It has often been recommended that the differing probability distributions of a group of experts should be reconciled in such a way as to preserve each instance of independence common to all of their distributions. When probability pooling is subject to a universal domain condition, along with state-wise aggregation, there are severe limitations on implementing this recommendation. In particular, when the individuals are epistemic peers whose probability assessments are to be accorded equal weight, universal preservation of independence is, with a (...) few exceptions, impossible. Under more reasonable restrictions on pooling, however, there is a natural method of preserving the independence of any fixed finite family of countable partitions, and hence of any fixed finite family of discrete random variables. (shrink)

The article tries to inquire a third way in normative ethics between consequentialism or utilitarianism and deontology or Kantianism. To find such a third way in normative ethics, one has to analyze the elements of these classical theories and to look if they are justified. In this article it is argued that an adequate normative ethics has to contain the following five elements: (1) normative individualism, i. e., the view that in the last instance moral norms and values can only (...) be justified by reference to the individuals concerned, as its basis; (2) consideration of the individuals' concerns and interests—aims, desires, needs, strivings—insofar as they have a justificatory function; (3) a pluralism of references of these concerns and hence of moral norms and values to all possible elements of actions; (4) the necessity of a principle of aggregation and weighing with regard to these concerns; (5) finally, as a central principle of aggregation and weighing, the principle of relative reference to self and others, operating as a generalizing meta-principle that guides the application of concrete principles and decisions. (shrink)

I argue that reliance on political testimony conflicts with two democratic values: the value of mutual justifiability and the value of equality of opportunity for political influence. Reliance on political testimony is characterized by a reliance on the assertions of others directly on a political question the citizen is asked to answer as part of a formal democratic decision procedure. Reliance on expert testimony generally, even in the context of political decision-making, does not similarly conflict with democratic values. As a (...) consequence of the argument, citizens have a pro tanto reason to rely on their own political judgment when determining their vote, and democratic societies have a reason to only ask citizens questions they are able to answer without reliance on political testimony. (shrink)

Institutional economics and discourse theory stand unconnected next to each other, in spite of the fact that they both ask for the legitimacy of institutions (normative) and the functioning and effectiveness of institutions (positive). Both use as theoretical constructions rational individuals and the concept of consensus for legitimacy. Whereas discourse theory emphasizes the conditions of a legitimate consensus and could thus enable institutional economics to escape the infinite regress of judging a consensus legitimate, institutional economics has a tested social science (...) paradigm (rational choice) of explaining and predicting the functioning of institutions. The article outlines a theoretical synthesis of the two theories by finding points in common and possibilities of fruitful combinations concerning the problem of legitimacy, institutional design and effectiveness of legal norms. Key Words: consensus • discourse theory • effectiveness of legal rules • institutional design • legitimacy • new institutional economics. (shrink)

I articulate a Global Best-System Account (GBSA) of laws of nature along broadly Mill–Ramsey–Lewis lines. The guiding idea is that the job of laws is to capture real patterns across time—where a pattern is real if it allows to compress information about matters of particular fact. The GBSA’s key ingredient is a definition of ‘best system’ in terms of a ranking method that meets a number of desiderata: it is rigorously defined; it outputs the ranking based on the candidate systems’ (...) epistemic virtues; it is objective, in that the output does not depend on one’s choice of basic concepts; it avoids two trivialization results (by Lewis, and Arrow-Okasha); and it does not appeal to naturalness, or other metaphysical notions in that vicinity. Although the GBSA is independent of the controversial thesis of Humean Supervenience, it satisfies the weaker thesis that laws of nature supervene on the total physical state of the world. Moreover, the resulting notion of lawhood is hyperintensional, unlike the neighboring notion of nomological necessity. Finally, GBSA-laws do not track naturalness, contra the Lewisian orthodoxy. (shrink)

The usual procedure in the theory of social choice consists in postulating some desirable properties which an aggregation procedure should verify and derive from them the features of a corresponding social choice function and the outcomes that arise at each possible profile of preferences. In this paper we invert this line of reasoning and try to infer, up from what we call social situations the criteria verified in the implicit aggregation procedure. This inference process, which extracts intensional from extensional information (...) can be seen as an exercise in “qualitative statistics”. (shrink)

In ‘Normative Uncertainty as a Voting Problem’, William MacAskill argues that positive credence in ordinal-structured or intertheoretically incomparable normative theories does not prevent an agent from rationally accounting for her normative uncertainties in practical deliberation. Rather, such an agent can aggregate the theories in which she has positive credence by methods borrowed from voting theory—specifically, MacAskill suggests, by a kind of weighted Borda count. The appeal to voting methods opens up a promising new avenue for theories of rational choice under (...) normative uncertainty. The Borda rule, however, is open to at least two serious objections. First, it seems implicitly to ‘cardinalize’ ordinal theories, and so does not fully face up to the problem of merely ordinal theories. Second, the Borda rule faces a problem of option individuation. MacAskill attempts to solve this problem by invoking a measure on the set of practical options. But it is unclear that there is any natural way of defining such a measure that will not make the output of the Borda rule implausibly sensitive to irrelevant empirical features of decision-situations. After developing these objections, I suggest an alternative: the McKelvey uncovered set, a Condorcet method that selects all and only the maximal options under a strong pairwise defeat relation. This decision rule has several advantages over Borda and mostly avoids the force of MacAskill’s objection to Condorcet methods in general. (shrink)

To investigate the relationship between logical reasoning and majority voting, we introduce logic with groups Lg in the style of Gentzen’s sequent calculus, where every sequent is indexed by a group of individuals. We also introduce the set-theoretical semantics of Lg, where every formula is interpreted as a certain closed set of groups whose members accept that formula. We present the cut-elimination theorem, and the soundness and semantic completeness theorems of Lg. Then, introducing an inference rule representing majority voting to (...) Lg, we introduce logic with majority voting Lv. Formalizing the discursive paradox in judgment aggregation theory, we show that Lv is inconsistent. Based on the premise-based and conclusion-based approaches to avoid the paradox, we introduce logic with majority voting for axioms Lva, where majority voting is applied only to non-logical axioms as premises to construct a proof in Lg, and logic with majority voting for conclusions Lvc, where majority voting is applied only to the conclusion of a proof in Lg. We show that both Lva and Lvc are syntactically complete and consistent, and we construct collective judgments based on the provability in Lva and Lvc, respectively. Then, we discuss how these systems avoid the discursive paradox. (shrink)

Individual rationality, or doing what is best for oneself, is a standard model used to explain and predict human behavior, and von Neumann–Morgenstern game theory is the classical mathematical formalization of this theory in multiple-agent settings. Individual rationality, however, is an inadequate model for the synthesis of artificial social systems where cooperation is essential, since it does not permit the accommodation of group interests other than as aggregations of individual interests. Satisficing game theory is based upon a well-defined notion of (...) being good enough, and does accommodate group as well as individual interests through the use of conditional preference relationships, whereby a decision maker is able to adjust its preferences as a function of the preferences, and not just the options, of others. This new theory is offered as an alternative paradigm to construct artificial societies that are capable of complex behavior that goes beyond exclusive self interest. (shrink)

This paper defends two related claims about belief. First, the claim that unlike numerical degrees of belief, comparative beliefs are primitive and psychologically real. Second, the claim that the fundamental norm of Probabilism is not that numerical degrees of belief should satisfy the probability axioms, but rather that comparative beliefs should satisfy certain constraints.

Recent impossibility theorems for fair risk assessment extend to the domain of epistemic justice. We translate the relevant model, demonstrating that the problems of fair risk assessment and just credibility assessment are structurally the same. We motivate the fairness criteria involved in the theorems as also being appropriate in the setting of testimonial justice. Any account of testimonial justice that implies the fairness/justice criteria must be abandoned, on pain of triviality.

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

Polanyi analyzes the historical deployment of a “formal” economic science starting from the “market-scarcity-instrumental rationality triptych.” This triptych, and the knowledge associated with it, is shown to be more than merely a “substantial” economic science’s interest in the triptych “need-nature-institution.” While we must agree with Polanyi that economism is ill-suited to the first triptych, we hesitate to accept his suggested alternative, a heterogeneous mixture of naturalism and institutionalism, essentialism and historicism.

We introduce a conceptual model for reaching group decisions. Our model extends a well-known, single-agent cognitive model, the recognition-primed decision (RPD) model. The RPD model includes a recognition phase and an evaluation phase. Group extensions of the RPD model, applicable to a group of RPD agents, have been considered in the literature, however the proposed models do not formalize how distributed and possibly inconsistent information can be combined in either phase. We show how such information can be utilized by aggregating (...) it using a specific social choice method, namely judgment aggregation. Our model is applicable to hierarchical groups of agents containing at least one RPD agent. (shrink)

Altruism is a popular economic explanation for a wide range of pro-social decisions and actions. It has been applied frequently in several different streams of literature, and is a descriptively compelling model of behavior. This paper provides a theoretical framework for the existence of ordinal and cardinal altruistic value functions, as well as altruistic utility functions, based on an altruistic preference relation. Representation theorems are developed to specify relatively weak conditions under which altruistic value and utility functions can be shown (...) to exist. In addition, conditions that lead to additive forms of these functions are provided. (shrink)

A small set of allocation principles is said to be behind several theories of distributive justice. However, disagreement about the appropriate relationship between these notions remains, so that compromises between principles may generate more agreement. Truncated utilitarianism is a prominent candidate. It demands maximising total wealth subject to a floor level of individual wealth for all people. Based on some well-known distributive notions, we developed a questionnaire setting and confronted student respondents with corresponding allocation problems, where an exogenously given poverty (...) line served as a floor. However, support for allocations resulting from this specific interpretation of truncated utilitarianism remained rather low. This is surprising because the respective solution was close to an equal split of resources, and aspects of efficiency and responsibility were explicitly introduced to promote more general acceptance. We argue that people may either wish to see higher floor levels or are more inequality averse than probably expected. Moreover, high support for an unconditional consideration of the poverty line can be witnessed, even though aspects of responsibility, but not efficiency arguments, display an influence. In general, attitudes with respect to the equality–efficiency trade-off are found to remain heterogeneous, although different equality concerns are prominent. Furthermore, trade-offs are moderated by the responsibility principle. (shrink)

In light of the so-called ‘chaos theorems’ from social choice theory, William Riker argues that the indeterminacy of majority rule leads to voting cycles making democratic decisions arbitrary and meaningless. Moreover, when the core is empty, majority instability correlates with the level of conflict among actors. This study uses laboratory committee decision-making experiments to provide an empirical test of both aspects of Riker’s argument. Committees make repeated majority decisions over 20 periods picking points from a two-dimensional policy space. The experiment (...) manipulates committee members’ preferences and thus varies the existence of a core and the level of conflict between group members. The experimental results contradict Riker’s interpretation of the chaos theorems’ implications. Thus, the core exhibits less attraction than generally assumed. Moreover, an empty core is not associated with increased majority rule instability. Instead, conflicting preferences lead to more instability irrespective of the existence of an equilibrium. (shrink)

This paper describes an unknown episode in the development of the theory of social choice. In the Summer 1949, while at RAND, Quine worked on Arrow’s (im)possibility theorem. This work was eventually published as a paper on (applied) set theory totally disconnected from social choice. The working paper directly linked to Arrow’s work was never published. I alluded to this (then unwritten) paper in a number of presentations I made on ‘Logic and Social Choice’ in Turku, Bucharest, Boston, Strasbourg and (...) Munich, between October 2013 and January 2015. It was eventually first presented during a conference at Queen Mary, University of London, 19–20 June 2015, on ‘Social Welfare, Justice and Distribution: Celebrating John Roemer’s Contributions to Economics, Political Philosophy and Political Science’, organized by Roberto Veneziani and Juan Moreno-Ternero. I am grateful to the participants for interesting reactions and comments, in particular Richard Arneson, Jon Elster, Marc Fleurbaey, Klaus Nehring and Gil Skillman. Jon Elster contacted Dagfinn Føllesdal, a well-known philosopher and a pre-eminent Quine scholar, who kindly responded to some queries. A more developed version was presented in Aix-en-Provence during the International Conference on Economic Philosophy and in Lund during the meeting of the Society for Social Choice and Welfare in June 2016. Comments of participants to these two events revealed to be very helpful, among which comments by Gilles Campagnolo, Christian List and John Weymark. While in Lund, I also greatly benefitted from conversations with Adrian Miroiu. Finally, I am very grateful to an Associate Editor of this journal for excellent suggestions and for detecting some very annoying slips. (shrink)

It is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair is looked upon as a subsystem with an assigned task. In this manner, the source of several difficulties is equated with the standard concern that the “whole need not be the sum of its parts.” These problems arise because the objectives assigned to subsystems need not be compatible (...) with that of the system. Knowing what causes the difficulties leads to resolutions. (shrink)

How should a group with different opinions (but the same values) make decisions? In a Bayesian setting, the natural question is how to aggregate credences: how to use a single credence function to naturally represent a collection of different credence functions. An extension of the standard Dutch-book arguments that apply to individual decision-makers recommends that group credences should be updated by conditionalization. This imposes a constraint on what aggregation rules can be like. Taking conditionalization as a basic constraint, we gather (...) lessons from the established work on credence aggregation, and extend this work with two new impossibility results. We then explore contrasting features of two kinds of rules that satisfy the constraints we articulate: one kind uses fixed prior credences, and the other uses geometric averaging, as opposed to arithmetic averaging. We also prove a new characterisation result for geometric averaging. Finally we consider applications to neighboring philosophical issues, including the epistemology of disagreement. (shrink)

It is now the majority view amongst philosophers and theologians that any world could have been better. This places the choice of which world to create into an especially challenging class of decision problems: those that are discontinuous in the limit. I argue that combining some weak, plausible norms governing this type of problem with a creator who has the attributes of the god of classical theism results in a paradox: no world is possible. After exploring some ways out of (...) the paradox, I conclude that the classical theist should accept Marilyn Adams’s view that no norms apply to gods. (shrink)

Pettit and List argue for realism about group agency, while at the same time try to retain a form of metaphysical and normative individualism on which human beings qualify as natural persons. This is an unstable and untenable combination of views. A corrective is offered here, on which realism about group agency leads us to the following related conclusions: in cases of group agency, the sort of rational unity that defines individual rational unity is realized at the level of a (...) whole group; rational unity is never a metaphysical given but always a product of effort and will; just as it can be realized within groups of human beings it can also be realized within parts of human beings, as well as within whole human lives; in cases of group agency, the rational unity that is achieved at the level of the group typically precludes rational unity at the level of its human constituents within their whole lives, though it can be realized within parts of those human lives. Along the way, a contrast is drawn between cases of genuine group agency and the cases of political agency envisaged by Rousseau and Rawls (and by Pettit and List) which leave individual human beings intact as separate agents in their own rights. (shrink)

Four criteria are discussed as important conditions of successful applications in Computer Supported Co-operative Work (CSCW). They are equality, mutual influence, new competence, and double-level language. The criteria originate in the experience of the International Co-operative Movement. They are examined and illustrated withreference to eight contemporary CSCW applications: meeting scheduling and support; bargaining; co-authoring; co-ordination; planning; design support and collaborative design.

In this paper I study the activity of mathematical problem-solving in scientific practice, focussing on enquiries in mathematical social science. I identify three salient phases of mathematical problem-solving and adopt them as a reference frame to investigate aspects of applications that have not yet received extensive attention in the philosophical literature.

In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In (...) this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem. (shrink)

Sen's Liberal Paradox has received a good deal of attention in the literature. However, it is worth re-opening the discussion since the solutions offered so far have serious problems and since there is more to say about the nature of the problem displayed by the Liberal Paradox. I propose a new solution to the paradox in the following sense: First, I argue that its range of applicability is not very broad. Second, there is nothing paradoxical about a conflict of the (...) principles involved in the Liberal Paradox. (Nagel's thesis of the ``fragmentation of value'' is important to make this point.) Third, I make a recommendation about how to remove conflicts when they occur in a restricted class of cases. For the other cases, no recommendation of similar appeal is available. But in the light of the first point, the availability of a generally applicable recommendation was not to be expected. (shrink)

Suppose we have a group of Bayesian agents, and suppose that theywould like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that thoseagents want the probabilities and utilities attached to this group agent to be aggregated from theindividual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data areavailable to them, viz., ex ante aggregation and ex post aggregation. The former aggregatesexpected utilities directly, whereas the latter aggregates probabilities and utilities (...) separately.A number of recent formal results show that both approaches have problematic implications. This studydiscusses the philosophical issues arising from those results. In this process, I hope to convincethe reader that these results about Bayesian aggregation are highly significant to decision theorists, butalso of immense interest to theorists working in areas such as ethics and political philosophy. (shrink)

According to a popular view of scientific methodology, scientific methods are prescriptive rules (methodological rules) which are justified in so far as they realize or promote the aims of science. This paper considers several different interpretations of the phrase aims of science, arguing that none of these interpretations allow aims to provide a satisfactory justification of methodological rules.

According to the mixed lexicographic/additive account of ‘better than’ and similar aggregative value comparatives like ‘healthier than’, values are multidimensional and different aspects of a value are aggregated into an overall assessment in a lexicographic way, based on an ordering of value aspects. It is argued that this theory can account for an acceptable definition of Chang’s notion of parity and that it also offers a solution to Temkin’s and Rachels’s Spectrum Cases without giving up the transitivity of overall betterness. (...) Formal details and proofs are provided in an “Appendix”. (shrink)

Michael Dorf and Charles Sabel invoke John Dewey’s “pragmatist account of thought and action” as the “backdrop” for their theory of democratic experimentalism, an approach to governance emphasizing judicially monitored local decision making within a system of decentralized administrative authority. Little credit for influence is given to the Austrian economist Friedrich Hayek and his classic liberal ideas. Indeed, Sabel has been highly critical of Hayek’s ideas. Yet, an argument can be made that (i) democratic experimentalism is at least loosely Hayekian (...) and (ii) a combined Deweyan-Hayekian analysis of Dorf and Sabel’s theory reveals some critical mistakes. One implication of my analysis is that Dewey and Hayek’s ideas are more compatible than most democratic theorists and political philosophers will admit. Evidence of this compatibility opens the door for creating and evaluating democratic experiments within a Deweyan-Hayekian theoretical framework, as well as extending the framework to other areas of political inquiry. (shrink)

Recent rapid advances in Artificial Intelligence and Machine Learning have raised many questions about the regulatory and governance mechanisms for autonomous machines. Many commentators, scholars, and policy-makers now call for ensuring that algorithms governing our lives are transparent, fair, and accountable. Here, I propose a conceptual framework for the regulation of AI and algorithmic systems. I argue that we need tools to program, debug and maintain an algorithmic social contract, a pact between various human stakeholders, mediated by machines. To achieve (...) this, we can adapt the concept of human-in-the-loop from the fields of modeling and simulation, and interactive machine learning. In particular, I propose an agenda I call society-in-the-loop, which combines the HITL control paradigm with mechanisms for negotiating the values of various stakeholders affected by AI systems, and monitoring compliance with the agreement. In short, ‘SITL = HITL + Social Contract.’. (shrink)

A new Arrovian impossibility is obtained without invoking independence of irrelevant alternatives type assumptions. The new conditions leading to the impossibility are based on the concept of power of enforcement, and specify how this power can (see A3) or cannot be expanded (see A1, A2 and A4).

This paper provides a generalized characterization of the family of independence conditions which are equivalent to independence of irrelevant alternatives by proposing a pair-based refinement of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document}-independence. Equipped with the new result, the relation between external independence conditions and independence of irrelevant alternatives is explored.

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the conditions on the aggregation procedure.

In this paper I analyse different justifications for the claim that the minor premise of the libertarian argument is true, namely, intuition, van Inwagen’s argument from moral responsibility and an argument from rationality. I claim none of these is satisfactory. I conclude by suggesting a possible way of interpreting the meaning of the free will intuition libertarians claim we have.

Judgment aggregation studies how individual opinions on a given set of propositions can be aggregated to form a consistent group judgment on the same propositions. Despite the simplicity of the problem, seemingly natural aggregation procedures fail to return consistent collective outcomes, leading to what is now known as the doctrinal paradox. The first occurrences of the paradox were discovered in the legal realm. However, the interest of judgment aggregation is much broader and extends to political philosophy, epistemology, social choice theory, (...) and computer science. The aim of this paper is to provide a concise survey of the discipline and to outline some of the most pressing questions and future lines of research. (shrink)

Political egalitarianism is at the core of most normative conceptions of democratic legitimacy. It finds its minimal expression in the “one person one vote” formula. In the literature on deliberative democracy, political equality is typically interpreted in a more demanding sense, but different interpretations of what political equality requires can be identified. In this paper I shall argue that the attempt to specify political equality in deliberative democracy is affected by a dilemma. I shall illustrate the political egalitarian’s dilemma by (...) a hypothetical choice between two informational bases for political equality: Rawlsian primary goods and Amartya Sen’s capability approach. The political egalitarian’s dilemma reveals a clash between the requirement of ensuring equal possibilities to participate in the democratic process and the requirement of subjecting substantive judgments to deliberative evaluation. As such, the dilemma is a variant of the procedure vs. substance dilemma that is well-known in democratic theory. While it has sometimes been argued that deliberative democracy solves the tension between procedure and substance, the political egalitarian’s dilemma shows that this tension continues within deliberative democracy. (shrink)

We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called (...) strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives. (shrink)

When is it legitimate for a government to ‘nudge’ its citizens, in the sense described by Thaler and Sunstein (2008)? In their original work on the topic, Thaler and Sunstein developed the _‘as judged by themselves’ (or AJBT) test_ to answer this question (Thaler and Sunstein 2008, p. 5). In a recent paper, Paul and Sunstein (2019) raised a concern about this test: it often seems to give the wrong answer in cases in which we are nudged to make a (...) decision that leads to what Paul calls a _personally transformative experience_, that is, one that results in our values changing (Paul 2014). In those cases, the nudgee will judge the nudge to be legitimate after it has taken place, but only because their values have changed as a result of the nudge. In this paper, I take up the challenge of finding an alternative test. I draw on my _aggregate utility account_ of how to choose in the face of what Ullmann-Margalit (2006) calls _big decisions_, that is, decisions that lead to these personally transformative experiences (Pettigrew 2019, Chapters 6 and 7). (shrink)

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input side (...) of the theory and the decision maker's preferences among risky acts on the output side. (shrink)