Franz Dietrich

Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice, we describe a framework for conceptualizing preference formation and preference change. In our model, an agent's preferences are based on certain "motivationally salient" properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient properties cease to be salient. Our approach captures endogenous preferences in various contexts and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice

Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a given set of beliefs in the first place. We offer an account of rational belief formation that closes some of the gap between Bayesianism and its reason-based alternative, formalizing the idea that an agent can have reasons for his or her (prior) beliefs, in addition to evidence or information in the ordinary Bayesian sense. Our analysis of reasons for belief is part of a larger programme of research on the role of reasons in rational agency (Dietrich and List, Nous, 2012a, in press; Int J Game Theory, 2012b, in press)

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints.

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71..

Behaviourism is the view that preferences, beliefs, and other mental states in social-scientific theories are nothing but constructs re-describing people's behaviour. Mentalism is the view that they capture real phenomena, on a par with the unobservables in science, such as electrons and electromagnetic fields. While behaviourism has gone out of fashion in psychology, it remains influential in economics, especially in ‘revealed preference’ theory. We defend mentalism in economics, construed as a positive science, and show that it fits best scientific practice. We distinguish mentalism from, and reject, the radical neuroeconomic view that behaviour should be explained in terms of brain processes, as distinct from mental states.

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments.

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. This framework is inspired by the doctrinal paradox of legal theory and arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory.

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods.

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not be a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known.

Tough anti-terrorism policies are often defended by focusing on a fixed minority of the population who prefer violent outcomes, and arguing that toughness reduces the risk of terrorism from this group. This reasoning implicitly assumes that tough policies do not increase the group of 'potential terrorists', i.e., of people with violent preferences. Preferences and their level of violence are treated as stable, exogenously fixed features. To avoid this unrealis- tic assumption, I formulate a model in which policies can 'brutalise' or 'appease' someone's personality, i.e., his preferences. This follows the endogenous prefer- ences approach, popular elsewhere in political science and economics. I formally decompose the effect of toughness into a (desirable) deterrence effect and an (un- desirable) provocation effect. Whether toughness is overall effi cient depends on which effect overweighs. I show that neglecting provocation typically leads to toughness exaggeration. This suggests that some tough anti-terrorism policies observable in the present and past can be explained by a neglect of provocation.

In a single framework, I address the question of the informational basis for evaluating social states. I particularly focus on information about individual welfare, individual preferences and individual (moral) judgments, but the model is also open to any other informational input deemed relevant, e.g. sources of welfare and motivations behind preferences. In addition to proving some possibility and impossibility results, I discuss objections against using information about only one aspect (e.g. using only preference information). These objections suggest a multi-aspect informational basis for aggregation. However, the multi-aspect approach faces an impossibility result created by a lack of inter-aspect comparability. The impossibility could be overcome by measuring information on non-cardinal scales.

[This version of the paper has been superseded by "Reason-based choice and context-dependence: An explanatory framework", forthcoming in Economics & Philosophy.] We introduce a “reason-based” way of rationalizing an agent’s choice behaviour, which explains choices by specifying which properties of the options or choice context the agent cares about (the “motivationally salient properties”) and how he or she cares about these properties (the “fundamental preference relation”). Reason-based rationalizations can explain non-classical choice behaviour, including boundedly rational and sophisticated rational behaviour, and predict choices in unobserved contexts, an issue neglected in standard choice theory. We characterize the behavioural implications of different reason-based models and distinguish two kinds of context-dependent motivation: “context-variant” motivation, where the agent cares about different properties in different contexts, and “context-regarding” motivation, where the agent cares not only about properties of the options, but also about properties relating to the context.

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem.

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all information spread over the individuals without the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs sufices. JEL classification: D70, D71..

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a).

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems.

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic.

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.

Imagine a group that faces a decision problem but does not agree on which decision procedure is appropriate. In that case, can a decision be reached that respects the procedural concerns of the group? There is a sense in which legitimate decisions are possible even if people disagree on which procedure to use. I propose to decide in favour of an option which maximizes the number of persons whose judged-right procedure happens to entail this decision given the profile. This decision rule is based not only ona profile in the standard sense, but in addition on a profile of judged-right procedures. To justify this decision rule, I present a set of simple axioms leading to it as the only solution.

There is a surprising disconnect between formal rational choice theory and philosophical work on reasons. The one is silent on the role of reasons in rational choices, the other rarely engages with the formal models of decision problems used by social scientists. To bridge this gap, we propose a new, reason-based theory of rational choice. At its core is an account of preference formation, according to which an agent’s preferences are determined by his or her motivating reasons, together with a ‘weighing relation’ between different combinations of reasons. By explaining how someone’s preferences may vary with changes in his or her motivating reasons, our theory illuminates the relationship between deliberation about reasons and rational choices. Although primarily positive, the theory can also help us think about how those preferences and choices ought to respond to normative reasons

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making.

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.

Economic models describe individuals in terms of underlying characteristics, such as taste for some good, sympathy level for another player, time discount rate, risk attitude, and so on. In real life, such characteristics change through experiences: taste for Mozart changes through listening to it, sympathy for another player through observing his moves, and so on. Models typically ignore change, not just for simplicity but also because it is unclear how to incorporate change. I introduce a general axiomatic framework for defining, analysing and comparing rival models of change. I show that seemingly basic postulates on modelling change together have strong implications, like irrelevance of the order in which someone has his experiences and ‘linearity’ of change. This is a step towards placing the modelling of change on solid axiomatic grounds and enabling non-arbitrary incorporation of change into economic models.

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires that revised beliefs incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application.

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate boundedly rational and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts.

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’.

There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill this gap in the literature, we present a simple axiomatic justification for indifference, avoiding any expectation reasoning, which is often considered problematic in infinite cases. Although the two-envelope paradox assumes an expectation-maximizing agent, we show that analogous paradoxes arise for agents using different decision principles such as maximin and maximax, and that our justification for indifference before opening applies here too.

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory.