panel sample that includes multiple cross-sectional panels from 48 countries. Multivariate regression analysis is used to control for potential confounding variables. The results provide only partial support for the predictions, with greater support among women than men. However, the prediction is not supported in sub-Saharan African countries, most likely owing to the nonequilibrium conditions observed in sub-Saharan Africa with respect to life expectancy. The applicability of the model to understanding HIV/AIDS risk behaviors is discussed. (shrink)

Causal decision theory attends to probabilities used to obtain an option's expected utility but for completeness should also attend to utilities of possible outcomes. A suitable formula for an option's expected utility uses a certain type of conditional utility.

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

We introduce an expected-value theory of linguistic modality that makes reference to expected utility and a likelihood-based confirmation measure for deontics and epistemics, respectively. The account is a probabilistic semantics for deontics and epistemics, yet it proposes that deontics and epistemics share a common core modal semantics, as in traditional possible-worlds analysis of modality. We argue that this account is not only theoretically advantageous, but also has far-reaching empirical consequences. In particular, we predict modal versions of reasoning fallacies from the (...) heuristics and biases literature. Additionally, we derive the modal semantics in an entirely transparent manner, as it is based on the compositional semantics of Korean modal expressions that are morphosyntactically decomposed into a conditional and an evaluative predicate. (shrink)

Predictive processing has begun to offer new insights into the nature of conscious experience—but the link is not straightforward. A wide variety of systems may be described as predictive machines, raising the question: what differentiates those for which it makes sense to talk about conscious experience? One possible answer lies in the involvement of a higher-order form of prediction error, termed expected free energy. In this paper we explore under what conditions the minimization of this new quantity might underpin conscious (...) experience. Our suggestion is that the minimisation of Expected Free Energy is not in itself sufficient for the occurrence of conscious experience. Instead, it is relevant only insofar as it helps deliver what Ward et al. ( 2011 ) have previously described as a _sense of our own poise over an action space_. Perceptual experience, we will argue, is nothing other than the process that puts current actions in contact with goals and intentions, enabling some creatures to know the space of options that their current situation makes available. This proposal fits with recent work suggesting a deep link between conscious contents and contents computed at an ‘intermediate’ level of processing, apt for controlling action. (shrink)

The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis's argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The aim of (...) this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of 'value propositions' are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions. (shrink)

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler. A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent (...) utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable. (shrink)

While all psychologically competent persons know that they will one day die, this knowledge is typically held at a distance, not fully assimilated. That is, while we do not doubt that we will die, there is another sense in which we cannot fully believe it either. However, on some rare occasions, we can grasp the reality of our mortal nature in a way that is seemingly revelatory, as if the fact is appreciated in a new way. Thomas Nagel calls this (...) experience ‘the expectation of nothingness’. But how can I be shocked by what I already know? After illustrating this phenomenon via examples including Tolstoy’s The Death of Ivan Ilyich, I draw on the work of Thomas Nagel, Tamar Szabo Gendler, Mark Johnston and others to articulate and explain our typical state of believing-yet-not-believing in our inevitable death, and offer a hypothesis as to how this condition is occasionally overcome, so that we grasp our mortality in a more psychologically integrated manner. (shrink)

Standard theories of expected utility require that preferences are complete, and/or Archimedean. We present in this paper a theory of decision under uncertainty for both incomplete and non-Archimedean preferences. Without continuity assumptions, incomplete preferences on a lottery space reduce to an order-extension problem. It is well known that incomplete preferences can be extended to complete preferences in the full generality, but this result does not necessarily hold for incomplete preferences which satisfy the independence axiom, since it may obviously happen that (...) the extension does not satisfy the independence axiom. We show, for incomplete preferences on a mixture space, that an extension which satisfies the independence axiom exists. We find necessary and sufficient conditions for a preorder on a finite lottery space to be representable by a family of lexicographic von Neumann–Morgenstern Expected Utility functions. (shrink)

Expectations play an important role in how people plan their lives and pursue their projects. People living in highly industrialized countries share a way of life that comes with high levels of emissions. Their expectations to be able to continue their projects imply their holding expectations to similarly high future levels of personal emissions. We argue that the frustration or undermining of these expectations would cause them significant harm. Further, the article investigates under what conditions people can be thought to (...) hold legitimate expectations, in particular about permissible levels of future emissions. We distinguish differing theories of understanding these conditions, namely authority-based and justice-based theories, that each allows us to systematically distinguish between legitimate and illegitimate expectations. Furthermore, with respect to individuals’ future permissible emissions we give several reasons for holding that such theories cannot identify a particular expectation to a specific level of personal emissions as the only legitimate one. Finally, we argue that the set of legitimate expectations that people hold with respect to a just and effective solution to climate change has normative significance in at least two ways: the differing but equally legitimate expectations ought to be taken into account when justifying what could count as such a solution and when determining the just way of arriving at and implementing such a solution. (shrink)

Utility theories—both Expected Utility (EU) and non-Expected Utility (non-EU) theories—offer numericalized representations of classical principles meant for the regulation of choice under conditions of risk—a type of formal representation that reduces the representation of risk to a single number. I shall refer to these as risk-numericalizing theories of decision. I shall argue that risk-numericalizing theories (referring both to the representations and to the underlying axioms that render numericalization possible) are not satisfactory answers to the question: “How do I take the (...) (best) means to my ends?” In other words, they are inadequate or incomplete as instrumental theories. They are inadequate because they are poor answers to the question of what it is for an option to be instrumental towards an end. To say it another way, they do not offer a sufficiently rich account of what it is for something to be a means (an instrument) toward an end. (shrink)

In this paper I show how the way experience presents things to us can be treated without attributing a representational content to experience. The basic claim that experience can present us with more things than the range of things available to us in thought is neutral with respect to the choice between a content account of experience and a naïve content-free account. I show how Meyer's theory of expectations in accounting for our experience of music supports the naïve account. Expectations (...) provide an account of the conditions that enable things to be salient in experience as targets for attention. Expectations do not provide a content to experience. (shrink)