John Broome has developed an account of rationality and reasoning which gives philosophical foundations for choice theory and the psychology of rational agents. We formalize his account into a model that differs from ordinary choice-theoretic models through focusing on psychology and the reasoning process. Within that model, we ask Broome’s central question of whether reasoning can make us more rational: whether it allows us to acquire transitive preferences, consistent beliefs, non-akratic intentions, and so on. We identify three structural types of (...) rationality requirements: consistency requirements, completeness requirements, and closedness requirements. Many standard rationality requirements fall under this typology. Based on three theorems, we argue that reasoning is successful in achieving closedness requirements, but not in achieving consistency or completeness requirements. We assess how far our negative results reveal gaps in Broome's theory, or deficiencies in choice theory and behavioral economics. (shrink)

In the emerging literature on judgment aggregation over logically connected proposi- tions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert know- ledge on, or particularly affected by, certain propositions the right to determine the collective judgment on those propositions. We identify a problem that generalizes Sen's 'liberal paradox'. Under plausible conditions, the assignment of rights to two or more individuals or subgroups is inconsistent with the (...) unanimity principle, whereby unanimously accepted propositions are collectively accepted. The inconsistency can be avoided if individual judgments or rights satisfy special conditions. (shrink)

People reason not only in beliefs, but also in intentions, preferences, and other attitudes. They form preferences from existing preferences, or intentions from existing beliefs and intentions, and so on. This often involves choosing between rival conclusions. Building on Broome (Rationality through reasoning, Hoboken, Wiley. https://doi.org/10.1002/9781118609088, 2013) and Dietrich et al. (J Philos 116:585–614. https://doi.org/10.5840/jphil20191161138, 2019), we present a philosophical and formal analysis of reasoning in attitudes, with or without facing choices in reasoning. We give different accounts of choosing, (...) in terms of a conscious activity or a partly subconscious process. Reasoning in attitudes differs fundamentally from reasoning _about_ attitudes, a form of theoretical reasoning in which one discovers rather than forms attitudes. We show that reasoning in attitudes has standard formal properties (such as monotonicity), but is indeterministic, reflecting choice in reasoning. Like theoretical reasoning, it need not follow logical entailment, but for a more radical reason, namely indeterminism. This makes reasoning in attitudes harder to model logically than theoretical reasoning. But it can be studied abstractly, using indeterministic consequence operators. (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List (2018, 2021). The nature, relevance, and implications of the tension are explained and assessed.

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...) and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

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

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)

Living organisms are exposed to numerous influencing factors. This holds also true for their infrastructures that are processing and transducing information like endocrine networks or nerval channels. Therefore, the ability to compensate for noise is crucial for survival. An efficient mechanism to neutralise disturbances is instantiated in form of parallel complementary communication channels exerting antagonistic effects at their common receivers. Different signal processing types share the ability to suppress noise, to widen the system’s regulation capacity, and to provide for variable (...) gains while leaving the transferred signal to a large extent unchanged. (shrink)

While ordinary decision theory focuses on empirical uncertainty, real decision-makers also face normative uncertainty: uncertainty about value itself. From a purely formal perspective, normative uncertainty is comparable to (Harsanyian or Rawlsian) identity uncertainty in the 'original position', where one's future values are unknown. A comprehensive decision theory must address twofold uncertainty -- normative and empirical. We present a simple model of twofold uncertainty, and show that the most popular decision principle -- maximising expected value (`Expectationalism') -- has different formulations, namely (...) Ex-Ante Expectationalism, Ex-Post Expectationalism, and hybrid theories. These alternative theories recommend different decisions, reasoning modes, and attitudes to risk. But they converge under an interesting (necessary and sufficient) condition. (shrink)

We present a new “reason-based” approach to the formal representation of moral theories, drawing on recent decision-theoretic work. We show that any moral theory within a very large class can be represented in terms of two parameters: a specification of which properties of the objects of moral choice matter in any given context, and a specification of how these properties matter. Reason-based representations provide a very general taxonomy of moral theories, as differences among theories can be attributed to differences in (...) their two key parameters. We can thus formalize several distinctions, such as between consequentialist and non-consequentialist theories, between universalist and relativist theories, between agent-neutral and agent-relative theories, between monistic and pluralistic theories, between atomistic and holistic theories, and between theories with a teleological structure and those without. Reason-based representations also shed light on an important but under-appreciated phenomenon: the “underdetermination of moral theory by deontic content”. (shrink)

Except for a patina of twenty-first century modernity, in the form of logic and language, philosophy is exactly the same now as it ever was; it has made no progress whatsoever. We philosophers wrestle with the exact same problems the Pre-Socratics wrestled with. Even more outrageous than this claim, though, is the blatant denial of its obvious truth by many practicing philosophers. The No-Progress view is explored and argued for here. Its denial is diagnosed as a form of anosognosia, a (...) mental condition where the affected person denies there is any problem. The theories of two eminent philosophers supporting the No-Progress view are also examined. The final section offers an explanation for philosophy 's inability to solve any philosophical problem, ever. The paper closes with some reflections on philosophy 's future. (shrink)

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. (shrink)

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. (shrink)

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). (shrink)

The child’s right to an open future aims at protecting the autonomy of the mature person into which a child will normally develop. The justification of state interventions into parental decisions which unduly restrict the options of the prospective adult has to address the problem that the value of autonomy is highly contested in modern pluralist societies. The article argues that the modern majority culture provides young adults with many more options than traditionalist religious communities. However, the options that can (...) be chosen in faith groups, such as the Amish, do not constitute a subset of the options available in the wider society. Therefore, state policies which pursue the goal of providing every child with the greatest possible set of options cannot be based on a neutralist version of political liberalism. The advocates of a child’s right to an open future must rely on a perfectionist version of liberalism which draws on the ideal of leading an autonomous life. Since liberal perfectionism has problematic implications, the article defends a neutralist position that largely refrains from state interference with the educational authority of fundamentalist religious communities. (shrink)

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

Through modern driver assistant systems, algorithmic decisions already have a significant impact on the behavior of vehicles in everyday traffic. This will become even more prominent in the near future considering the development of autonomous driving functionality. The need to consider ethical principles in the design of such systems is generally acknowledged. However, scope, principles and strategies for their implementations are not yet clear. Most of the current discussions concentrate on situations of unavoidable crashes in which the life of human (...) beings is existentially affected. In this paper, we argue that ethical considerations should be mandatory for any algorithmic decision of autonomous vehicles, instead of a limitation to hazard situations. Such an ethically aligned behavior is relevant because autonomous vehicles, like any other traffic participants, operate in a shared public space, where every behavioral decision impacts the operational possibilities of others. These possibilities concern the fulfillment of a road-user’s safety, utility and comfort needs. We propose that, to operate ethically in such space, an autonomous vehicle will have to take its behavior decisions according to a just distribution of operational possibilities among all traffic participants. Using an application on a partially-autonomous prototype vehicle, we describe how to apply and implement concepts of distributive justice to the driving environment and demonstrate the impact on its behavior in comparison to an advanced but egoistic decision maker. (shrink)

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. (shrink)

While the importance of social norms for shaping and transforming communities is uncontested, their nature and normativity are controversial. Most recent theorists take social norms to arise if members hold certain attitudes, such as expectations on others, perhaps along with certain behaviours. Yet attitudes do not create norms, let alone social norms or social normativity. Social norms are instead ‘made’: through a social process. Social norming processes are special communication processes, often non-verbal and informal. We present different versions of a (...) process-based account of social norms and social normativity. The process-based view brings social norms closer to legal norms, as processes represent social ‘acts’, just as laws and contracts arise through acts rather than mere attitudes, for instances acts of voting or signing. (shrink)

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by environmental (...) factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

Does pre-voting group deliberation improve majority outcomes? To address this question, we develop a probabilistic model of opinion formation and deliberation. Two new jury theorems, one pre-deliberation and one post-deliberation, suggest that deliberation is beneficial. Successful deliberation mitigates three voting failures: (1) overcounting widespread evidence, (2) neglecting evidential inequality, and (3) neglecting evidential complementarity. Formal results and simulations confirm this. But we identify four systematic exceptions where deliberation reduces majority competence, always by increasing Failure 1. Our analysis recommends deliberation that (...) is 'participatory', 'neutral', but not necessarily 'equal', i.e., that involves substantive sharing, privileges no evidences, but might privilege some persons. (shrink)

A probability aggregation rule assigns to each profile of probability functions across a group of individuals (representing their individual probability assignments to some propositions) a collective probability function (representing the group's probability assignment). The rule is “non-manipulable” if no group member can manipulate the collective probability for any proposition in the direction of his or her own probability by misrepresenting his or her probability function (“strategic voting”). We show that, except in trivial cases, no probability aggregation rule satisfying two mild (...) conditions (non-dictatorship and consensus preservation) is non-manipulable. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

Replicating or exceeding human intelligence, not just in particular domains but in general, has always been a major goal of Artificial Intelligence (AI). We argue here that “human intelligence” is not only ill-defined, but often conflated with broader aspects of human psychology. Standard arguments for replicating it are morally unacceptable. We then suggest a reframing: that the proper goal of AI is not to replicate humans, but to complement them by creating diverse intelligences capable of collaborating with humans. This goal (...) renders issues of theory of mind, empathy, and caring, or community engagement, central to AI. It also challenges AI to better understand the circumstances in which human intelligence, including human moral intelligence, fails. (shrink)

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. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem (...) generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (ii) (...) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

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’. (shrink)

There is a prevalent notion among cognitive scientists and philosophers of mind that computers are merely formal symbol manipulators, performing the actions they do solely on the basis of the syntactic properties of the symbols they manipulate. This view of computers has allowed some philosophers to divorce semantics from computational explanations. Semantic content, then, becomes something one adds to computational explanations to get psychological explanations. Other philosophers, such as Stephen Stich, have taken a stronger view, advocating doing away with semantics (...) entirely. This paper argues that a correct account of computation requires us to attribute content to computational processes in order to explain which functions are being computed. This entails that computational psychology must countenance mental representations. Since anti-semantic positions are incompatible with computational psychology thus construed, they ought to be rejected. Lastly, I argue that in an important sense, computers are not formal symbol manipulators. (shrink)

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. (shrink)

We present an abstract model of rationality that focuses on structural properties of attitudes. Rationality requires coherence between your attitudes, such as your beliefs, values, and intentions. We define three 'logical' conditions on attitudes: consistency, completeness, and closedness. They parallel the familiar logical conditions on beliefs, but contrast with standard rationality conditions like preference transitivity. We establish a formal correspondence between our logical conditions and standard rationality conditions. Addressing John Broome's programme 'rationality through reasoning', we formally characterize how you can (...) (not) become more logical by reasoning. Our analysis connects rationality with logic, and enables logical talk about multi-attitude psychology. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light (...) of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)

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.. (shrink)

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). (shrink)

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore (...) suggest restricting independence to premises, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent. (shrink)

This paper examines three cases of the clash between science and philosophy: Zeno’s paradoxes, the Frame Problem, and a recent attempt to experimentally refute skepticism. In all three cases, the relevant science claims to have resolved the purported problem. The sciences, construing the term broadly, are mathematics, artificial intelligence, and psychology. The goal of this paper is to show that none of the three scientific solutions work. The three philosophical problems remain as vibrant as ever in the face of robust (...) scientific attempts to dispel them. The paper concludes by examining some consequences of this persistence. (shrink)

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. (shrink)

International law grants states, as representatives of their peoples, the right to use and exploit the natural resources located on their territories. The aim of this paper is to clarify how the doctrine of peoples’ sovereignty over natural resources is related to their right to political self-determination. Three different perceptions of this relationship are examined. First, the view that peoples have collective ownership rights over the natural resources to be found on their territories is criticized and rejected. Thereafter, it is (...) argued that instrumentalist reasons fail to explain why a people’s right to political self-determination implies sovereignty over natural resources. Instead, it is suggested to consider sovereignty over natural resources a necessary component of a people’s authority over the territory where their right to self-determination is realized. The proposed solution provides a sensible framework for dealing with practical issues, as can be exemplified by post-secession conf licts over natural resources. (shrink)

Sometimes analogy researchers talk as if the freshness of an experience of analogy resides solely in seeing that something is like something else -- seeing that the atom is like a solar system, that heat is like flowing water, that paint brushes work like pumps, or that electricity is like a teeming crowd. But analogy is more than this. Analogy isn't just seeing that the atom is like a solar system; rather, it is seeing something new about the atom, an (...) observation enabled by 'looking' at atoms from the perspective of one's understanding of solar systems. The question for analogy researchers then is this: Where does this new knowledge about atoms come from? How can an analogy provide new knowledge and new understanding? (shrink)

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. (shrink)

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. (shrink)

We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.

This paper offers an explanation for why some parts of philosophy have made no progress. Philosophy has made no progress because it cannot make progress. And it cannot because of the nature of the phenomena philosophy is tasked with explaining—all of it involves consciousness. Here, it will not be argued directly that consciousness is intractable. Rather, it will be shown that a specific version of the problem of consciousness is unsolvable. This version is the Problem of the Subjective and Objective. (...) Then it is argued that the unsolvability of this latter problem is why there are other unsolvable philosophy problems. (shrink)

This symposium in the overlap of philosophy and decision theory is described well by its title “Beliefs in Groups”. Each word in the title matters, with one intended ambiguity. The symposium is about beliefs rather than other attitudes such as preferences; these beliefs take the form of probabilities in the first three contributions, binary yes/no beliefs (‘judgments’) in the fourth contribution, and qualitative probabilities (‘probability grades’) in the fifth contribution. The beliefs occur in groups, which is ambiguous between beliefs of (...) groups as a whole and beliefs of group members. The five contributions – all of them interesting, we believe – address several aspects of this general theme. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, (...) which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

Recently, on the History Channel, artificial intelligence (AI) was singled out, with much wringing of hands, as one of the seven possible causes of the end of human life on Earth. I argue that the wringing of hands is quite inappropriate: the best thing that could happen to humans, and the rest of life of on planet Earth, would be for us to develop intelligent machines and then usher in our own extinction.

It is possible to survey humankind and be proud, even to smile, for we accomplish great things. Art and science are two notable worthy human accomplishments. Consonant with art and science are some of the ways we treat each other. Sacrifice and heroism are two admirable human qualities that pervade human interaction. But, as everyone knows, all this goodness is more than balanced by human depravity. Moral corruption infests our being. Why?

The open-domain Frame Problem is the problem of determining what features of an open task environment need to be updated following an action. Here we prove that the open-domain Frame Problem is equivalent to the Halting Problem and is therefore undecidable. We discuss two other open-domain problems closely related to the Frame Problem, the system identification problem and the symbol-grounding problem, and show that they are similarly undecidable. We then reformulate the Frame Problem as a quantum decision problem, and show (...) that it is undecidable by any finite quantum computer. (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (shrink)