Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...) necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We propose a novel formulation of these concepts, and demonstrate its advantages over leading alternatives. We present a sound and complete algorithm for computing explanatory factors with respect to a given context and set of agentive preferences, allowing users to identify necessary and sufficient conditions for desired outcomes at minimal cost. Experiments on real and simulated data confirm our method’s competitive performance against state of the art XAI tools on a diverse array of tasks. (shrink)

In this paper, we provide a detailed review of previous classifications of 2 × 2 games and suggest a mathematically simple way to classify the symmetric 2 × 2 games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a (...) method for using a stereographic projection to create a compact 2-d representation of the game space. (shrink)

This article contributes to the debate around the abilities of large language models such as GPT-3, dealing with: firstly, evaluating how well GPT does in the Turing Test, secondly the limits of such models, especially their tendency to generate falsehoods, and thirdly the social consequences of the problems these models have with truth-telling. We start by formalising the recently proposed notion of reversible questions, which Floridi & Chiriatti propose allow one to ‘identify the nature of the source of their (...) answers’, as a probabilistic measure based on Item Response Theory from psychometrics. Following a critical assessment of the methodology which led previous scholars to dismiss GPT’s abilities, we argue against claims that GPT-3 completely lacks semantic ability. Using ideas of compression, priming, distributional semantics and semantic webs we offer our own theory of the limits of large language models like GPT-3, and argue that GPT can competently engage in various semantic tasks. The real reason GPT’s answers seem senseless being that truth-telling is not amongst them. We claim that these kinds of models cannot be forced into producing only true continuation, but rather to maximise their objective function they strategize to be plausible instead of truthful. This, we moreover claim, can hijack our intuitive capacity to evaluate the accuracy of its outputs. Finally, we show how this analysis predicts that a widespread adoption of language generators as tools for writing could result in permanent pollution of our informational ecosystem with massive amounts of very plausible but often untrue texts. (shrink)

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by (...) an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power.We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core.We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera. (shrink)

Canonical economic agents act so as to maximize a single, representative, utility function. However, there is accumulating evidence that heterogeneity in thought processes may be an important determinant of individual behavior. This paper investigates the implications of a vector-valued generalization of the Expected Utility paradigm, which permits agents either to deliberate as per Homo economics, or to act impulsively. This generalized decision theory is applied to explain the crowding-out effect, irrational educational investment decisions, persistent social inequalities, the pervasive influence (...) of non-cognitive ability on socio-economic outcomes, and the dynamic relationships between non-cognitive ability, cognitive ability, and behavioral biases. These results suggest that the generalized decision theory warrants further investigation. (shrink)

Both economists and psychologists are interested in understanding decision making under uncertainty. Yet, they rely on different concepts to analyse human behaviour: economists use economic preference parameters rooted in utility theory, while psychologists use personality traits to describe responses to uncertain situations. Using a large sample of university students, this study examines and contrasts five economic preference parameters and six psychological personality traits that are commonly used to study individuals’ attitudes towards uncertainty. A novelty of this paper is including both (...) the economic concept of ambiguity aversion as well as the personality trait of ambiguity intolerance. We find that standard economic preference measures based on incentivized choice tasks seem to capture rather different characteristics than psychological personality traits. In contrast, economic preference measures obtained from self-assessment questions appear more related to personality traits, especially ambiguity intolerance. (shrink)

This study analyses the sensitivity of public goods contributions through the lens of psychological motives. We report the results of a public goods experiment in which subjects were induced with the motives of care and anger through autobiographical recall. Subjects’ preferences, beliefs, and perceptions under each motive are compared with those of subjects experiencing a neutral autobiographical recall control condition. We find, but only for those subjects with the highest comprehension of the game, that care elicits significantly higher contributions (...) than anger, with the control treatment in between. This positive influence of the care motive on unconditional giving is accounted for partly by preferences for giving and partly by beliefs concerning greater contributions by others. Anger also affects attention to own and other’s payoffs and perceptions of the game’s incentive structure. (shrink)

In this paper, a problem for utility theory - that it would have an agent who was compelled to play “Russian Roulette’ with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values of possible (...) total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of ‘risk’. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between ‘utilities’ and ‘values’. (shrink)

This paper provides evidence for the following novel insights: (1) People’s economic decisions depend on their psychological motives, which are shaped predictably by the social context. (2) In particular, the social context influences people’s other-regarding preferences, their beliefs and their perceptions. (3) The influence of the social context on psychological motives can be measured experimentally by priming two antagonistic motives—care and anger—in one player towards another by means of an observance or a violation of a fairness norm. (...) Using a mediation approach, we find that the care motive leads to higher levels of cooperation which are driven by more optimistic beliefs, a different perception of the game as well as by a shift towards more pro-social preferences. (shrink)

Machine learning-based AI algorithms lack transparency. In this article, I offer an interpretation of AI’s explainability problem and highlight its ethical saliency. I try to make the case for the legal enforcement of a strong explainability requirement: human organizations which decide to automate decision-making should be legally obliged to demonstrate the capacity to explain and justify the algorithmic decisions that have an impact on the wellbeing, rights, and opportunities of those affected by the decisions. This legal duty can be derived (...) from the demands of Rawlsian public reason. In the second part of the paper, I try to show that the argument from the limitations of human cognition fails to get AI off the hook of public reason. Against a growing trend in AI ethics, my main argument is that the analogy between human minds and artificial neural networks fails because it suffers from an atomistic bias which makes it blind to the social and institutional dimension of human reasoning processes. I suggest that developing interpretive AI algorithms is not the only possible answer to the explainability problem; social and institutional answers are also available and in many cases more trustworthy than techno-scientific ones. (shrink)

The article discusses the process of “conceptual borrowing”, according to which, when a new discipline emerges, it develops its technical vocabulary also by appropriating terms from other neighbouring disciplines. The phenomenon is likened to Carl Schmitt’s observation that modern political concepts have theological roots. The authors argue that, through extensive conceptual borrowing, AI has ended up describing computers anthropomorphically, as computational brains with psychological properties, while brain and cognitive sciences have ended up describing brains and minds computationally and informationally, (...) as biological computers. The crosswiring between the technical languages of these disciplines is not merely metaphorical but can lead to confusion, and damaging assumptions and consequences. The article ends on an optimistic note about the self-adjusting nature of technical meanings in language and the ability to leave misleading conceptual baggage behind when confronted with advancement in understanding and factual knowledge. (shrink)

Psychological observations are by now well integrated into economics, especially in the theory of finance, as can also be seen in the Nobel Prize awarded to Thaler. On the contrary, Simon’s attempt to reforge economic theory on the paradigm of bounded rationality failed. Starting from the birth of the neoclassical paradigm, we’ll describe the attempt to give it psychological foundations with a direct measurement of utility, then the axiomatic turn of the paradigm and its first anomalies. We’ll then sum up (...) the debate on rationality, taking place in the group of economists led by Simon, which brought to the rational expectations hypothesis. Finally, we’ll discuss the development of behavioral economics and its progressive acceptance in economic theory. This historical reconstruction allows us to understand the actual hard core of the neoclassical paradigm and the growing need of the paradigm for practical flexibility that determines how to choose arguments, methods and evidence that can be useful to its development, including psychological ones. (shrink)

This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem 3 provides (...) a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems. (shrink)

Several philosophers have expressed concerns with some recent uses of the term ‘cognition’. Underlying a number of these concerns are claims that cognition is only located in the brain and that no compelling case has been made to use ‘cognition’ in any way other than as a cause of behavior that is representational in nature. These concerns center on two primary misapprehensions: First, that some adherents of dynamical cognitive science think DCS implies the thesis of extended cognition and the rejection (...) of representation, and second, that cognition is mistakenly equated with behavior. We make three points in response to these claims: First, there is no thoroughly entrenched conception of cognition as distinct from behavior that is being illegitimately disregarded. Second, we present Shapiro’s exposition of dynamical systems theory as revealing a misunderstanding of the way that dynamical models are used in explanations of cognition and related phenomena. Accordingly, a proper conception of DCS’s methods facilitates an appreciation of extended cognition as a legitimate phenomenon of scientific investigation. Finally, we demonstrate that practicing cognitive scientists and psychologists are far more pluralistic in the phenomena they apply ‘cognition’ to than is suggested by some. At the heart of our disagreement with these concerned folks is that although we think it likely that some cognitive phenomena are representational, non-extended, and only in-between the ears, we also think there are good conceptual and empirical reasons to believe that many cognitive phenomena are non-representational, extended, and not confined to the brain. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the psychology (...) of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)

Scientific theories of consciousness identify its contents with the spatiotemporal structure of neural population activity. We follow up on this approach by stating and motivating Dynamical Emergence Theory, which defines the amount and structure of experience in terms of the intrinsic topology and geometry of a physical system’s collective dynamics. Specifically, we posit that distinct perceptual states correspond to coarse-grained macrostates reflecting an optimal partitioning of the system’s state space—a notion that aligns with several ideas and results from computational neuroscience (...) and cognitive psychology. We relate DET to existing work, offer predictions for empirical studies, and outline future research directions. (shrink)

The Battle of the Sexes game, which captures both coordination and conflict problems, has been applied to a wide range of situations. We show that, by reducing distributional conflict and enhancing coordination, turn taking supported by a “turn taking with independent randomizations” strategy allows players to engage in intertemporal sharing of the gain from cooperation. Using this insight, we decompose the benefit from turn taking into conflict-mitigating and coordination-enhancing components. Our analysis suggests that an equilibrium measure of the “degree (...) of intertemporal conflict” provides an intuitive way to understand the sources of welfare gain from turn taking in the repeated Battle of the Sexes game. We find that when this equilibrium measure is lower, players behave less aggressively and the welfare gain from turn taking is higher. (shrink)

In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status quo and the (...) lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence. (shrink)

This paper investigates the existence of pure strategy Nash equilibria in discontinuous and nonquasiconcave games. We introduce a new notion of continuity, called weakly continuous security, which is weaker than the most known weak notions of continuity, including the surrogate point secure of SSYM game of Carbonell-Nicolau and Mclean (Econ Theory, 2018a), the continuous security of Barelli and Meneghel (Econometrica 81:813–824, 2013), C-security of McLennan et al. (Econometrica 79:1643–1664 2011), generalized weakly transfer continuity of Nessah (Economics 47:659–662, 2011), generalized (...) better-reply security of Carmona (Econ Theory 48:1–4, 2011), Barelli and Soza (On the existence of Nash equilibria in discontinuous and qualitative games, 2009), Barelli and Meneghel (Econometrica 81:813–824, 2013), lower single deviation property of Reny (Further results on the existence of Nash equilibria in discontinuous games. University of Chicago, 2009), better-reply security of Reny (Econometrica 67:1029–1056, 1999) and the results of Prokopovych (Econ Theory 48:5–16, 2011, Econ Theory 53:383–402, 2013) and Carmona (J Econ Theory 144:1333–1340, 2009). We show that a compact, convex and weakly continuous secure Hausdorff locally convex topological vector space game has a pure strategy Nash equilibrium. Moreover, it holds in a large class of discontinuous games. (shrink)

Economics bases the choice theory on the mental experiment that introduces the choice correspondence, which associates to every set of possible actions the subset of preferred actions. If some conditions are satisfied, then the choice correspondence implies a binary preference ordering on actions and an ordinal utility function. This approach applies both to decisions under certainty and decisions under uncertainty. The preference ordering depends on the consequence of actions. Under certainty, there is only one consequence to every action, while, under (...) uncertainty, many consequences are possible, associated with the states of the world. These consequences are represented by the action itself, the states of the world, and the corresponding outcomes. Current theories consider only outcomes, but some theories include state dependent preference. Preference for the action itself is not considered, but it might be relevant. The rationality of the theory is a different question from the rationality of the decision-maker. Moreover, the rationality of the theory may imply the rationality of a preference ordering, but this does not require the rationality of the decision-maker. It is only assumed that he/she behaves according to the calculation made by the theorist. The rationality of the preference ordering requires the rationality of the preference on outcomes, of the expectations on the events, and of their connection with the preference ordering on actions. The normative relevance of rational preferences is removed by the introduction of many alternative rational theories, which justify contrasting behaviors in identical situations. (shrink)

This volume reflects the ‘philosophy of science in practice’ approach and takes a fresh look at traditional philosophical problems in the context of natural, social, and health research. Inspired by the work of Nancy Cartwright that shows how the practices and apparatuses of science help us to understand science and to build theories in the philosophy of science, this volume critically examines the philosophical concepts of evidence, laws, causation, and models and their roles in the process of scientific reasoning. (...) Each chapter is an important one in the philosophy of science, while the volume as a whole deals with these philosophical concepts in a unified way in the context of actual scientific practice. This volume thus aims to contribute to this new direction in the philosophy of science.​. (shrink)

The proposed European Artificial Intelligence Act (AIA) is the first attempt to elaborate a general legal framework for AI carried out by any major global economy. As such, the AIA is likely to become a point of reference in the larger discourse on how AI systems can (and should) be regulated. In this article, we describe and discuss the two primary enforcement mechanisms proposed in the AIA: the _conformity assessments_ that providers of high-risk AI systems are expected to conduct, and (...) the _post-market monitoring plans_ that providers must establish to document the performance of high-risk AI systems throughout their lifetimes. We argue that the AIA can be interpreted as a proposal to establish a Europe-wide ecosystem for conducting AI auditing, albeit in other words. Our analysis offers two main contributions. First, by describing the enforcement mechanisms included in the AIA in terminology borrowed from existing literature on AI auditing, we help providers of AI systems understand how they can prove adherence to the requirements set out in the AIA in practice. Second, by examining the AIA from an auditing perspective, we seek to provide transferable lessons from previous research about how to refine further the regulatory approach outlined in the AIA. We conclude by highlighting seven aspects of the AIA where amendments (or simply clarifications) would be helpful. These include, above all, the need to translate vague concepts into verifiable criteria and to strengthen the institutional safeguards concerning conformity assessments based on internal checks. (shrink)

Accountability is present in many types of social relations; for example, the accountability of elected representatives to voters is the key characteristic of representative democracy. We distinguish between two institutional mechanisms of accountability, i.e., opportunity to punish and requirement of a justification, and examine the separate and combined effects of these mechanisms on individual behavior. For this purpose, we designed a decision-making experiment where subjects engage in a three-player trust game with two senders and one responder. We ask (...) whether holding the responder accountable increases senders’ and responders’ contributions in a trust game. When restricting the analysis to the first round, the requirement of justification seems to have a positive impact on senders’ contributions. When the game is played repeatedly, the experience of previous rounds dominates the results and significant treatment effects are no longer seen. We also find that responders tend to justify their choices in terms of reciprocity, which is in line with observed behavior. Moreover, the treatment combining punishment and justification hinders justifications that appeal to pure self-interest. (shrink)

In this article, I focus on the role of computer simulations as exploratory strategies. I begin by establishing the non-theory-driven nature of simulations. This refers to their ability to characterize phenomena without relying on a predefined conceptual framework that is provided by an implemented mathematical model. Drawing on Steinle’s notion of exploratory experimentation and Gelfert’s work on exploratory models, I present three exploratory strategies for computer simulations: (1) starting points and continuation of scientific inquiry, (2) varying the parameters, and (3) (...) scientific prototyping. (shrink)

When von Neumann's and Morgenstern's Theory of Games and Economic Behavior appeared in 1944, one thought that a complete theory of strategic social behavior had appeared out of nowhere. However, game theory has, to this very day, remained a fast-growing assemblage of models which have gradually been united in a new social theory - a theory that is far from being completed even after recent advances in game theory, as evidenced by the work of the three (...) Nobel Prize winners, John F. Nash, John C. Harsanyi, and Reinhard Selten. Two of them, Harsanyi and Selten, have contributed important articles to the present volume. This book leaves no doubt that the game-theoretical models are on the right track to becoming a respectable new theory, just like the great theories of the twentieth century originated from formerly separate models which merged in the course of decades. For social scientists, the age of great discover ies is not over. The recent advances of today's game theory surpass by far the results of traditional game theory. For example, modem game theory has a new empirical and social foundation, namely, societal experiences; this has changed its methods, its "rationality. " Morgenstern (I worked together with him for four years) dreamed of an encompassing theory of social behavior. With the inclusion of the concept of evolution in mathematical form, this dream will become true. Perhaps the new foundation will even lead to a new name, "conflict theory" instead of "game theory. (shrink)

The paper first summarizes the author's decision-theoretical model of moral behavior, in order to compare the moral implications of the act-utilitarian and of the rule-utilitarian versions of utilitarian theory. This model is then applied to three voting examples. It is argued that the moral behavior of act-utilitarian individuals will have the nature of a noncooperative game, played in the extensive mode, and involving action-by-action maximization of social utility by each player. In contrast, the moral behavior of rule-utilitarian individuals (...) will have the nature of a cooperative game, played in the normal mode, and involving a firm commitment by each player to a specific moral strategy (viz. to the strategy selected by the rule-utilitarian choice criterion) — even if some individual actions prescribed by this strategy, when considered in isolation, should fail to maximize social utility. The most important advantage that rule utilitarianism as an ethical theory has over act utilitarianism lies in its ability to give full recognition to the moral and social importance of individual rights and personal obligations. It is easy to verify that action-by-action maximization of social utility, as required by act utilitarianism, would destroy these rights and obligations. In contrast, rule utilitarianism can fully recognize the moral validity of these rights and obligations precisely because of its commitment to an overall moral strategy, independent of action-by-action social-utility maximization. The paper ends with a discussion of the voter's paradox problem. The conventional theory of rational behavior cannot avoid the paradoxical conclusion that, in any large electorate, voting is always an irrational activity because one's own individual vote is extremely unlikely to make any difference to the outcome of any election. But it can be shown that, by using the principles of rule-utilitarian theory, this paradox can easily be resolved and that, in actual fact, voting, even in large electorates, may be perfectly rational action. More generally, the example of rule utilitarianism shows what an important role the concept of a rational commitment can play in the analysis of rational behavior. (shrink)

One major fault line in foundational theories of cognition is between the so-called “representational” and “non-representational” theories. Is it possible to formulate an intermediate approach for a foundational theory of cognition by defining a conception of representation that may bridge the fault line? Such an account of representation, as well as an account of correspondence semantics, is offered here. The account extends previously developed agent-based pragmatic theories of semantic information, where meaning of an information state is defined by its interface (...) role, to a theory that accommodates a notion of representation and correspondence semantics. It is argued that the account can be used to develop an intermediate approach to cognition, by showing that the major sources of tension between “representational” and “non-representational” theories may be eased. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised (...) learning methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and (...) seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions. (shrink)

In experimental economics one can confront a “don’t!”, as in “do not deceive your participants!”, as well as a “do!”, as in “incentivize choice making!”. Neither exists in experimental psychology. Further controversies exist in data collection methods, e.g., play strategy (vector) method in game experiments, and how to guarantee external and internal validity by describing experimental scenarios by field-related vignettes or by abstract, often formal, rules as it is used in decision and game theory. We emphasize that differences (...) between the experimental methodology of the two disciplines are minor rather than substantial and suggest that such differences should be resolved, as much as possible, through empirical research. Rather than focusing on familiar debates, we suggest to substitute the revealed-motive approach in experimental economics by designs whose data not only inform about choice, but also about the reasoning dynamics. (shrink)

Third-party punishment (TPP) has been shown to be an effective mechanism for maintaining human cooperation. However, it is puzzling how third-party punishment can be maintained, as punishers take on personal costs to punish defectors. Although there is evidence that punishers are preferred as partners because third-party punishment is regarded by bystanders as a costly signal of trustworthiness, other studies show that this signaling value of punishment can be severely attenuated because third-party helping is viewed as a stronger signal of trustworthiness (...) than third-party punishment. Third-party helpers donate their payoffs to victims of defection in games instead of punishing defectors as third-party punishers do. Then, under what circumstances can third-party punishment be maintained by costly signaling when helping is also present? We show that punishers are preferred over helpers by fourth-party individuals as their delegates to deter potential exploitation. This suggests that costly signaling can facilitate the maintenance of third-party punishment in partner choice with delegation interactions. (shrink)

In the spirit of Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944), we introduce a notion of network stability. We study the structure of stable economic networks and their associated stable payoff allocations by analyzing the conditions under which complete networks and star networks (both with desirable property of inclusiveness) are stable. We also address conditions for existence and uniqueness of stable set of networks.

There is growing evidence to support the claim that we react differently to robots than we do to other objects. In particular, we react differently to robots with which we have some form of social interaction. In this paper I critically assess the claim that, due to our tendency to become emotionally attached to social robots, permitting their harm may be damaging for society and as such we should consider introducing legislation to grant social robots rights and (...) protect them from harm. I conclude that there is little evidence to support this claim and that legislation in this area would restrict progress in areas of social care where social robots are a potentially valuable resource. (shrink)

Escalation of commitment causes people to continue a failing course of action. We study the role of construal level in such escalation of commitment. Consistent with the widely held view of construal level as a primed effect, we employed a commonly used prime for manipulating this construct in a laboratory experiment. Our findings revealed that the prime failed to produce statistically significant differences in construal level, which was measured using the Behavior Identification Form. Furthermore, there was no effect of the (...) prime on escalation of commitment, or on constructs that have previously been linked to construal level such as the perceived importance of feasibility considerations relative to desirability considerations, and the number of pros and cons that subjects can think of.Interestingly, however, subjects’ actual construal level scores on the BIF were found to significantly affect escalation. Specifically, our findings show that people with a low construal level are less willing to continue a failing project. This relation is mediated by the perceived importance of the feasibility of the project relative to its desirability. For people with a low construal level, the perceived importance of feasibility relative to desirability is higher, which in turn makes escalation of commitment less likely.Our findings are consistent with prior research suggesting that priming construal level may not always be effective. Thus, while construal level has typically been regarded as a state-like variable that can be primed, in this study, we show that construal level may also be considered as a trait. (shrink)

Many critics of dual-process models have mistaken long lists of descriptive terms in the literature for a full-blown theory of necessarily co-occurring properties. These critiques have distracted attention from the cumulative progress being made in identifying the much smaller set of properties that truly do define Type 1 and Type 2 processing. Our view of the literature is that autonomous processing is the defining feature of Type 1 processing. Even more convincing is the converging evidence that the key feature of (...) Type 2 processing is the ability to sustain the decoupling of secondary representations. The latter is a foundational cognitive requirement for hypothetical thinking. (shrink)

We propose a two-step guessing game to measure the depth of thinking. We apply this method to the P beauty contest game. Using our method, we find that 81% of subjects do not make choice following best response reasoning while the classical method would suggest only 12%. The result suggests that the classical method has the fundamental problem that it cannot distinguish if a submitted number is due to best response reasoning or not. It also suggests that traditional (...) level k analysis falsely attributes some sophistication to random players, and that the degree of false attribution is large. Our procedure provides an alternative way to identify whether the individual has best response reasoning which is essential for any positive level of depth of thinking and differentiates between the depth of thinking and random choice, and hence provides a very different conclusion, which is suggestive of limitations of the classical method. (shrink)

We propose a solution concept for games that are played among players with present-biased preferences that are possibly naive about their own, or about their opponent’s future time inconsistency. Our perception-perfect outcome essentially requires each player to take an action consistent with the subgame perfect equilibrium, given her perceptions concerning future types, and under the assumption that other present and future players have the same perceptions. Applications include a common pool problem and Rubinstein bargaining. When players are naive about their (...) own time inconsistency and sophisticated about their opponent’s, the common pool problem is exacerbated, and Rubinstein bargaining breaks down completely. (shrink)

There is a great deal of literature on matching, theoretical, and empirical, concerning stable assignments and mechanisms that achieve them. The starting point of this study is an interesting question about assignment procedures: given a situation where some agents (the senior workers) on one side have a priority status, which changes the classical theory. The core of game may not be stable. We prove the existence of a quasi stable constrained core. This constrained core may not be a lattice (...) but it is a finite and disjoint union of complete lattices that check the properties of the core’s classical assignment game. We study the manipulability questions that derive. (shrink)

In two experiments, participants had to choose between a sure and a risky option. The sure option was presented either in a gain or a loss frame. Need was defined as a minimum score the participants had to reach. Moreover, choices were made under two different time constraints and with three different levels of induced need to be reached within a fixed number of trials. The two experiments differed with respect to the specific amounts to win and the need levels. (...) The $$2 \times 2 \times 3$$2×2×3 design was a within-subject design. Data were evaluated on an overall and on a group level, the latter based on participants’ stated risk preference and on revealed preferences using cluster analysis across subjects. Overall, the results showed riskier behavior when the choice options were presented as losses as compared to gains and when the induced need was highest. Time limits enhanced the framing effect. (shrink)

The principle of differential marginality (Casajus in Theory and Decis 71(2):163-–174) for cooperative games is a very appealing property that requires equal productivity differentials to translate into equal payoff differentials. In this paper we apply this property to axiomatic characterizations of values. We show that differential marginality implies additivity and symmetry under certain conditions. Based on this result, we propose new characterizations of the equal division and the equal surplus division values. Finally, we characterize two classes of convex combinations of (...) values, i.e., α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-egalitarian Shapley values and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-equal surplus division values, by employing differential marginality and establishing the uniqueness of these values on inessential games. (shrink)

While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still approximating (...) level-k, QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling. (shrink)

Optimization is about finding the best available object with respect to an objective function. Mathematics and quantitative sciences have been highly successful in formulating problems as optimization problems, and constructing clever processes that find optimal objects from sets of objects. As computers have become readily available to most people, optimization and optimized processes play a very broad role in societies. It is not obvious, however, that the optimization processes that work for mathematics and abstract objects should be readily applied (...) to complex and open social systems. In this paper we set forth a framework to understand when optimization is limited, particularly for complex and open social systems. (shrink)

Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent’s priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on (...) the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging and Jeffrey conditioning is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed. (shrink)

It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker’s preferences satisfy quasisupermodularity, single-crossing, and a nondecreasing log-differences property, the worst-case relative performance index can be represented as the lower envelope of two extremal performance ratios. The latter is used to characterize the agent’s optimal robust decision, which has (...) implications both computationally and for obtaining closed-form solutions. We illustrate our results in an application which compares the performance of relative robustness to solutions that optimize worst-case payoffs, maximum absolute regret, and expected payoffs under a Laplacian prior. (shrink)

This paper considers a one-stage Cournot duopoly of R&D. We characterize the Nash equilibrium of the one-stage game and provide a comparison with the two-stage version of the same Cournot model of R&D/product market competition. We look at R&D expenditures, profits, output and welfare. Under perfect symmetry, the one-stage model always leads to higher profits when the spillover parameter is not equal to 1/2. Moreover, the one-stage model implies more R&D expenditure and higher welfare if and only if the (...) spillover parameter is greater than 1/2. The insights are robust to an n -firm generalization, but the differences between the one-stage game and the two-stage game disappear as the market becomes perfectly competitive. (shrink)

The problem of algorithmic fairness is typically framed as the problem of finding a unique formal criterion that guarantees that a given algorithmic decision-making procedure is morally permissible. In this paper, I argue that this is conceptually misguided and that we should replace the problem with two sub-problems. If we examine how most state-of-the-art machine learning systems work, we notice that there are two distinct stages in the decision-making process. First, a prediction of a relevant property is made. Secondly, a (...) decision is taken based (at least partly) on this prediction. These two stages have different aims: the prediction is aimed at accuracy, while the decision is aimed at allocating a given good in a way that maximizes some context-relative utility measure. Correspondingly, two different fairness issues can arise. First, predictions could be biased in discriminatory ways. This means that the predictions contain systematic errors for a specific group of individuals. Secondly, the system’s decisions could result in an allocation of goods that is in tension with the principles of distributive justice. These two fairness issues are distinct problems that require different types of solutions. I here provide a formal framework to address both issues and argue that this way of conceptualizing them resolves some of the paradoxes present in the discussion of algorithmic fairness. (shrink)

We introduce possibilistic beliefs into strategic games, describing a player’s belief about his opponents’ strategies as the set of their strategies he regards as possible. We formulate possibilistic strategic games where each player has preferences over his own strategies conditional on his possibilistic belief about his opponents’ strategies. We define several solution concepts for possibilistic strategic games such as (strict) equilibria, rationalizable sets, iterated elimination of never-best responses, and iterated elimination of strictly dominated strategies, and we study their properties and (...) relationships. We develop a class of possibilistic strategic games called possibilistic supermodular games to relate supermodular games to possibilistic strategic games. Lastly, we discuss a direction of extending our possibilistic framework to games with incomplete information. (shrink)

In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all those (...) convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Epistemic Logic. 'Formal epistemology' is a term coined in the late 1990s for a new constellation of interests in philosophy, the origins of which are found in earlier works of epistemologists, philosophers of science and logicians. It addresses a growing (...) agenda of problems concerning knowledge, belief, certainty, rationality, deliberation, decision, strategy, action and agent interaction - and it does so using methods from logic, probability, computability, decision and game theory. The volume also includes a thorough index and suggestions for further reading, and thus offers a complete teaching and research package for students as well as research scholars of formal epistemology, philosophy, logic, computer science, theoretical economics and cognitive psychology. (shrink)

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us make (...) the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice. (shrink)