Traditional portfolio selection models mainly obtain the optimized portfolio ratio by focusing on the prices of financial products. However, investors’ multiple preferences and risk appetites are also significant factors that should be taken into account. In consideration of these two factors simultaneously, we propose a double-hierarchy model in this paper. Specifically, the first hierarchy quantifies investors’ risk appetite based on a historical simulation method and probabilistic preference theory. This hierarchy can be utilized to describe investors’ variable risk appetites (...) and ensure the obtained investment ratios meet investors’ immediate risk requirements. Then, using the cross-efficiency evaluation principle, the optimal investment ratios can be derived by fusing investors’ multiple preferences and risk appetites in the second hierarchy. Lastly, an illustrative example about evaluating the 10 largest capitalized stocks on the Shenzhen Stock Exchange is given to verify the feasibility and effectiveness of our newly proposed model. We make the theoretical contribution to improve the traditional portfolio selection model, especially considering investors’ subjective preferences and risk appetite. Moreover, the proposed model can be practical for assisting investors with their investment strategies in real life. (shrink)

Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In (...) each case preferencedefects serve as a diagnostic tool, indicating purely epistemic defects. (shrink)

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain (...) or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves (...) one’s conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’. (shrink)

Decision-theoretic representation theorems have been developed and appealed to in the service of two important philosophical projects: in attempts to characterise credences in terms of preferences, and in arguments for probabilism. Theorems developed within the formal framework that Savage developed have played an especially prominent role here. I argue that the use of these ‘Savagean’ theorems create significant difficulties for both projects, but particularly the latter. The origin of the problem directly relates to the question of whether we can (...) have credences regarding acts currently under consideration and the consequences which depend on those acts; I argue that such credences are possible. Furthermore, I argue that attempts to use Jeffrey’s non-Savagean theorem in the service of these two projects may not fare much better. (shrink)

The problems of access—retrieving linguistic structure from some mental grammar —and disambiguation—choosing among these structures to correctly parse ambiguous linguistic input—are fundamental to language understanding. The literature abounds with psychological results on lexical access, the access of idioms, syntactic rule access, parsing preferences, syntactic disambiguation, and the processing of garden‐path sentences. Unfortunately, it has been difficult to combine models which account for these results to build a general, uniform model of access and disambiguation at the lexical, idiomatic, and syntactic (...) levels. For example, psycholinguistic theories of lexical access and idiom access and parsing theories of syntactic rule access have almost no commonality in methodology or coverage of psycholinguistic data. This article presents a single probabilistic algorithm which models both the access and disambiguation of linguistic knowledge. The algorithm is based on a parallel parser which ranks constructions for access, and interpretations for disambiguation, by their conditional probability. Low‐ranked constructions and interpretations are pruned through beam‐search; this pruning accounts, among other things, for the garden‐path effect. I show that this motivated probabilistic treatment accounts for a wide variety of psycholinguistic results, arguing for a more uniform representation of linguistic knowledge and for the use of probabilistically‐enriched grammars and interpreters as models of human knowledge of and processing of language. (shrink)

Experimental research shows that human sentence processing uses information from different levels of linguistic analysis, for example, lexical and syntactic preferences as well as semantic plausibility. Existing computational models of human sentence processing, however, have focused primarily on lexico‐syntactic factors. Those models that do account for semantic plausibility effects lack a general model of human plausibility intuitions at the sentence level. Within a probabilistic framework, we propose a wide‐coverage model that both assigns thematic roles to verb–argument pairs and (...) determines a preferred interpretation by evaluating the plausibility of the resulting (verb, role, argument) triples. The model is trained on a corpus of role‐annotated language data. We also present a transparent integration of the semantic model with an incremental probabilistic parser. We demonstrate that both the semantic plausibility model and the combined syntax/semantics model predict judgment and reading time data from the experimental literature. (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)

I develop a probabilistic account of coherence, and argue that at least in certain respects it is preferable to (at least some of) the main extant probabilistic accounts of coherence: (i) Igor Douven and Wouter Meijs’s account, (ii) Branden Fitelson’s account, (iii) Erik Olsson’s account, and (iv) Tomoji Shogenji’s account. Further, I relate the account to an important, but little discussed, problem for standard varieties of coherentism, viz., the “Problem of Justified Inconsistent Beliefs.”.

Uncertainty in Post-Reformation Catholicism provides a historical account of early modern probabilism and its theological, intellectual, and cultural implications. First developed in the second half of the sixteenth century, probabilism represented a significant and controversial novelty in Catholic moral theology. By the second half of the seventeenth century, probabilism became and has since been associated with moral, intellectual, and cultural decadence. Stefania Tutino challenges this understanding and claims that probabilism played a central role in addressing the challenges that geographical and (...) cultural expansions posed to traditional Catholic theology. Tutino argues that early modern theologians used probabilism to integrate major changes within the post-Reformation Catholic theological and intellectual system. Probabilist theologians realized that their time was characterized by many changes that traditional theology was not equipped to deal with, which consequently provoked an exponential growth of uncertainties, doubts, and dilemmas of conscience. Probabilism represented the result of their efforts to appreciate, come to terms with, and manage that uncertainty. Uncertainty in Post-Reformation Catholicism reinterprets probabilism as a way of dealing with moral and epistemological doubts in quickly changing times, a way that still may be useful today. Uncertainty in Post-Reformation Catholicism argues that probabilism played a central role in addressing the challenges that a geographically and intellectually expanding world posed to traditional Catholic theology. Early modern probabilist theologians realized that their time was characterized by many changes and novelties that traditional theology was not equipped to deal with, and that consequently provoked an exponential growth of uncertainties, doubts, and dilemmas of conscience. These theologians used probabilism as a means to integrate changes and novelties within the post-Reformation Catholic theological and intellectual system. Seen in this light, probabilism represented the result of their attempts to appreciate, come to terms with, and manage uncertainty. The problem of uncertainty was not only crucial then, but remains central even today. Despite the unprecedented amount of information available to us, we are becoming less able to formulate arguments based on facts, and more dependent on a cacophony of opinions that often simply reproduce our own implicit or explicit biases, prejudices, and preconceived preferences. (shrink)

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters depends (...) on the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay. (shrink)

Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is (...) also hard to reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms. (shrink)

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an (...) autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone. (shrink)

The area of smart power grids needs to constantly improve its efficiency and resilience, to provide high quality electrical power in a resilient grid, while managing faults and avoiding failures. Achieving this requires high component reliability, adequate maintenance, and a studied failure occurrence. Correct system operation involves those activities and novel methodologies to detect, classify, and isolate faults and failures and model and simulate processes with predictive algorithms and analytics. In this paper, we showcase the application of a complex-adaptive, self-organizing (...) modeling method, and Probabilistic Boolean Networks, as a way towards the understanding of the dynamics of smart grid devices, and to model and characterize their behavior. This work demonstrates that PBNs are equivalent to the standard Reinforcement Learning Cycle, in which the agent/model has an interaction with its environment and receives feedback from it in the form of a reward signal. Different reward structures were created to characterize preferred behavior. This information can be used to guide the PBN to avoid fault conditions and failures. (shrink)

The basic theory of preference relations contains a trivial part reflected by axioms A1 and A2, which say that preference relations are preorders. The next step is to find other axims which carry the theory beyond the level of the trivial. This paper is to a great part a critical survey of such suggested axioms. The results are much in the negative — many proposed axioms imply too strange theorems to be acceptable as axioms in a general theory of preference. (...) This does not exclude, of course, that they may well be reasonable axioms for special calculi of preference. I believe that many axioms which are rejected here may be plausible if their range of application is restricted by conditions which are possible to formulate only in a language richer than that of the propositional calculus, e.g. in one containing modal operators or probabilistic concepts. (shrink)

To the extent that we have reasons to avoid these “bad B -properties”, these arguments provide reasons not to have an incoherent credence function b — and perhaps even reasons to have a coherent one. But, note that these two traditional arguments for probabilism involve what might be called “pragmatic” reasons (not) to be (in)coherent. In the case of the Dutch Book argument, the “bad” property is pragmatically bad (to the extent that one values money). But, it is not clear (...) whether the DBA pinpoints any epistemic defect of incoherent agents. The same can be said for Representation Theorem arguments, since they involve the structure of an agent’s preferences. (shrink)

I evaluate two contractualist approaches to the ethics of risk: mutual constraint and the probabilistic, ex ante approach. After explaining how these approaches address problems in earlier interpretations of contractualism, I object that they fail to respond to diverse risk preferences in populations. Some people could reasonably reject the risk thresholds associated with these approaches. A strategy for addressing this objection is considering individual risk preferences, similar to those Buchak discusses concerning expected-utility approaches to risk. I defend (...) the risk-preferences-adjusted contractualist approach, which calculates a population’s average risk preference and permits risk thresholds below that preference, only. (shrink)

The present study assessed the degree to which probabilistic reasoning performance and thinking style influenced perception of risk and self-reported levels of terrorism-related behaviour change. A sample of 263 respondents, recruited via convenience sampling, completed a series of measures comprising probabilistic reasoning tasks (perception of randomness, base rate, probability, and conjunction fallacy), the Reality Testing subscale of the Inventory of Personality Organization (IPO-RT), the Domain-Specific Risk-Taking Scale, and a terrorism-related behaviour change scale. Structural equation modelling examined three progressive (...) models. Firstly, the Independence Model assumed that probabilistic reasoning, perception of risk and reality testing independently predicted terrorism-related behaviour change. Secondly, the Mediation Model supposed that probabilistic reasoning and reality testing correlated, and indirectly predicted terrorism-related behaviour change through perception of risk. Lastly, the Dual-Influence Model proposed that probabilistic reasoning indirectly predicted terrorism-related behaviour change via perception of risk, independent of reality testing. Results indicated that performance on probabilistic reasoning tasks most strongly predicted perception of risk, and preference for an intuitive thinking style (measured by the IPO-RT) best explained terrorism-related behaviour change. The combination of perception of risk with probabilistic reasoning ability in the Dual-Influence Model enhanced the predictive power of the analytical-rational route, with conjunction fallacy having a significant indirect effect on terrorism-related behaviour change via perception of risk. The Dual-Influence Model possessed superior fit and reported similar predictive relations between intuitive-experiential and analytical-rational routes and terrorism-related behaviour change. The discussion critically examines these findings in relation to dual-processing frameworks. This includes considering the limitations of current operationalisations and recommendations for future research that align outcomes and subsequent work more closely to specific dual-process models. (shrink)

Experimental studies of speech production involving compensations for auditory and somatosensory perturbations and adaptation after training suggest that both types of sensory information are considered to plan and monitor speech production. Interestingly, individual sensory preferences have been observed in this context: subjects who compensate less for somatosensory perturbations compensate more for auditory perturbations, and \textit{vice versa}. We propose to integrate this sensory preference phenomenon in a model of speech motor planning using a probabilistic model in which speech units (...) are characterized both in auditory and somatosensory terms. Sensory preference is implemented in the model according to two approaches. In the first approach, which is often used in motor control models accounting for sensory integration, sensory preference is attributed to the relative precision (i.e., inverse of the variance) of the sensory characterization of the speech motor goals associated with phonological units (which are phonemes in the context of this paper). In the second, ``more original’’ variant, sensory preference is implemented by modulating the sensitivity of the comparison between the predicted sensory consequences of motor commands and the sensory characterizations of the phonemes. We present simulation results using these two variants, in the context of the adaptation to an auditory perturbation, implemented in a 2-dimensional biomechanical model of the tongue. Simulation results show that both variants lead to qualitatively similar results. Distinguishing them experimentally would require precise analyses of partial compensation patterns. However, the second proposed variant implements sensory preference without changing the sensory characterizations of the phonemes. This dissociates sensory preference and sensory characterizations of the phonemes, and makes the account of sensory preference more flexible. Indeed, in the second variant the sensory characterizations of the phonemes can remain stable, when sensory preference varies as a response to cognitive or attentional control. This opens new perspectives for capturing speech production variability associated with aging, disorders and speaking conditions. (shrink)

I survey the difficulties of several probabilistic views of non-deductive argument and of inductive probability and propose to explicate non-deductive reasoning in terms of rational preference. Following a critical examination of Popper’s allegedly deductive theory of rational preference, I draw upon the work of Popper and Rescher to present my view which includes: (i) the conjecturing of a set of alternative answers to or theories or hypotheses about the questions prompting the inquiry and (ii) the “reduction” of this set (...) via plausibilistic principles of rational preference. (shrink)

I survey the difficulties of several probabilistic views of non-deductive argument and of inductive probability and propose to explicate non-deductive reasoning in terms of rational preference. Following a critical examination of Popper’s allegedly deductive theory of rational preference, I draw upon the work of Popper and Rescher to present my view which includes: (i) the conjecturing of a set of alternative answers to or theories or hypotheses about the questions prompting the inquiry and (ii) the “reduction” of this set (...) via plausibilistic principles of rational preference. (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)

There have been two principal paradigms for the formulation of the causal relation--logical implication and functional relationship. In this paper, I present a case for preferring the functional relationship formulation and then discuss how the functional relationship formulation may be implemented in the probabilistic case in a manner analogous to the way others have implemented the logical implication formulation in the probabilistic case. I show how the "local independence" assumption found in many models used in the behavioral and (...) social sciences is a consequence of the functional relation concept of probabilistic causality. I also discuss why causal relations are underdetermined in experience and are to be dealt with pragmatically in a hypothesis-testing framework. (shrink)

Dutch Book Arguments. B is susceptibility to sure monetary loss (in a certain betting set-up), and F is the formal role played by non-Pr b’s in the DBT and the Converse DBT. Representation Theorem Arguments. B is having preferences that violate some of Savage’s axioms (and/or being unrepresentable as an expected utility maximizer), and F is the formal role played by non-Pr b’s in the RT.

The primary aim of this thesis is to examine some of the arguments that have been leveled against the idea that all value bearing entities are comparable. A secondary aim is to investigate some putative properties of the relation ‘better than', especially transitivity and vagueness. Also, some of the consequences of accepting incomparability are investigated, both with regards to other value theoretical issues, such as the implications for monadic value predicates, and with regards to more applied issues, such as the (...) comparison of risks. PAPER I is a critical examination of the so-called small-improvement argument for incomparability. It is demonstrated that the value structure this argument is able to distinguish is compatible not only with incomparability but also with a kind of evaluative indeterminacy that is distinct from incomparability. PAPER II argues that if the possibility of non-conventional value relations is granted it follows that some things that have value are neither good, bad, nor neutral. This counterintuitive conclusion is reached by combining two individually plausible analyses of value. PAPER III addresses the phenomenon of incomplete preferences. It is shown how it is possible to model incomplete preference orderings by means of probabilistic preferences, and how to reveal an agent's incomplete preference ordering within a behaviorist framework. PAPER IV examines another version of the small-improvement argument designed to establish the rationality of incomplete preferences. It is argued that while there might be reasons to believe each of the premises in this version, there is a conflict between these reasons. The conflict is such that we are not provided with a reason to believe the conjunction of the premises. And without support for the conjunction of the premises the small-improvement argument for incomparability fails. PAPER V defends the common sense claim that ‘better than' is transitive against the compelling counterexamples provided by Larry Temkin and Stuart Rachels. It is demonstrated that the contradiction that follows from accepting Temkin and Rachels' premises trades on the vagueness of ‘better than', and so does not warrant the rejection of transitivity, but rather the conclusion that ‘better than' is vague. PAPER VI applies the notions of incommensurability and incomparability to comparative risk analysis. It is argued that if risks are incommensurable, and thereby resistant to accurate comparisons in terms of severity, we cannot perform accurate and cost effective trade-offs between risks and their associated benefits. (shrink)

This chapter presents a model of risk‐taking behaviour. That is, it describes some simpler patterns of preference than real people ever have, and then discusses some strategies that would make sense for people with these simple preferences when faced with choices between risky options. These strategies can also make sense for people, with the more complicated preferences. The chapter also discusses some more detailed assumptions about snobs' preferences. There are several ways in which the Snobs can find (...) their way through risky situations. The chapter considers two. The first is, in effect, to refuse to reason probabilistically. Given every risky prospect they can decide what the most likely outcome is, equate it to a certainty of that outcome, and choose accordingly. In more complex situations something closer to real probabilistic reasoning will be needed. And this is the second way in which preferences such as those of the snobs can come to terms with risk. (shrink)

Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.

Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Most of the action in the literature concerns stage ii). Assuming that stage i) has been (...) adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not. In this paper we scrutinize the state of play regarding stage i). We critically examine several of the leading accounts of degrees of belief: reducing them to corresponding betting behavior (de Finetti); measuring them by that behavior (Jeffrey); and analyzing them in terms of preferences and their role in decision-making more generally (Ramsey, Lewis, Maher). We argue that the accounts fail, and so they are unfit to subserve arguments for probabilism. We conclude more positively: ‘degree of belief’ should be taken as a primitive concept that forms the basis of our best theory of rational belief and decision: probabilism. (shrink)

Probabilistic coherence is not an absolute requirement of rationality; nevertheless, it is an ideal of rationality with substantive normative import. An idealized rational agent who avoided making implicit logical errors in forming his preferences would be coherent. In response to the challenge, recently made by epistemologists such as Foley and Plantinga, that appeals to ideal rationality render probabilism either irrelevant or implausible, I argue that idealized requirements can be normatively relevant even when the ideals are unattainable, so long (...) as they define a structure that links imperfect and perfect rationality in a way that enables us to make sense of the notion of better approximations to the ideal. I then analyze the notion of approximation to the ideal of coherence by developing a generalized theory of belief functions that allows for incoherence, and showing how such belief functions can be ordered with regard to greater or lesser coherence. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise (...) degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of (...) the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model. (shrink)

I present a conceptual framework for classifying generalist and particularist approaches to conspiracy theories (CTs). Specifically, I exploit a probabilistic version of the hexagon of opposition which allows for systematically visualising the logical relations among basic philosophical positions concerning CTs. The probabilistic interpretation can also account for positions, which make weaker claims about CTs: e.g. instead of claiming ‘every CT is suspicious’ some theorists might prefer to claim ‘most CTs are suspicious’ and then ask about logical consequences of (...) such claims. Finally, I illustrate the proposed conceptual framework by selected claims about CTs drawn from the CT research literature. (shrink)

How do we come to like the things that we do? Each one of us starts from a relatively similar state at birth, yet we end up with vastly different sets of aesthetic preferences. These preferences go on to define us both as individuals and as members of our cultures. Therefore, it is important to understand how aesthetic preferences form over our lifetimes. This poses a challenging problem: to understand this process, one must account for the many (...) factors at play in the formation of aesthetic values and how these factors influence each other over time. A general framework based on basic neuroscientific principles that can also account for this process is needed. Here, we present such a framework and illustrate it through a model that accounts for the trajectories of aesthetic values over time. Our framework is inspired by meta-analytic data of neuroimaging studies of aesthetic appraisal. This framework incorporates effects of sensory inputs, rewards, and motivational states. Crucially, each one of these effects is probabilistic. We model their interactions under a reinforcement-learning circuitry. Simulations of this model and mathematical analysis of the framework lead to three main findings. First, different people may develop distinct weighing of aesthetic variables because of individual variability in motivation. Second, individuals from different cultures and environments may develop different aesthetic values because of unique sensory inputs and social rewards. Third, because learning is stochastic stemming from probabilistic sensory inputs, motivations, and rewards, aesthetic values vary in time. These three theoretical findings account for different lines of empirical research. Through our study, we hope to provide a general and unifying framework for understanding the various aspects involved in the formation of aesthetic values over time. (shrink)

Economics prefers complete explanations: general over partial equilibrium, microfoundational over aggregate. Similarly, probabilistic accounts of causation frequently prefer greater detail to less as in typical resolutions of Simpson’s paradox. Strategies of causal refinement equally aim to distinguish direct from indirect causes. Yet, there are countervailing practices in economics. Representative-agent models aim to capture economic motivation but not to reduce the level of aggregation. Small structural vector-autoregression and dynamic stochastic general-equilibrium models are practically preferred to larger ones. The distinction between (...) exogenous and endogenous variables suggests partitioning the world into distinct subsystems. The tension in these practices is addressed within a structural account of causation inspired by the work of Herbert Simon’s, which defines cause with reference to complete systems adapted to deal with incomplete systems and piecemeal evidence. The focus is on understanding the constraints that a structural account of causation places on the freedom to model complex or lower-order systems as simpler or higher-order systems and on to what degree piecemeal evidence can be incorporated into a structural account. (shrink)

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision (...) weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism. (shrink)

This chapter of the Handbook of Utility Theory aims at covering the connections between utility theory and social ethics. The chapter first discusses the philosophical interpretations of utility functions, then explains how social choice theory uses them to represent interpersonal comparisons of welfare in either utilitarian or non-utilitarian representations of social preferences. The chapter also contains an extensive account of John Harsanyi's formal reconstruction of utilitarianism and its developments in the later literature, especially when society faces uncertainty rather than (...) probabilistic risk. (shrink)

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill (...) this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. (shrink)