This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule (...) called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons. (shrink)

Complex problem solving is often an integration of perceptual processing and deliberate planning. But what balances these two processes, and how do novices differ from experts? We investigate the interplay between these two in the game of SET. This article investigates how people combine bottom-up visual processes and top-down planning to succeed in this game. Using combinatorial and mixed-effect regression analysis of eye-movement protocols and a cognitive model of a human player, we show that SET players deploy both bottom-up (...) and top-down processes in parallel to accomplish the same task. The combination of competition and cooperation of both types of processes is a major factor of success in the game. Finally, we explore strategies players use during the game. Our findings suggest that within-trial strategy shifts can occur without the need of explicit meta-cognitive control, but rather implicitly as a result of evolving memory activations. (shrink)

Germany has just started a public debate on priority-setting, rationing and cost-effectiveness due to the cost explosion within the German health care system. To date, the costs for German health care run at 11,6 % of its Gross Domestic Product (GDP, 278,3 billion €) that represents a significant increase from the 5,9 % levels present in 1970. In response, the German Parliament has enacted several major and minor legal reforms over the last three decades for the sake of cost containment (...) and maintaining stability of the health care system. The Statutory Health Insurance—SHI (Gesetzliche Krankenversicherung—GKV) is based on the fundamental principle of solidarity and provides an ethical and legal framework for implementing equity, comprehensiveness and setting the principles and rules for financing and providing health care services and benefits. Within the SHI system, several major actors can be identified: the Federal Ministry of Health, the 16 state ministries of health, the Federal Joint Committee (G-BA), the physicians (with their associations) and the hospitals (with their organizations) on the provider side, and the sickness funds with their associations on the purchasers’ side. This article reviews the structure and complexities of the German health care system with its major players and participants. The focus will be put on relevant ethical, legal and economic aspects for prioritization, rationalization, rationing and cost-effectiveness of medical benefits and services. In conclusion, this article pleads for open discussion on the challenging subject of priority-setting instead of accepting the implicit and non-transparent rationing of medical services that currently occurs at many different levels within the health care system, as it stands today. (shrink)

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents (...) move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes (...) of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation. (shrink)

Two justifications of backward induction (BI) in generic perfect information games are formulated using Bonanno's (1992; Theory and Decision 33, 153) belief systems. The first justification concerns the BI strategy profile and is based on selecting a set of rational belief systems from which players have to choose their belief functions. The second justification concerns the BI path of play and is based on a sequential deletion of nodes that are inconsistent with the choice of rational belief (...) functions. (shrink)

We investigate cardinal invariants related to the structure of dense sets of rationals modulo the nowhere dense sets. We prove that , thus dualizing the already known [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. 183 59–80, Theorem 3.6]. We also show the consistency of each of and . Our results answer four questions of Balcar, Hernández and Hrušák [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. (...) 183 59–80, Questions 3.11]. (shrink)

The Monty-Hall Problem ($MHP$) has been used to argue against a subjectivist view of Bayesianism in two ways. First, psychologists have used it to illustrate that people do not revise their degrees of belief in line with experimenters' application of Bayes' rule. Second, philosophers view $MHP$ and its two-player extension ($MHP2$) as evidence that probabilities cannot be applied to single cases. Both arguments neglect the Bayesian standpoint, which requires that $MHP2$ (studied here) be described in different terms than usually applied (...) and that the initial set of possibilities be stable (i.e., a focusing situation). This article corrects these errors and reasserts the Bayesian standpoint; namely, that the subjective probability of an event is always conditional on a belief reviser's specific current state of knowledge. (shrink)

A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the structure of the game and rationality held before the start of the game does not imply that backward induction will be played. To derive backward induction, a “forward belief” condition is formulated (...) in terms of revised rather than initial beliefs. Alternative notions of rationality as well as the use of knowledge instead of belief are also studied within this framework. Footnotes1 I would like to thank Wlodek Rabinowicz and three anonymous referees for very helpful comments. (shrink)

We study some properties of the quotient forcing notions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{tr(I)} = \wp(2^{< \omega})/tr(i)}$$\end{document} and PI = B(2ω)/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2ω. We show that the remainder forcing RI = Qtr(I)/PI is σ-closed in these cases. We also study the cardinal invariant of the continuum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, the distributivity (...) number of the quotient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Dense(\mathbb{Q})/nwd}$$\end{document}, in order to show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\wp(\mathbb{Q})/nwd}$$\end{document} collapses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, thus answering a question addressed in Balcar et al. (Fundamenta Mathematicae 183:59–80, 2004). (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not (...) enough to guarantee that an equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

In this paper, I reply to Seungbae Park’s (2020) critique of the view I defend in Chapter 6 of The Relativity of Theory: Key Positions and Arguments in the Contemporary Scientific Realism/Antirealism Debate (Cham: Springer, 2020), namely, Relative Realism. Relative Realism is the view that, of a set of competing scientific theories, the more predictively successful theory is comparatively true. Comparative truth is a relation between competing theories. So, to say that T1 is comparatively true is to say that T1 (...) is closer to the truth than its competitors, T2, T3, ..., Tn. Park offers two arguments against Relative Realism. The first is an argument by analogy to NBA players, which is supposed to show that, contrary to what the relative realist argues, absolute judgments about the (approximate) truth and (predictive) success of competing theories are rationally justified. The second is what Park calls “The Argument from Double Spaces,” which is supposed to show that, contrary to what the relative realist argues, relative judgments about the (comparative) truth of competing theories are not rationally justified. I argue that Park’s arguments fail to do what he wants them to do. (shrink)

Game-theoretic solution concepts such as Nash and Bayesian equilibrium start from an assumption that the players’ sets of possible payoffs, measured in units of von Neumann–Morgenstern utility, are common knowledge, and they go on to define rational behavior in terms of equilibrium strategy profiles that are either pure or independently randomized and which, in applications, are often taken to be uniquely determined or at least tightly constrained. A mechanism through which to obtain a common knowledge of payoff functions (...) measured in units of utility is not part of the model. This paper describes an operational method of constructing a state of common knowledge of the key parameters of the players’ utility functions in terms of conditional small bets on the game’s outcome. When the rationality criterion of joint coherence is applied in this setting, the solution of a game is typically characterized by a convex set of correlated equilibria. In the most general case, where players are risk averse, the parameters of the equilibria are risk-neutral probabilities, interpretable as products of subjective probabilities and relative marginal utilities for money, as in financial markets. Risk aversion generally enlarges the set of equilibria and may present opportunities for Pareto-improving modifications of the rules of the game. (shrink)

In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player's decision problem, a solution valid for all real-world instantiations, regardless of context. "Permissiveness" would constrain the theory to designate as admissible for a player any conjecture consistent with the function's designation of admissible strategies for the other players. Given permissiveness (...) and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. (shrink)

The model of incomplete cooperative games incorporates uncertainty into the classical model of cooperative games by considering a partial characteristic function. Thus the values for some of the coalitions are not known. The main focus of this paper is 1-convexity under this framework. We are interested in two heavily intertwined questions. First, given an incomplete game, how can we fill in the missing values to obtain a complete 1-convex game? Second, how to determine in a rational, fair, and efficient (...) way the payoffs of players based only on the known values of coalitions? We illustrate the analysis with two classes of incomplete games—minimal incomplete games and incomplete games with defined upper vector. To answer the first question, for both classes, we provide a description of the set of 1-convex extensions in terms of its extreme points and extreme rays. Based on the description of the set of 1-convex extensions, we introduce generalisations of three solution concepts for complete games, namely the τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-value, the Shapley value and the nucleolus. For minimal incomplete games, we show that all of the generalised values coincide. We call it the average value and provide different axiomatisations. For incomplete games with defined upper vector, we show that the generalised values do not coincide in general. This highlights the importance and also the difficulty of considering more general classes of incomplete games. (shrink)

Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition ‘strong rationalizability’), then the true (or actual) strategy profile is path equivalent to a (...) Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C8 , the set of profiles that survive the iterative deletion of inferior profiles. (shrink)

This is the second part of a two-part paper. It can be read independently of the first part provided that the reader is prepared to go along with the unorthodox views on game theory which were advanced in Part I and are summarized below. The body of the paper is an attempt to study some of the positive implications of such a viewpoint. This requires an exploration of what is involved in modeling “rational players” as computing machines.

A generalization of the standard n-person game is presented, with flexible information requirements suitable for players constrained by bounded rationality. Strategies (complete contingency plans) are replaced by "policies," i. e., end-mean pairs of candidate goals and "controls" (partial contingency plans). The existence of individual objective functions over the joint policy choice set is axiomatized in terms of primitive preference and probability orders. Conditions are given for the existence of pure policy Nash equilibrium points in n-person games, and pure policy (...) Nash bargaining and equilibrium threat solutions in 2-person policy games. Connectedness of the policy and payoff sets is not required. (shrink)

Game theory has proved a useful tool in the study of simple economic models. However, numerous foundational issues remain unresolved. The situation is particularly confusing in respect of the non-cooperative analysis of games with some dynamic structure in which the choice of one move or another during the play of the game may convey valuable information to the other players. Without pausing for breath, it is easy to name at least 10 rival equilibrium notions for which a serious case (...) can be made that here is the “right” solution concept for such games. (shrink)

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein (), charges an agent for doing costly computation; the second, initiated by Neyman (), does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in (...) a decision problem to be Turing machines, and charge players for the “complexity” of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases. (shrink)

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the (...) SEU preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. (shrink)

Value analysis establishes a way to practice functional analysis which enables to think all matter as sets of functions. The study of the correlations between the phases of activation of these functions leads to consider the aggregation of correlated activation functions as an attractor in a configuration space. This point of view allows figuring out general behaviors reducing the conceptual gap between microeconomics and macroeconomics. Then, based on a characterization of complex adaptive systems in terms of functional attractors, the theory (...) links together value and physical magnitudes, like work or energy and action. The evolution of these systems is studied from the viewpoints of learning or of voluntary and involuntary interactions with others described in the ultimate way by the strategies, or operators, of which they make use. Three kinds of uncertainties are emphasized among which the uncertainty between the structure and the business outlook of a system is recreated through an analogy between physics and economics. The rationality of the complex functional systems economics is based on value and on market or environment awareness. Equilibria establish potential of agents or players whose profiles are built through the equivalence between a time-dependent payoff at equilibrium and the regular value of the corresponding attractor. The law of supply and demand is naturally founded on unbiased profiles of agents and can be a means of uncertainty reduction and of growth. Freedoms are opportunities to grow, when they result in confidence, and to bear risks in decision-making through an innovative process. (shrink)

In the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations in the (...) newly introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.prepared by Sandro Márcio da Silva Preto.E-mail: [email protected]:https://doi.org/10.11606/T.45.2021.tde-17062021-163257. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem (...) that that difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

Wlodek Rabinowicz suggested in an e-mail conversation (2001) to me that one might be able to use a particular Hats Puzzle to make a Dutch Book against a group of individually rational persons. I present a fanciful story here that has the same structure as Rabinowicz’s Dutch Book.

Suppose that you do not do what you have previously decided to do. Are you to be charged with irrationality? A number of otherwise divergent theories of practical rationality hold that by default, you are; there are rational pressures, it is claimed, that favor the long-term stability and eventual execution of distal intentions. The article challenges this view by examining how these purported pressures can be spelled out. Is intention a normative commitment to act? Are intentions reasons for action (...) – or at least for retaining one's intention until the time to act has come? Or is the rationality of ‘doing as you decide’ governed by diachronic wide-scope norms, as Michael Bratman and John Broome suggest? All of these approaches are shown to raise severe problems, which suggests a more modest view: diachronic pressures on intending are at each point in time confined to the very next instant. (shrink)

Scholars from various philosophical schools of thought, including cultural relativism, hermeneutics, and postmodernism, have recently critiqued rationalism in light of new developments in the cognitive sciences. Each of these new developments set into motion new inquiries in each school philosophical school of thought. Now, in Facets of Rationality, a distinguished team of scholars examines these new inquiries and bring rationality back into the mainstream of the social sciences. The unique feature of this book lies in its multidisciplinary exploration of (...) class='Hi'>rational concerns and in discovering the integral meaning of rationality as viewed by the perspectives of different disciplines. As such, it will of considerable interest to those involved with the study and teaching of philosophy, theoretical psychology, cognitive science, political theory, and linguistics. (shrink)

Two recent papers (Cubitt and Sugden, 1994; Samuelson, 1992) have established impossibility results which cast doubt on the coherence of the assumption of ’common knowledge of rationality'. It is shown that the Cubitt–Sugden result is the more powerful of the two impossibilities. Second, it is proved that the existence of a quasi-strict equilibrium is sufficient to construct sets which satisfy the Cubitt–Sugden axioms. This fact is used to establish that their impossibility result cannot arise in 2-player games. Finally, it is (...) shown that if a weak symmetry postulate is added, a new impossibility result arises for this class of games. (shrink)

In his disputatio, Johann Peter von Ludewig provides a history of rational philosophy among the Arabs and sets out to contextualize the Turks’ attitude to it. Like many Lutheran scholars of the time, Ludewig believed that Islam, as a religion, impeded the development of rational philosophy in the Arab world. However, unlike those philosophers, he examines external influences that may have fed the interest of Arab Muslims in rational philosophy, especially dialectic. Unlike Orthodox Lutherans, such as Pfeiffer (...) and Kromayer, in his conclusion, Ludewig prays that Muslim philosophers cultivate reason to overcome the "deceit of Muhammadanists" toward rational worship. The use of the contentious and seemingly oxymoronic phrase “rational worship” (logikē latreia: λογική λατρεία, from Rom. 12:1), combining “rationality” and “worship” together refects, to a certain extent, the Enlightenment belief that reason could be used to understand the nature of God against any type of irrational religiosity. The idea of worshipping God rationally and equating God with reason shows the intellectual engagement of Protestant scholars with Enlightenment rationalism. (shrink)

The kind of collective improvisation attained by the “free jazz” at the beginning of the sixties sets a challenge to analytic theories of collective intentionality, that emphasize the role played by future-directed plans in the interlocking and interdependent intentions of the individual participants, because in the free jazz case the performers’ interdependence or [interplay] stems from an intuitive understanding between musicians. Otherwise said: what happens musically is not planned in advance, but arises from spontaneous interactions in the group. By looking (...) at the way jazz improvisers take up the challenge of making music together without a pre-conceived notion as to what kind of effect they will achieve and without a pre-set code of agreements, my aim has been to clarify what kind of strategies — other than advanced action plans and joint commitments — are used by improvising musicians to integrate their improvisations into a unified shared activity. In developing this proposal I initially drawn pre-theoretically on one paradigmatic study case — Ornette Coleman’s double quartet Free Jazz, A collective Improvisation and brought it in conversation with Husserl’s phenomenology of time. In a final move, I brought this phenomenological frame into dialogue with some recent readings of the predictive coding model. All in all, what we learned from the Free Jazz case is that the interdependence and interlocking of attitudes among individual participants characteristic of shared intention is not determined by a future-directed plan and the rational pressure to be responsive to and coordinate with others, it typically engages. Rather, in the free jazz case, the performers’ connection and interplay depend on the players’ readiness to feel each other out, by listening to each other playing, in a way that no doubt presupposes the Husserlian retention-protention scheme. (shrink)

A large class of games is that of non-cooperative, extensive form games of perfect information. When the length of these games is finite, the method used to reach a solution is that of a backward induction. Working from the terminal nodes, dominated strategies are successively deleted and what remains is a unique equilibrium. Game theorists have generally assumed that the informational requirement needed to solve these games is that the players have common knowledge of rationality. This assumption, however, has (...) given rise to several problems and paradoxes. Most notably, it has been shown that the common knowledge assumption makes the theory of the game inconsistent at some information set. The present paper shows that a) no common knowledge of rationality need be assumed for the backward induction solution to hold. Rather, it is sufficient that the players have a number of levels of knowledge proportional to the length of the game, and b) it is also necessary that the number of levels of knowledge is finite and proportional to the length of the game. For a higher number of levels of knowledge, inconsistencies arise. (shrink)

This book draws the limits of our thoughts and consciousness between the mind and mind-independent reality by using mathematical logic with the support of neurology. The author combines the Analytical and Continental traditions with each other's virtues. If Kant were alive today, he would have had to write such a book. Diagnosing the limits between immanence and transcendence of the consciousness depends on defining some transcendental a priori categories in between as some basic axioms of the mind. Although this is (...) a paradoxical attempt every philosopher falls into, the author non-paradoxically identifies these non-intentional cognitive categories by using mathematical category theory. This basic model of the mind allows us to follow the logical possibilities in between that the mind can set up in its relationship with mind-independence. In this way, the author defines the intentional categories of consciousness by using mathematical set theory and obtains a self-representational higher-order theory of consciousness (SHOT). Finally, he combines the intentional and non-intentional categories with an algebraic topography and obtains a model of the mind. The architectural structure of the mind is the problematic skeleton of philosophy with all its sub-branches as a human aura that can be traced throughout the six Cartesian meditations. The philosophical anthropology depicted eventually emerged as a purely naturalistic, shamanic prototype metaphysics radically different from the monotheistic Western tradition that began with Plato. The reasoning had started from mathematics, but unexpectedly arrived at an archaic metaphysics. This philosophical theory is called "Anthropogonia", after Hesiod's Theogonia. After Anthropogonia, logically, truth-seekers in these ancient, imperial religions must retreat from their historically constructed Platonic realist theology to their shamanic roots. The naturalist architecture of the mind requires such a naturalized doctrine and art. (shrink)

Decision theory comprises, first, a mathematical formalization of the relations among value, belief, and preference; and second, a set of prescriptions for rational preference. Both aspects of the theory are embodied in a single mathematical proof. The problem in the foundations of decision theory is to explain how elements of one and the same proof can serve both functions. I hope to solve this problem in a way that anchors the decision-theoretic norms of rational preference in fundamental intuitions (...) about rationality in general. I will thus depart from the tradition of anchoring those norms in intui-tions about gambling strategies or preference structures of the sort that are the special concern of the theory itself. Although my interpretation is meant to capture what is right about the decision-theoretic conception of rational preference, it will lead me to argue that there is also something fundamentally wrong about that conception. In my view, decision theory tells us how to be rational in our preferences because it tells us how to have preferences that make sense; but there are ways of making sense that outrun, and may in fact conflict with, the prescriptions of decision theory. (shrink)

In this paper, I review the literature on rational choice theory to scrutinize a number of criticisms that philosophers have voiced against its usefulness in economics. The paper has three goals: first, I argue that the debates about RCT have been characterized by disunity and confusion about the object under scrutiny, which calls into question the effectiveness of those criticisms. Second, I argue that RCT is not a single and unified choice theory—let alone an empirical theory of human behavior—as (...) some critics seem to suppose. Rather, there are several variants of RCT used in economics. Third, I propose that we think of RCT as a set of distinct research strategies to appreciate its diversity. This account implies that the effectiveness of any criticism depends on the variant of RCT we are considering. (shrink)

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types (...) of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return. (shrink)

A measure of good and bad is internal to something falling under it when that thing falls under the measure in virtue of what it is. The concept of an internal standard has broad application. Compare the external breed standards arbitrarily imposed at a dog show with the internal standards of health at work in the veterinarian's office. This paper is about practical standards, measures of acting well and badly, and so measures deployed in deliberation and choice. More specifically, it (...) is about the attempt to explain the unconditional validity of certain norms (say, of justice and prudence) by showing them to be internal to our agency and the causality it involves. This is constitutivism. Its most prominent incarnations share a set of assumptions about the nature of agency and our knowledge of it: conceptualism, formalism and absolutism. This essay investigates the merits and viability of rejecting all of them while still seeking the ground of practical normativity in what we are, in our fundamental activity. (shrink)

Structured argumentation formalisms, such as ASPIC +, offer a formal model of defeasible reasoning. Usually such formalisms are highly parametrized and modular in order to provide a unifying framework in which different forms of reasoning can be expressed. This generality comes at the price that, in their most general form, formalisms such as ASPIC + do not satisfy important rationality postulates, such as non-interference. Similarly, links to other forms of knowledge representation, such as reasoning with maximal consistent sets of rules, (...) are insufficiently studied for ASPIC + although such links have been established for other, less complex forms of structured argumentation where defeasible rules are absent. Clearly, for a formal model of defeasible reasoning it is important to understand for which range of parameters the formalism displays a behavior that adheres to common standards of consistency, logical closure and logical relevance and can be adequately described in terms of other well-known forms of knowledge representation. In this paper we answer this question positively for a fragment of ASPIC + without the attack form undercut by showing that it satisfies all standard rationality postulates of structured argumentation under stable and preferred semantics and is adequate for reasoning with maximal consistent sets of defeasible rules. The study is general in that we do not impose any other requirements on the strict rules than to be contrapositable and propositional and in that we also consider priorities among defeasible rules, as long as they are ordered by a total preorder and lifted by weakest link. In this way we generalize previous similar results for other structured argumentation frameworks and so shed further light on the close relations between assumption-based argumentation and ASPIC +. (shrink)

This essay some first steps toward the naturalization of what I call rational intentionality or alternatively type II intentionality. By rational or type II intentionality, I mean that full combination of rational powers and content-bearing states that is paradigmatically enjoyed by mature intact human beings. The problem I set myself is to determine the extent to which the only currently extant approach to the naturalization of the intentional that has the singular virtue of not being a non-starter (...) can be aggregated up into an account of rational intentionality. I have in mind a broadly defined family of accounts whose main members are the indicator/information-theoretic approach of Dretske (1988), the asymmetric dependence theory of Jerry Fodor (1987, 1990, 1994) and the teleo-semantics of Ruth Millikan (1984, 1993). Somewhat inaccurately, I will call this family of approaches the information-theoretic family. To be sure, there is only a rough family resemblance among the members of the information-theoretic family. Indeed, several intense quarrels divide the members of that family one from another, but the precise outcome of those internecine struggles is not directly relevant to the aims of this essay. ² Taken collectively, the information-theoretic family yields a compelling picture of the place of at least a crude form of intentionality -- what I call frog-like or type I intentionality -- in the natural order. Though frog-like or type I intentionality is, I think, a genuine species of intentionality, it may subsist in the absence of rational powers. It is that species of intentionality enjoyed by irritable creatures who, following Brandom (1994). (shrink)

The value of rational choice theory for the social sciences has long been contested. It is argued here that, in the debate over its role, it is necessary to distinguish between claims that people maximise manifest payoffs, and claims that people maximise their utility. The former version has been falsified. The latter is unfalsifiable, because utility cannot be observed. In principle, utility maximisation can be adapted to fit any form of behaviour, including the behaviour of non-human organisms. Allegedly 'inconsistent' (...) behaviour is also impossible to establish without qualification. This utility-maximising version of rational choice theory has the character of a universal 'explanation' that can be made to 'fit' any set of events. This is a sign of weakness rather than strength. In its excessive quest for generality, utility-maximising rational choice theory fails to focus on the historically and geographically specific features of socio-economic systems. As long as such theory is confined to ahistorical generalities, then it will remain highly limited in dealing with the real world. Instead we have to consider the real social and psychological determinants of human behaviour. (shrink)

The Barth–Krabbe–Hintikka–Hintikka Problem, independently raised by Barth and Krabbe and Hintikka and Hintikka Sherlock Holmes confronts modern logic: Toward a theory of information-seeking through questioning. Indiana University Press, Bloomington, 1983), is the problem of characterizing the strategic reasoning of the players of dialogical logic and game-theoretic semantics games from rational preferences rather than rules. We solve the problem by providing a set of preferences for players with bounded rationality and specifying strategic inferences from those preferences, for a (...) variant of logical dialogues. This solution is generalized to both game-theoretic semantics and orthodox dialogical logic. (shrink)

Wlodek Rabinowicz suggested in an e-mail conversation (2001) to me that one might be able to use a particular Hats Puzzle to make a Dutch Book against a group of individually rational persons. I present a fanciful story here that has the same structure as Rabinowicz’s Dutch Book. For a more academic version of the same idea, see Luc Bovens and Wlodek Rabinowicz 2010 "The Puzzle of the Hats" Luc Bovens & Wlodek Rabinowicz *Synthese* 172 (1):57-78.

This paper reconsiders Rubinstein's alternating-offer bargaining game with complete information. We define rationalizability and trembling- hand rationalizability (THR) for multi-stage games with observed actions. We show that rationalizability does not exclude perpetual disagreement or delay, but that THR implies a unique solution. Moreover, this unique solution is the unique subgame perfect equilibrium (SPE). Also, we reconsider an extension of Rubinstein's game where a smallest money unit is introduced: THR rules out the non-uniqueness of SPE in some particular case. Finally, we (...) investigate the assumption of boundedly rational players. Perpetual disagreement is excluded, but not delay. Furthermore, we cannot use the asymmetric Nash bargaining solution as an approximation of the alternating-offer bargaining model once the players are boundedly rational ones. (shrink)

This article aims to study the coordination of the defenders’ tactical and technical behaviour of successful teams to recover the ball according to contextual variables. A total of 15,369 events and 49 to 12,398 different patterns in 32 games of the 2014 FIFA World Cup’s play-offs were detected and analysed. Results evidenced a T-pattern of the first defender pressuring the ball carrier and his teammates concentrating at the same zone to cover him or space, leading to ball recovery. Field zones, (...) first defender tactical and technical behaviours, and ball carrier first touch constituted opportunities for defenders to coordinate themselves. Moreover, the third defender had a predominant role in his teammates’ temporisation and covering zone behaviours. In the draw, first half, second-tier quality of opponent and play-offs excluding third place and final matches, the ball regularly shifted from upper to lower field zones in short periods, resulting in ball recovery or shot on goal conceded. Defenders performed behaviours farther from the ball carrier, and player-marking were most recurrent to an effective defence. This study’s findings could help coaches give specific tips to players regarding interpersonal coordination in defence and set strategies to make tactical behaviour emerge globally. (shrink)

A significant problem in constructing the theory of rational choice (and rationality in gen­eral) at the moment is the question of explaining irrationality, or rather the fact that an agent can act irrationally for an external observer, and the models used for it may not work. However, the agent himself “inside”, if you find yourself in his “logic”, acts clearly rationally upon verification. It’s just that his “rationality” and the “rationality” of an ex­ternal observer turn out to be different, (...) hence they do not coincide, and hence this leads to a discrepancy in the language of their description of each other. To resolve this prob­lem and find a theoretical basis for the connection between the physiological states of or­ganisms and testable the theoretical constructs, and thus obtaining the opportunity, with­out changing the optics, to work with all agents, regardless of the types of rationality they have, psychological approaches have increasingly become involved. But for them, the basic problem is always “rootedness” in the “material substrate”. This work largely suggests and shows which mechanism can allow this problem to be solved. The paper draws atten­tion to the fact that the combination of the theory of predictive processing and the theory of cognitive dissonance turns out to be extremely promising for this task. This is due to the fact that both of these theories are engaged in reducing surprise or inconsistency (prediction errors and dissonance), with the former providing the latter with valuable and informative context within the broader perception – prediction – action framework (known as active inference) and also helps us to separate dissonant cognitive elements from dissonant psychological states, while considering them as part of the same process of perception and cognition. All this allows us to set a fundamental theoretical basis for the connection between the physiological states of organisms and testable theoretical con­structs about the degree of rationality of a particular agent, and, thus, gain access to the internal information processes in the brain for study. (shrink)

Human beings are peculiar. In laboratory experiments, they often cooperate in one-shot prisoners’ dilemmas, they frequently offer 1/2 and reject low offers in the ultimatum game, and they often bid 1/2 in the game of divide-the-cake All these behaviors are puzzling from the point of view of game theory. The first two are irrational, if utility is measured in a certain way.1 The last isn’t positively irrational, but it is no more rational than other possible actions, since there are (...) infinitely many other Nash equilibria besides the one in which both players bid 1/2. At the same time, these behaviors seem to indicate that people are sometimes inclined to be cooperative, fair, and just. In his stimulating new book, Brian Skyrms sets himself the task of showing why these inclinations evolved, or how they might have evolved, under the pressure of natural selection. The goal is not to justify our ethical intuitions, but to explain why we have them.2.. (shrink)

Resource constraints in developing countries compel policy makers to ration the provision of healthcare services. This article examines one such set of Guidelines: A patient dialysing in the state sector in South Africa may not refuse renal transplantation when a kidney becomes available. Refusal of transplantation can lead to exclusion from the state-funded dialysis programme. This Guideline is legally acceptable as related to Constitutional stipulations which allow for rationing healthcare resources in South Africa. Evaluating the ethical merit of the Guideline, (...) and exploring the ethical dilemma it poses, proves a more complex task. We examine the actions of healthcare professionals as constrained by the Guideline. From a best interests framework, we argue that in these circumstances directing patient decision making is not necessarily unethical or unacceptably paternalistic. We then scrutinise the guideline itself through several different ethical ‘lenses’. Here, we argue that bioethics does not provide a definitive answer as to the moral merit of rationing dialysis under these circumstances, however it can be considered just in this context. We conclude by examining a potential pitfall of the Guideline: Unwilling transplant recipients may not comply with immunosuppressive medication, which raises questions for policies based on resource management and rationing. (shrink)

In the article, a yes–no model of influence is generalized to a multi-choice framework. We introduce and study the weighted influence indices of a coalition on a player in a social network where the players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to the mutual influence among players, the final decision of each player may be different from his original inclination. In a particular case, the decision (...) of the player is closer to the inclination of the influencing coalition than his inclination was, i.e., the distance between the inclinations of the player and of the coalition is greater than the distance between the decision of the player and the inclination of the coalition in question. The weighted influence index which captures such a case is called the weighted positive influence index. We also consider the weighted negative influence index where the final decision of the player goes farther away from the inclination of the coalition. We consider several influence functions defined in the generalized model of influence and study their properties. The concept of a follower of a given coalition and its particular case, a perfect follower, are defined. The properties of the set of followers are analyzed. (shrink)

There is a general consensus among economists that the notion of rationality plays a central role in microeconomics. It is important to note, however, that they are far from agreement on the meaning of this notion. It would be difficult to lay out a set of welldefined concepts of rationality, but it might be useful to distinguish three quite different approaches around which economists tend to situate themselves when characterising this notion. I prefer to refer to three "approaches" rather than (...) to three concepts, as I did in the title of the paper, because the concepts of rationality which correspond to these approaches cannot be isolated easily. Indeed, their unsettled definitions often overlap, and even when they purport to be related to opposing approaches, they are more or less interrelated. In any case, I propose to refer to these three approaches as "rationality-purposefulness", "rationality-efficiency", and "rationality-consistency". According to rationalitypurposefulness, an action is rational if and only if it is oriented towards the satisfaction of the agent's purpose, as most Austrian economists would tend to say. According to rationality-efficiency, an action is rational if and only if it actually maximises a positively valued magnitude such as utility or profit, as many neoclassical economists would say, especially when adopting a traditional approach. By contrast, rationality-consistency states that choices are rational if and only if it they are consistent as a set, which implies in particular that they are transitive. (shrink)