A transformative decision rule transforms a given decision probleminto another by altering the structure of the initial problem,either by changing the framing or by modifying the probability orvalue assignments. Examples of decision rules belonging to thisclass are the principle of insufficient reason, Isaac Levi'scondition of E-admissibility, the de minimis rule, andthe precautionary principle. In this paper some foundationalissues concerning transformative decision rules are investigated,and a couple of formal properties of this class of rules (...) areproved. (shrink)

The concept of transformative decision rules provides auseful tool for analyzing what is often referred to as the`framing', or `problem specification', or `editing' phase ofdecision making. In the present study we analyze a fundamentalaspect of transformative decision rules, viz. permutability. A setof transformative decision rules is, roughly put, permutable justin case it does not matter in which order the rules are applied.It is argued that in order to be normatively reasonable, sets oftransformative (...) class='Hi'>decision rules have to satisfy a number ofstructural conditions that together imply permutability. Thisformal result gives support to a non-sequential theory of framing,i.e., a theory which prescribes no uniform order in which differentsteps in the framing process have to be performed. (shrink)

This study was conducted to corroborate findings that females invoke a decision rule that is significantly different from that of their male counterparts when making ethical value judgements. In addition, the study examines whether the same decision rule is used by men and women for all types of ethical situations. The results show that males and females use different decision rules when making ethical evaluations, although there are types of situations where there are no significant differences (...) in decision rules used by men and women. The results do not suggest that any one particular decision rule is used by the majority of either males or females in different types of ethical judgements. There is a greater diversity in decision rules used by females than by males. (shrink)

Gigerenzer, Todd, and the ABC Research Group give an interesting account of simple decision rules in a variety of contexts. I agree with their basic idea that animals use simple rules. In my commentary I concentrate on some aspects of their treatment of decision rules in behavioural ecology.

Adam Elga (Philosophers’ Imprint, 10(5), 1–11, 2010) presents a diachronic puzzle to supporters of imprecise credences and argues that no acceptable decision rule for imprecise credences can deliver the intuitively correct result. Elga concludes that agents should not hold imprecise credences. In this paper, I argue for a two-part thesis. First, I show that Elga’s argument is incomplete: there is an acceptable decision rule that delivers the intuitive result. Next, I repair the argument by offering a more elaborate (...) diachronic puzzle that is more difficult for imprecise Bayesians to avoid. (shrink)

The paper introduces the concept of polar decision rules and establishes that majority rules are polar rules. We identify second best rules and penultimate rules in cases that majority rules are optimal or the most inferior, respectively. We especially specify the almost expert rule and the almost majority rule as the secondary rules of the expert and majority rules, respectively.

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards; they require that the expected utility for the federation be maximized or that the expected utilities for people from different states be equal. We discuss an analytic result that characterizes the decision rule with maximum expected utility, set up a class of models that display interstate (...) dependencies and run simulations for different dependency scenarios in the European Union. We find that, under positive correlations, the welfare distribution tends to be less sensitive to the choice of the decision rule, whereas it can be important under negative correlations. The results that Beisbart and Bovens (SCW 29, p. 581, 2007) have found for two types of models without interstate dependencies are relatively stable. There are exceptions, though, under which the way the welfare distribution is shaped by a decision rule is significantly affected by dependencies. (shrink)

We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We set up a simple model and obtain roughly the following results. If the interests of people from the same constituency are uncorrelated, then a weighted rule with square root weights does best in terms of both ideals. If there are perfect correlations, then the utilitarian ideal requires proportional weights, (...) whereas the egalitarian ideal requires equal weights. We investigate correlations that are in between these extremes and provide analytic arguments to connect our results to Barberà and Jackson (J Polit Econ 114(2):317–339, 2006) and to Banzhaf voting power. (shrink)

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A (...) class='Hi'>decision rule is optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns. (shrink)

A transformative decision rule alters the representation of a decision problem, either by changing the set of alternative acts or the set of states of the world taken into consideration, or by modifying the probability or value assignments. A set of transformative decision rules is order-independent in case the order in which the rules are applied is irrelevant. The main result of this paper is an axiomatic characterization of order-independent transformative decision rules, based (...) on a single axiom. It is shown that the proposed axiomatization resolves a problem observed by Teddy Seidenfeld in a previous axiomatization by Peterson. (shrink)

We introduce two novel frameworks for choice under complete uncertainty. These frameworks employ intervals to represent uncertain utility attaching to outcomes. In the first framework, utility intervals arising from one act with multiple possible outcomes are aggregated via a set-based approach. In the second framework the aggregation of utility intervals employs multi-sets. On the aggregated utility intervals, we then introduce min–max decision rules and lexicographic refinements thereof. The main technical results are axiomatic characterizations of these min–max decision (...) rules and these refinements. We also briefly touch on the independence of introduced axioms. Furthermore, we show that such characterizations give rise to novel axiomatic characterizations of the well-known min–max decision rule?mnx?mnx in the classical framework of choice under complete uncertainty. (shrink)

Dynamical simulations of male and female mating strategies illustrate how traits such as restrictedness constrain, and are constrained by, local ecology. Such traits cannot be defined solely by genotype or by phenotype, but are better considered as decision rules gauged to ecological inputs. Gangestad & Simpson's work draws attention to the need for additional bridges between evolutionary psychology and dynamical systems theory.

To handle epistemic and pragmatic risks, Gärdenfors and Sahlin (1982, 1988) design a decision procedure for cases in which probabilities are indeterminate. Their procedure steps outside the traditional expected utility framework. Must it do this? Can the traditional framework handle risk? This paper argues that it can. The key is a comprehensive interpretation of an option's possible outcomes. Taking possible outcomes more broadly than Gärdenfors and Sahlin do, expected utility can give risk its due. In particular, Good's (1952) (...) class='Hi'>decision procedure adequately handles indeterminate probabilities and the risks they generate. (shrink)

The implementation of the Wujciak algorithm as a new rule for organ allocation by Eurotransplant is of considerable interest for the theorist of choice making. In the process reformers accepted the status quo in principle but expected that their potential opponents would be willing to make minimal or 'tolerable' concessions. Thereby the consensual introduction of new dimensions of value and reforms of allocation practices based thereupon became viable. The paper characterizes a decision procedure based on ‘almost lexicographically pre-ordering established (...) values and practices’ in a stylized manner, presents a formal reconstruction of it and points out some of its potential implications for rule choices in general. (shrink)

The theory of direct reference suggests revising probability theory so that a probability attaches to a proposition given a way of understanding the proposition. The revisions make probabilities relative but do not change their structure.

We develop a utilitarian framework to assess different decision rules for the European Council of Ministers. The proposals to be decided on are conceptualized as utility vectors and a probability distribution is assumed over the utilities. We first show what decision rules yield the highest expected utilities for different means of the probability distri- bution. For proposals with high mean utility, simple bench- mark rules (such as majority voting with proportional weights) tend to outperform (...) class='Hi'>rules that have been proposed in the political arena. For proposals with low mean utility, it is the other way round. We then compare the expected utilities for smaller and larger countries and look for Pareto- dominance relations. Finally, we provide an extension of the model, discuss its restrictions, and compare our approach with assessments of decision rules that are based on the Penrose measure of voting power. (shrink)

Animals depleting one patch of resources must decide when to leave and switch to a fresh patch. Foraging theory has predicted various decision mechanisms; which is best depends on environmental variation in patch quality. Previously we tested whether these mechanisms underlie human decision making when foraging for external resources; here we test whether humans behave similarly in a cognitive task seeking internally generated solutions. Subjects searched for meaningful words made from random letter sequences, and as their success rate (...) declined, they could opt to switch to a fresh sequence. As in the external foraging context, time since the previous success and the interval preceding it had a major influence on when subjects switched. Subjects also used the commonness of sequence letters as a proximal cue to patch quality that influenced when to switch. Contrary to optimality predictions, switching decisions were independent of whether sequences differed little or widely in quality. (shrink)

The choice of a social decision rule for a federal assembly affects the welfare distribution within the federation. But which decision rules can be recommended on welfarist grounds? In this paper, we focus on two welfarist desiderata, viz. (i) maximizing the expected utility of the whole federation and (ii) equalizing the expected utilities of people from different states in the federation. We consider the European Union as an example, set up a probabilistic model of decision making (...) and explore how different decision rules fare with regard to the desiderata. We start with a default model, where the interests, and therefore the votes of the different states are not correlated. This default model is then abandoned in favor of models with correlations. We perform computer simulations and find that decision rules with a low acceptance threshold do generally better in terms of desideratum (i), whereas the rules presented in the Accession Treaty and in the (still unratified) Constitution of the European Union tend to do better in terms of desideratum (ii). The ranking obtained regarding desideratum (i) is fairly stable across different correlation patterns. (shrink)

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. In (...) synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists. (shrink)

Like many theorists before him, Paul Weirich has set out to find the Holy Grail of classical game theory: the solution concept that identifies the uniquely rational solution to every non-cooperative game. In this book, he reports an intermediate stage in his quest. He cannot actually identify the unique solution for every game but, he believes, he has found a new concept of equilibrium that is a necessary property of that solution.

The objective of this article is to propose a precise characterization of the collective practice behind at least an important part of the phenomena named “decision by consensus”. First, I provide descriptions of the use of this rule, and give a definition of the non-opposition rule, both as a specific sequence of acts and as a stopping rule. Second, I challenge the usual way of understanding the non-opposition rule by contrast with voting, stating that the contrast between logic of (...) approval and logic of consent also has to be taken into account. Third, I examine the conditions of its use. The non-opposition rule satisfies groups whose concern is to decide without dividing. Finally, from the analytic benefit of opening up decision by consensus as the use of the non-opposition rule, I will examine, in a fourth part, whether consensus in decision-making is as democratic a procedure as is sometimes thought. (shrink)

Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where (...) probabilities and utilities are indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory. (shrink)

It is commonly thought that moral rules and principles, such as ‘Keep your promises,’ ‘Respect autonomy,’ and ‘Distribute goods according to need ,’ should play an essential role in our moral deliberation. Particularists have challenged this view by arguing that principled guidance leads us to engage in worse decision making because principled guidance is too rigid and it leads individuals to neglect or distort relevant details. However, when we examine empirical literature on the use of rules and (...) principles in other domains, we find that people can learn to use rules discriminately and that rule-based models tend to outperform even expert judgment. I argue that this evidence poses a problem for the moral particularist. If the particularist claims that we should not rely on decision-making rules when making practical decisions and it turns out that these rules help us make better decisions, then the particularists’ prescriptive account is deficient. However, if the particularist claims that we should rely on practical decision-making rules but not on moral rules, she needs to explain how practical rules are different from moral rules and why we should rely on the former but not the latter. (shrink)

The purpose of this paper is to show how some of the controversial questions concerning utilitarianism can be clarified by the modelling techniques and the other analytical tools of decision theory (and, sometimes, of game theory). It is suggested that the moral rules of utilitarian ethics have a logical status similar to that of the normative rules (theorems) of such formal normative disciplines as decision theory and game theory.The paper argues that social utility should be defined, (...) not in hedonistic or in ideal-utilitarian terms, but rather in terms of individual preferences, in accordance with the author's equiprobability model of moral value judgments. (shrink)

The volume _Rationality and Decision Making: From Normative Rules to Heuristics_ analyses rational and irrational decision making by individuals as well as by groups. The contributors adopt methodological, logical, linguistic, psychological, historical, and evolutionary perspectives.

The rapidly increasing role of automation throughout the economy, culture and our personal lives has generated a large literature on the risks of algorithmic decision-making, particularly in high-stakes legal settings. Algorithmic tools are charged with bias, shrouded in secrecy, and frequently difficult to interpret. However, these criticisms have tended to focus on particular implementations, specific predictive techniques, and the idiosyncrasies of the American legal-regulatory regime. They do not address the more fundamental unease about the prospect that we might one (...) day replace judges with algorithms, no matter how fair, transparent, and intelligible they become. The aim of this paper is to propose an account of the source of that unease, and to evaluate its plausibility. I trace foundational unease with algorithmic decision-making in the law to the powerful intuition that there is a basic moral and legal difference between showing that something is true of many people just like you and showing that it is true of you. Human judgment attends to the exception; automation insists on blindly applying the rule. I show how this intuitive thought is connected to both epistemological arguments about the value of statistical evidence, as well as to court-centered conceptions of the rule of law. Unease with algorithmic decision-making in the law thus draws on an intuitive principle that underpins a disparate range of views in legal philosophy. This suggests the principle is deeply ingrained. Nonetheless, I argue that the powerful intuition is not as decisive as it may seem, and indeed runs into significant epistemological and normative challenges. At an epistemological level, I show how concerns about statistical evidence's ability to track the truth can be resolved by adopting a probabilistic, rather than modal, conception of truth-tracking. At a normative level, commitment to highly individualized decision-making co-exists with equally ingrained and competing principles, such as consistent application of law. This suggests that the “rule of law” may not identify a discrete set of institutional arrangements, as proponents of a court-centric conception would have it, but rather a more loosely defined set of values that could potentially be operationalized in multiple ways, including through some level of algorithmic adjudication. Although the prospect of replacing judges with algorithms is indeed unsettling, it does not necessarily entail unreasonable verdicts or an attack on the rule of law. (shrink)

Rules are a central component of such diverse enterprises as law, morality, language, games, religion, etiquette, and family governance, but there is often confusion about what a rule is, and what rules do. Offering a comprehensive philosophical analysis of these questions, this book challenges much of the existing legal, jurisprudential, and philosophical literature, by seeing a significant role for rules, an equally significant role for their stricter operation, and making the case for rules as devices for (...) the allocation of power among decision-makers. (shrink)

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal normal-form games. In (...) synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists. (shrink)

My dissertation focuses on problems that arise when a group makes decisions that are in reasonable ways connected to the beliefs and values of the group members. These situations are represented by models of decision-theoretic aggregation: Suppose a model of individual rationality in decision-making applies to each of a group of agents. Suppose this model also applies to the group as a whole, and that this group model is aggregated from the individual models. Two questions arise. First, what (...) sets of reasonable conditions can we consistently impose on the aggregation? Second, what can we learn from insights gained in such models, in particular for ethics and political philosophy? The dissertation has three parts, each using a different model of individual rationality. Each part contains essays addressing questions of either the first or the second kind with regard to its underlying model. Part I uses a social-choice-theoretic model, in which agents are only assumed to rank alternatives. Arrow's "Impossibility Theorem" shows that certain conditions that it would be natural to impose on all aggregation cannot be so imposed, on pain of contradiction. I discuss the impact of this result on the evaluation of majority rule and on democratic theory. I also discuss Sen's "Liberal Paradox", which addresses the possibility of incorporating rights into a social-choice theoretic model. Part II uses the von Neumann/Morgenstern theory of expected utility. A result under this model has been regarded as providing an argument for utilitarianism. I locate a place within utilitarianism where the theorem can do some work. To prepare the ground, I interpret the von Neumann/Morgenstern theory as part of a theory of deliberation. Thereby, this version of expected utility theory can be embedded into the philosophy of practical reasoning. The underlying model in Part III is Bayesian decision theory. Whereas the other two inquiries focus on the philosophical assessment of formal results, the third makes a formal contribution. One essay surveys the area, and a second explores a curious phenomenon that occurs in determining outcomes under one type of Bayesian aggregation. (shrink)

Using automated systems to avoid the need for human discretion in government contexts – a scenario we call ‘rule by automation’ – can help us achieve the ideal of a free and equal society. Drawing on relational theories of freedom and equality, we explain how rule by automation is a more complete realization of the rule of law and why thinkers in these traditions have strong reasons to support it. Relational theories are based on the absence of human domination and (...) hierarchy, which automation helps us achieve. Nevertheless, there is another understanding of relational theories where what matters is the presence of valuable relationships with those in power. Exploring this further might help us see when and why we should accept human discretion. (shrink)

Many studies have highlighted a substantial "bureaucracy domination" in procedures relating to migrants’ access to territory. This form of domination is marked by highly discretionary and arbitrary practices, enacted by the administrative authorities of the state. Only minor attention, however, has been devoted to the arbitrariness of judicial decisions and to the judicial role in general in the numerous proceedings that increasingly affect the path of migrants. This path is the main object of this paper. The study focuses on Italian (...) case law in expulsion and detention proceedings of irregular third country national citizens and asylum seekers and presents qualitative empirical research on decisions issued by the competent national authorities. The results have been analysed using a selection of theoretical tools, all referable to the general concept of the rule of law. The judicial decisions on pre-removal detention proceedings in two case studies are examined: the jurisprudence on detention of irregular migrants, in different offices of the Justice of the Peace in Italy; and the case law on detention of asylum seekers in the Ordinary Tribunal of Rome. The assumption underlying the research is that various conceptions of the rule of law may have different explanatory power when it comes to explaining the empirical results. To verify this hypothesis, the study proposes an overview of the main rule of law doctrines in the Western tradition of political and legal thought and applies the method of historical-conceptual analysis. As a result, the explanatory power of six theoretical models of the rule of law was verified against the data with the view to highlight the virtues and vices of the respective explanatory frameworks. This article reaches a two-fold conclusion. First, as far as the explanatory frameworks are concerned: the results of the two case studies cannot be fully explained by any of the models considered in this study. This fact alone casts doubts on the explanatory power of these theories and calls for further research on judicial decision-making more generally. Secondly, a key finding of the study regarding the notions of discretion and arbitrariness is that the judicial approach which assures the highest protection of rights is also the one that is most easily influenced by arbitrariness. The author argues that this paradox can be easily dissolved by paying attention to the plural dimensions of arbitrariness. If we consider arbitrariness from a legal point of view, i.e. as an illegal decision, it is unsurprising that the authority that most uses its discretionary powers is also the one most at risk of abusing these discretionary powers and hence of exercising arbitrary power. However, if we consider arbitrariness from the point of view of philosophical-political theory, i.e. as a form of domination characterised by the absence of sufficient justification, it is unsurprising that the judicial approach which assures the highest protection of rights is also the one that takes its own role as guarantor of these rights and of the constitutional democratic legal order as such most seriously. This judicial approach thus most often risks exercising its power in criticisable ways, as compared to an authority much more in line with the requirements of law enforcement agencies. Keywords: migration, discretion, justice, arbitrariness, civil rights, Rechtsstaat, expulsion, mixed constitution. (shrink)