A necessary and sufficient condition for linear aggregation of SSB utility functionals is presented. Harsanyi's social aggregation theorem for von Neumann–Morgenstern utility functions is shown to be a corollary to this result. Two generalizations of Fishburn and Gehrlein's conditional linear aggregation theorem for SSB utility functionals are also established.

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result is the (...) identification of the continuity condition necessary for the revelation of linear utility. (shrink)

Epistemic utility theory seeks to establish epistemic norms by combining principles from decision theory and social choice theory with ways of determining the epistemic utility of agents’ attitudes. Recently, Moss, 1053–69, 2011) has applied this strategy to the problem of finding epistemic compromises between disagreeing agents. She shows that the norm “form compromises by maximizing average expected epistemic utility”, when applied to agents who share the same proper epistemic utility function, yields the result that agents must (...) form compromises by splitting the difference between their credence functions. However, this “split the difference” norm is in conflict with conditionalization, since applications of the two norms don’t commute. A common response in the literature seems to be to abandon the procedure of splitting the difference in favor of compromise strategies that avoid non-commutativity. This would also entail abandoning Moss’ norm. I explore whether a different response is feasible. If agents can use epistemic utility-based considerations to agree on an order in which they will apply the two norms, they might be able to avoid diachronic incoherence. I show that this response can’t save Moss’ norm, because the agreements concerning the order of compromising and updating it generates are not stable over time, and hence cannot avoid diachronic incoherence. I also show that a variant of Moss’ norm, which requires that the weights given to each agent’s epistemic utility change in a way that ensures commutativity, cannot be justified on epistemological grounds. (shrink)

We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discounting functions to characterize impatience. There are several unexpected benefits of this extension, apart from the ability to directly estimate structural parameters of theoretical interest.

In searching for an appropriate utility function in the expected utility framework, we formulate four properties that we want the utility function to satisfy. We conduct a search for such a function, and we identify Pareto utility as a function satisfying all four desired properties. Pareto utility is a flexible yet simple and parsimonious two-parameter family. It exhibits decreasing absolute risk aversion and increasing but bounded relative risk aversion. It is applicable irrespective of the probability (...) distribution relevant to the prospect to be evaluated. Pareto utility is therefore particularly suited for catastrophic risk analysis. A new and related class of generalized exponential (gexpo) utility functions is also studied. This class is particularly relevant in situations where absolute risk tolerance is thought to be concave rather than linear. (shrink)

Econometric analysis of discrete choice has made considerable use of random utility models to interpret observed choice behavior. Much empirical research concerns choice problems in which persons act with partial knowledge of the utilities of the feasible actions. Economists use random expected utility models to analyze such choice problems. A common practice is to specify fully the expectations that persons hold, in which case choice analysis reduces to inference on preferences alone. However, the expectations assumptions made in empirical (...) research rarely have much foundation. To enable more credible research, this paper considers inference when one specifies a set of expectations that decision makers may plausibly hold. I first pose the idea in abstraction and then specialize to binary response with linear utilities, where the analysis is particularly straightforward. I initially assume that decision makers possess unique subjective probability distributions on the states of nature and make choices that maximize expected utility. I later consider the possibility that persons place only partial probabilistic structure on the states of nature and make undominated choices. (shrink)

A pure-strategy equilibrium existence theorem is extended to include games with non-expected utility players. It is shown that to guarantee the existence of a Nash equilibrium in pure strategies, the linearity of preferences in the probabilities can be replaced by the weaker requirement of quasiconvexity in the probabilities.

The majority consensus in the empirical literature is that probability weighting functions are typically inverse-S shaped, that is, people tend to overweight small and underweight large probabilities. A separate stream of literature has reported event-splitting effects and shown that they can explain violations of expected utility. This leads to the questions whether the observed shape of weighting functions is a mere consequence of the coalesced presentation and, more generally, whether preference elicitation should rely on presenting lotteries in a canonical (...) split form instead of the commonly used coalesced form. We analyze data from a binary choice experiment where all lottery pairs are presented in both split and coalesced forms. Our results show that the presentation in a split form leads to a better fit of expected utility theory and to probability weighting functions that are closer to linear. We thus provide some evidence that the extent of probability weighting is not an ingrained feature, but rather a result of processing difficulties. (shrink)

Based on the assumption that the long-term value of a venture capital satisfies the algebraic Brownian motion, we develop a continuous-time exit model of venture capital under different exit modes, namely, initial public offering and mergers and acquisitions. The employee incentive problem is analyzed jointly with the exit decision of the firm in terms of the exit timing and the exit mode. Further, the problem of capital exit is considered from two perspectives, namely, optimal venture capital and social welfare maximization, (...) and the differences between these exit decisions are compared. Our model predicts that the timing of an IPO, the purpose of which is to maximize the utility of the capitalists, lags behind the exit timing, whose purpose is to maximize social welfare. Using a numerical analysis, this paper also proves that increasing the production efficiency, lowering the interest rates, and improving risk management can make the exit decision of venture capitalists converge with that of maximizing social welfare. (shrink)

This commentary emphasizes two problem areas mentioned by Burt. First, that within-family designs do not eradicate stratification confounds. Second, that the linear/additive model of genetic causes of form and variation is not supported by recent progress in molecular biology. It concludes with an appeal for a (biologically and psychologically) more realistic model of such causes.

Background:The management of challenging behaviours in inpatient with intellectual disability and/or autism spectrum disorders can lead to an escalation of control measures. In these complex situations where patients have an intellectual disability/autism spectrum disorder accompanied by a psychiatric comorbidity, the experiences of caregivers related to the crisis management have rarely been studied.Purpose:This study examined the moral experiences of caregivers related to challenging behaviours’ management and alternatives to control measures.Research design:Using Charles Taylor’s hermeneutic framework, a 2-month focused ethnography with a participatory (...) approach was used.Participants and research context:Sixteen caregivers were interviewed in a Canadian mental health setting for adults with intellectual disability/autism spectrum disorder and psychiatric comorbidity.Ethical considerations:The research was conducted in compliance with the Declaration of Helsinki and local Research Ethics Board approval. Written informed consent was collected systematically from participants.Findings:By accounting for caregivers’ moral experiences, this study sheds light on a neglected dimension of the care relationship: the vulnerability of the caregiver. We highlight the main barriers and facilitators to alternatives to control measures. First, a caregiver’s vulnerability was characterised by the overall impact of challenging behaviours and the moral distress associated with the use of control measures and exclusion mechanisms of intellectual disability/autism spectrum disorder patients. Second, a strong ambiguity between care and control measures and a lack of inclusive approaches were identified as the two main barriers to challenging behaviour management. Third, the involvement, both professional and personal, of caregivers was deemed necessary to implement alternatives to control measures.Discussion:A conflict of values opposes two conceptions of autonomy: a rational autonomy, which is counterproductive to the reduction of control measures, versus a relational autonomy based on shared vulnerability.Conclusion:The recognition of caregiver’s vulnerability is a benchmark to create alternative approaches, which defuse the logic of control and promote an ethics of care within which caregivers’ self-concern can be understood as fostering mutual respect. (shrink)

The desirable gambles framework offers the most comprehensive foundations for the theory of lower pre- visions, which in turn affords the most general ac- count of imprecise probabilities. Nevertheless, for all its generality, the theory of lower previsions rests on the notion of linear utility. This commitment to linearity is clearest in the coherence axioms for sets of desirable gambles. This paper considers two routes to relaxing this commitment. The first preserves the additive structure of the desirable gambles (...) framework and the machinery for coherent inference but detaches the interpretation of desirability from the multiplicative scale invariance axiom. The second strays from the additive combination axiom to accommodate repeated gambles that return rewards by a non-stationary processes that is not necessarily additive. Unlike the first approach, which is a conservative amendment to the desirable gambles framework, the second is a rad- ical departure. Yet, common to both is a method for describing rewards called discounted utility. (shrink)

No existing normative decision theory adequately handles risk. Expected Utility Theory is overly restrictive in prohibiting a range of reasonable preferences. And theories designed to accommodate such preferences (for example, Buchak's (2013) Risk‐Weighted Expected Utility Theory) violate the Betweenness axiom, which requires that you are indifferent to randomizing over two options between which you are already indifferent. Betweenness has been overlooked by philosophers, and we argue that it is a compelling normative constraint. Furthermore, neither Expected nor Risk‐Weighted Expected (...) Utility Theory allow for stakes‐sensitive risk‐attitudes—they require that risk matters in the same way whether you are gambling for loose change or millions of dollars. We provide a novel normative interpretation of Weighted‐Linear Utility Theory that solves all of these problems. (shrink)

Orthodox expected utility theory imposes too stringent restrictions on what attitudes to risk one can rationally hold. Focusing on a life-and-death gamble, I identify as the main culprit the theory’s Linearity property, according to which the utility of a particular change in the risk of a bad outcome is independent of the original level of risk. Finally, I argue that a recent non-standard Bayesian decision theory, that does not have this property, handles risky gambles better than the orthodox (...) theory. (shrink)

This chapter sets out the theorems, and presents some examples that show in a rough way how the theorems work. It explains separability precisely, and states the theorems. The chapter starts the work of interpreting the theorems, and also explains the significance of their conclusions from a formal, mathematical point of view. It then discusses a significant assumption that is used in the proofs of the theorems. The published proofs of both the separability theorems depend on an assumption that may (...) be objectionable in some contexts. These theorems are about an ordering defined on a field of alternatives. If an ordering can be represented by an additively separable utility function, the theorem shows it can be represented by a whole family of additively separable functions. Each member of the family is an increasing linear transform of the others, and the family includes every increasing linear transform of each of its members. (shrink)

By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena (...) game over the Pasadena game, and that would have been claimed for the St Petersburg game over the Altadena, can be contradicted without fear of inconsistency with the axioms of utility theory. However, insistence upon dominance can be made to yield a contradiction of the Archimedean axiom of utility theory. CiteULike Connotea Del.icio.us What's this? (shrink)

We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” regarding peer disagreement and show that the view cannot respect it. Based on this result we argue against the view. The restriction is the following one: if an agent, $$\hbox {i}$$ i, assigns an equal or higher weight to another agent, $$\hbox {j}$$ j,, he must be willing—in exchange for a positive and certain payment—to accept an offer to let a completely rational and (...) sympathetic $$\hbox {j}$$ j choose for him whether to accept a bet with positive expected utility. If $$\hbox {i}$$ i assigns a lower weight to $$\hbox {j}$$ j than to himself, he must not be willing to pay any positive price for letting $$\hbox {j}$$ j choose for him. Respecting the constraint entails, we show, that the impact of disagreement on one’s degree of belief is not independent of what the disagreement is discovered to be. (shrink)

We study a class of representation mechanisms, based on reports made by a random subset of agents, called representatives, in a collective choice problem with quasi-linear utilities. We do not assume the existence of a common prior probability describing the distribution of preference types. In addition, there is no benevolent planner. Decisions will be carried out by an individual who cannot be assumed impartial, a self-interested executive. These assumptions impose new constraints on Mechanism Design. A robust mechanism is defined (...) as maximizing expected welfare under a vague prior probability distribution, and over a set of mechanisms which is at the same time immune from opportunistic manipulations by the executive, and compatible with truthful revelation of preferences by representatives. Robust mechanisms are characterized and their existence is shown. Sampling Groves mechanisms are shown to be robust. (shrink)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs (...) linearly, but achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

Chance Neutrality is the thesis that, conditional on some proposition being true, its chance of being true should be a matter of practical indifference. The aim of this article is to examine whether Chance Neutrality is a requirement of rationality. We prove that given Chance Neutrality, the Principal Principle entails a thesis called Linearity; the centerpiece of von Neumann and Morgenstern’s expected utility theory. With this in mind, we argue that the Principal Principle is a requirement of practical rationality (...) but that Linearity is not and, hence, that Chance Neutrality is not rationally required. (shrink)

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann-Morgenstern utilities, he has done nothing to establish any con- nection between the notion of von Neumann-Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. The present article defends Harsanyi against the (...) Sen-Weymark cri- tique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann-Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

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)

According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the (...) transitivity assumption (I, II). Second, I discuss some objections; this will also bring out some features of the view defended here, like the essentially comparative nature of choice (III). Then, I discuss certain proposals that promise to avoid my conclusion (IV). Finally, I go into some implications concerning the nature of rational decision making (V). To accept some intransitivities as rational does not make our life easier; it can even lead to hard choices. However, it does not lead to skepticism about rational choice. (shrink)

For linear distribution classes, mean-variance and expected utility specifications have been shown in the literature to be fully compatible when studying the concepts of risk aversion, prudence, risk vulnerability and temperance. This paper shows that such compatibility does hold for the concept of standard risk aversion but not for the concepts of proper risk aversion and proper prudence.

Discrete choice experiments—selecting the best and/or worst from a set of options—are increasingly used to provide more efficient and valid measurement of attitudes or preferences than conventional methods such as Likert scales. Discrete choice data have traditionally been analyzed with random utility models that have good measurement properties but provide limited insight into cognitive processes. We extend a well-established cognitive model, which has successfully explained both choices and response times for simple decision tasks, to complex, multi-attribute discrete choice data. (...) The fits, and parameters, of the extended model for two sets of choice data (involving patient preferences for dermatology appointments, and consumer attitudes toward mobile phones) agree with those of standard choice models. The extended model also accounts for choice and response time data in a perceptual judgment task designed in a manner analogous to best–worst discrete choice experiments. We conclude that several research fields might benefit from discrete choice experiments, and that the particular accumulator-based models of decision making used in response time research can also provide process-level instantiations for random utility models. (shrink)

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences (...) of their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to …lling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our …rst theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the speci…c kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

As Active Mining is a new concept among data mining and/or knowledge discovery in databases communities, in order to validate the effectiveness, it is important to carry out empirical studies using practical data. Based on the concept of Active User Reaction, this paper develops a causal model from liver function test data in a medical domain. To develop the model, we have set a problem to predict the values of ICG test from given observation data and experts' background knowledge. We (...) therefore employ a framework of meta-learning and structural equation modeling. In this paper meta-learning means learning about mined results from multiple data-mining techniques. Structural equation modeling enables us to describe flexible models from background knowledge. The construction of the causal model contains two phases: meta-learning and the model building. The meta-learning phase utilizes both the linear regression and the neural network as data mining techniques, then examines the predictability on the given data set. Mining models are n-folded learned from the training data set. Each of the prediction accuracy of the mining models is compared using with the testing data. On the model building phase, we use structural equation modeling to develop a causal model based on results of meta-learning and background knowledge. We again compare the accuracy of the causal model with each of the mining models. Consequently we have developed the causal model, which is comprehensible and have good predictive performance, via the meta-learning phase. Through the empirical study, we have got the conclusion that the framework of meta-learning is effective in data mining in a difficult medical domain. (shrink)

This paper reports the results of an experiment designed to uncover the stochastic structure of individual preferences over lotteries. Unlike previous experiments, which have presented subjects with pair-wise choices between lotteries, our design allowed subjects to choose between two lotteries or (virtually) any convex combination of the two lotteries. We interpret the mixtures of lotteries chosen by subjects as a measure of the stochastic structure of choice. We test between two alternative interpretations of stochastic choice: the random utility interpretation (...) and the deterministic preferences interpretation. The main findings of the experiment are that the typical subject prefers mixtures of lotteries rather than the extremes of a linear lottery choice set. The distribution of choices does not change between a first and second asking of the same question. We argue that this provides support for the deterministic preferences interpretation over the random utility interpretation of stochastic choice. As a subsidiary result, we find a small proportion of subjects make choices that violate transitivity, but the level of intransitive choice falls significantly over time. (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

As the capabilities of artificial intelligence systems improve, it becomes important to constrain their actions to ensure their behaviour remains beneficial to humanity. A variety of ethical, legal and safety-based frameworks have been proposed as a basis for designing these constraints. Despite their variations, these frameworks share the common characteristic that decision-making must consider multiple potentially conflicting factors. We demonstrate that these alignment frameworks can be represented as utility functions, but that the widely used Maximum Expected Utility paradigm (...) provides insufficient support for such multiobjective decision-making. We show that a Multiobjective Maximum Expected Utility paradigm based on the combination of vector utilities and non-linear action–selection can overcome many of the issues which limit MEU’s effectiveness in implementing aligned AI. We examine existing approaches to multiobjective AI, and identify how these can contribute to the development of human-aligned intelligent agents. (shrink)

We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...) group in question? According to the credal judgement aggregation principle, linear pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this chapter, I give an argument for linear pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. -/- The present article defends Harsanyi against the (...) Sen–Weymark critique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann–Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

This paper describes an AFOSR-supported basic research program that focuses on developing a new framework for combining hard with soft data in order to improve space situational awareness. The goal is to provide, in an automatic and near real-time fashion, a ranking of possible threats to blue assets (assets trying to be protected) from red assets (assets with hostile intentions). The approach is based on Conceptual Spaces models, which combine features from traditional associative and symbolic cognitive models. While Conceptual Spaces (...) are revolutionary, they lack an underlying mathematical framework. Several such frameworks have attempted to represent Conceptual Spaces, but by far the most robust is the model developed by Holender. His model utilizes integer linear programming in order to obtain an overall similarity value between observations and concepts that support the formation of hypotheses. This paper will describe a method for building Conceptual Spaces models for threats that utilizes ontologies as a means to provide a clear semantic foundation for this inferencing process; in particular threat ontologies and space domain ontologies are developed and employed in this approach. A space situational awareness use-case is presented involving a kinetic kill scenario and results are shown to assess the performance of this fusion-based inferencing framework. (shrink)

When an individual’s action is only one among a large number of similar actions and does not seem to make any difference to the bad collective outcome, can it nonetheless be condemned by act utilitarianism? This question has currently regained interest with papers, e.g., by Shelly Kagan, Julia Nefsky, and Felix Pinkert. Christopher Morgan-Knapp and Charles Goodman answer the question in the affirmative for miniscule emissions in the context of climate change. They use expected utility analysis as Kagan did (...) in consumer ethics. The assumptions about the impact of emissions vary according to some underlying empirical scenarios, all of which are possible. Individual actions might be relevant in the sense of contributing to a mere linear accumulation of emissions; or they might be relevant by leading to an accumulation in the form of crossing thresholds, be it one or several, Finally, such actions might not be relevant at all. To give an answer that solves the problem and that is based solely on expected utility analysis is impossible. Therefore, the view of Morgan-Knapp and Goodman must be rejected. (shrink)

It is commonplace to suppose that the theory of individual rational choice is considerably less problematic than the theory of collective rational choice. In particular, it is often assumed by philosophers, economists, and other social scientists that an individual's choices among outcomes accurately reflect that individual's underlying preferences or values. Further, it is now well known that if an individual's choices among outcomes satisfy certain plausible axioms of rationality or consistency, that individual's choice-behavior can be interpreted as maximizing expected (...) class='Hi'>utility on a utility scale that is unique up to a linear transformation. Hence, there is, in principle, an empirically respectable method of measuring individuals' values and a single unified schema for explaining their actions as value maximizing. (shrink)