Axioms Of Rationality Research Articles

Von Neumann–Morgenstern Axioms of Rationality and Inequalities in Analysis

Von Neumann–Morgenstern Axioms of Rationality and Inequalities in Analysis

Step-by-step negotiations and the Nash bargaining solution: Efficiency-free characterizations

Real-world bargainings often proceed step-by-step: the agents make intermediate agreements today and continue to negotiate tomorrow to reach a final agreement. We consider two natural properties of the bargaining solutions in such step-by-step negotiations and show that the Nash solution is the only solution that satisfies either of them, a very weak axiom of individual rationality, and Nash’s axioms except for Pareto optimality.

Collective or individual rationality in the Nash bargaining solution: efficiency-free characterizations

AbstractIn the classical bargaining problem, we propose a very mild axiom of individual rationality, which we call possibility of utility gain. This requires that for at least one bargaining problem, there exists at least one player who reaches a higher utility level than their disagreement utility. This paper shows that the Nash solution (Nash in Econometrica 18(2):155–162, 1950) is characterized by possibility of utility gain and continuity with respect to feasible sets together with Nash’s axioms except weak Pareto optimality. We also show that in Nash’s theorem, weak Pareto optimality can be replaced by conflict-freeness (introduced by Rachmilevitch in Math Soc Sci 76(C):107–109, 2015). This demands that when the agreement most preferred by all players is feasible, this should be chosen. Furthermore, we provide alternative and unified proofs for other efficiency-free characterizations of the Nash solution. This clarifies the role of each axiom in the related results.

On rational choice from lists of sets

We analyze the rationality of a Decision Maker (DM) who chooses from lists of sets of alternatives. We propose and study four general classes of choice mechanism, representing the DM’s choice-behavior, and a new axiom, that we call No-Regret (NR). We show that the NR axiom, suggesting that alternatives disregarded as of no interest for the DM be ignored, is a rationality axiom that encompasses some compelling properties of the classical choice model and extends them to the proposed general framework of choice from lists of sets of alternatives.

Evaluating deep generative models on cognitive tasks: a case study

We present a detailed case study evaluating selective cognitive abilities (decision making and spatial reasoning) of two recently released generative transformer models, ChatGPT and DALL-E 2. Input prompts were constructed following neutral a priori guidelines, rather than adversarial intent. Post hoc qualitative analysis of the outputs shows that DALL-E 2 is able to generate at least one correct image for each spatial reasoning prompt, but most images generated are incorrect, even though the model seems to have a clear understanding of the objects mentioned in the prompt. Similarly, in evaluating ChatGPT on the rationality axioms developed under the classical Von Neumann-Morgenstern utility theorem, we find that, although it demonstrates some level of rational decision-making, many of its decisions violate at least one of the axioms even under reasonable constructions of preferences, bets, and decision-making prompts. ChatGPT’s outputs on such problems generally tended to be unpredictable: even as it made irrational decisions (or employed an incorrect reasoning process) for some simpler decision-making problems, it was able to draw correct conclusions for more complex bet structures. We briefly comment on the nuances and challenges involved in scaling up such a ‘cognitive’ evaluation or conducting it with a closed set of answer keys (‘ground truth’), given that these models are inherently generative and open-ended in responding to prompts.

Nonlinear desirability as a linear classification problem

This paper presents an interpretation as classification problem for standard desirability and other instances of nonlinear desirability (convex coherence and positive additive coherence). In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject respects these axioms on the basis of a finite set of acceptable and a finite set of rejectable gambles can be reformulated as a binary classification problem where the family of classifiers used changes with the axioms considered. Moreover, by borrowing ideas from machine learning, we show the possibility of defining a feature mapping, which allows us to reformulate the above nonlinear classification problems as linear ones in higher-dimensional spaces. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to provide a practical tool to check the rationality of an agent.

Complexity in insurance selection: Cross-classified multilevel analysis of experimental data

This paper uses laboratory experiments to test the predictions of expected utility theory applied to the context of coverage selection and the effects of complexity on the quality of decision making. Participants choose from menus of stylized insurance plans that vary across three measures of complexity. In each menu one insurance plan stochastically dominates the other options. Out of the three complexity measures, Coverage Similarity and State Complexity, have a statistically significant negative effect on participants’ ability to choose efficiently. Individuals’ decisions can be predicted by the expected utility paradigm only to a certain extent. When the number of payoff relevant states associated with an insurance plan increases, participants violate rationality axioms by selecting first order dominated plans. Similarly, the rate of dominated choices increases when the difference in the level of coverage between plans in the same choice menu is low.

The Role of the Axiom of Islamic Rationality in the Decision to Purchase halal-labeled Cosmetics (Study on Students of Mamba'ul Hikam Islamic Boarding School)

Abstract. This study aims to analyze the significant influence between the rationality of Islamic consumption and the decision to purchase cosmetics labeled halal on consumers, especially Islamic boarding school students Mambaul Hikam. This research uses descriptive quantitative methods. The population used was all female students, with a total sample of 40 respondents taken using purposive sampling technique. Data were analysis performed through regression analysis using SPSS version 22. Results of regression analysis in this study is a positive significant effect halal label to the rationality of Islamic consumer on purchasing decisions purchase halal cosmetics.
 Keywords: Islamic Consumption Rationality; Cosmetics; Halal Label; Purchase Decision

Full farsighted rationality

An abstract game consists of a set of states, preferences over states, and an effectivity correspondence specifying what coalitions are allowed to replace one state by another one. Agents are called farsighted if, when deciding whether to support a coalition's move, they compare the status quo to the long term outcome following their deviation. Yet, this definition of farsightedness ignores a coalition's option to remain at the status quo allowing another coalition to move: agents are not fully farsighted. Therefore, we introduce extended expectation functions, which assign to each state a list of pairs consisting of a state and a coalition that is expected to move from the former to the latter. They endow agents with an expectation about what any deviation vis-a-vis maintaining the status quo entails. We impose three rationality axioms and provide a characterization of extended expectation functions that satisfy our axioms in terms of coalition behavior.

Dynamic decision making under ambiguity: An experimental investigation

Neoclassical economic theory assumes that whenever agents tackle dynamic decisions under ambiguity, preferences are represented by the Subjective Expected Utility (SEU) model and prior beliefs are updated according to Bayes rule, upon the arrival of partial information. Nevertheless, when one considers non-neutral ambiguity attitudes, either the axiom of dynamic consistency or of consequentialism should be relaxed. Using data from an economic experiment on dynamic choice under ambiguity, we study which of the two rationality axioms people violate, along with the question of whether this violation is part of a conscious planning strategy or not. The combination of the two, allows us to classify non-SEU subjects to three behavioural types: resolute, naïve and sophisticated. The hypothesis of Bayesian updating is rejected for more than half of the experimental population. For ambiguity non-neutral subjects, we find that the majority are sophisticated, a few are naïve and very few are resolute.

Decision-making nei Pazienti sottoposti a Trattamento Dialitico

Introduction: Before becoming an object of cognitive science, the topic of decision-making has questioned thinkers from all ages and disciplines: philosophers, mathematicians, logicians, economists and more. More recent studies have highlighted the neuroscientific basis of decision-making and the complex cognitive strategies involved in economic and social decisions, such as gambling. Aims: This paper aims to focus attention on the role of stress in influencing individuals’ decision-making skills, especially in situations of risk and uncertainty. In particular, if on the one hand it is intended to investigate the relationship between stress and decisions of dialysis patients, on the other hand it is intended to highlight the so-called disjunction effect according to which decision-making situations with an uncertain outcome may lead to violate the axioms of neoclassical rationality. Method: Starting from an analysis of the literature on decision making, attention will be focused on stress factors that influence the decision making behaviour and cognitive strategies of the dialysis-treated patients. Conclusion: The review highlights the need to further investigate the disjunction effect and opens the way to the possibility of conducting experimental research to verify the presence of this effect in the specific case of these patients. Keywords: decision-making; disjunction effect; caregivers; dialysis patients

What are the appropriate axioms of rationality for reasoning under uncertainty with resource-constrained systems?

When constrained by limited resources, how do we choose axioms of rationality? The target article relies on Bayesian reasoning that encounter serious tractability problems. We propose another axiomatic foundation: quantum probability theory, which provides for less complex and more comprehensive descriptions. More generally, defining rationality in terms of axiomatic systems misses a key issue: rationality must be defined by humans facing vague information.

The Strong Consistency of Neutral and Monotonic Binary Social Decision Rules

The purpose of this paper is to investigate the strong consistency of neutral and monotonic binary social decision rules. Individuals are assumed to satisfy von Neumann-Morgenstern axioms of individual rationality. The main result of the paper shows that there does not exist any neutral and monotonic non-null non-dictatorial binary social decision rule which is strongly consistent. The relationship between restricted preferences and the existence of strong equilibria is also investigated. It is shown that for every non-dictatorial social decision function satisfying the conditions of independence of irrelevant alternatives, neutrality, monotonicity and weak Pareto-criterion there exists a profile of individual orderings satisfying value-restriction corresponding to which there is no strong equilibrium.

Range Utility Theory for Uncertain Cash-flows

We provide the behavioral foundations of a preference model for risky payoff streams, a broad domain having lotteries, income streams under certainty, and repeated lotteries as special cases. For an individual who cares not only about total profit at the end, but also about partial profits, a standard set of rational axioms yield Bell's (1974) discounted incremental utility model. The model captures the intuition of time as inherently uncertain. To this bedrock, we add the notion that preferences are affected by range effects. The result is a behavioral model with a broad domain and consistent with a plethora of phenomena (bias towards short payback periods, the four-fold patterns for risk and time, preference reversals for risk and time, temporal patterns of decreasing or increasing impatience, and magnitude effects).

Stochastic choice over menus

Models of choice over menus aim at capturing the effect of some behavioral or non-standard element of decision-making on the behavior of a single decision-maker. These models are usually compared with the standard model of choice over menus, in which the decision-maker chooses a menu whose best item is better than that of all other available ones. However, in many empirical settings such as experimental studies, choice data come from a population of decision-makers with possibly heterogeneous attitudes and tastes. This heterogeneity can make the observed choices over menus stochastic. This fact calls for a stochastic characterization of models of choice over menus to be able to better compare and contrast different models empirically. In this paper, I do this task for the standard model, which would be an extension of the random utility model to the realm of choice over menus. In particular, I provide the necessary and sufficient conditions, i.e., axioms on (stochastic) choice data over menus for it to be consistent with a population of decision-makers each of whom behaves according to the standard model. The axioms that characterize the model are the axiom of revealed stochastic preferences over singletons and three rationality axioms.

Bounded rationality in C. elegans is explained by circuit-specific normalization in chemosensory pathways

Rational choice theory assumes optimality in decision-making. Violations of a basic axiom of economic rationality known as “Independence of Irrelevant Alternatives” (IIA) have been demonstrated in both humans and animals and could stem from common neuronal constraints. Here we develop tests for IIA in the nematode Caenorhabditis elegans, an animal with only 302 neurons, using olfactory chemotaxis assays. We find that in most cases C. elegans make rational decisions. However, by probing multiple neuronal architectures using various choice sets, we show that violations of rationality arise when the circuit of olfactory sensory neurons is asymmetric. We further show that genetic manipulations of the asymmetry between the AWC neurons can make the worm irrational. Last, a context-dependent normalization-based model of value coding and gain control explains how particular neuronal constraints on information coding give rise to irrationality. Thus, we demonstrate that bounded rationality could arise due to basic neuronal constraints.

Context dependent process heuristics and choice analysis – A note on two interacting themes linked to behavioural realism

This note is written to remind us of the recognition of behavioural realism in the economic literature over 60 years ago, which seems to have been given limited recognition in the formal axiomatic development of economic theories commonly associated with the application of discrete choice models, especially where the interest is on obtaining welfare measures such as willingness to pay estimates of specific attributes for use in cost-benefit analysis. We need to be reminded from time to time of the importance of context dependency in defining a choice problem and the value that behavioural realism can add despite risks of violating often some axioms of economic rationality and utility maximisation.

Dynamic Random Utility

We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process ( U t ) of utilities. We show first that even when ( U t ) is arbitrary, dynamic random utility imposes new testable across‐period restrictions on behavior, over and above period‐by‐period analogs of the static random utility axioms. An important feature of dynamic random utility is that behavior may appear history‐dependent, because period‐ t choices reveal information about U t , which may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that imposing natural Bayesian rationality axioms restricts the form of randomness that ( U t ) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allow us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model.

Rationalism in International Relations: Concepts, Theoretical Limits and Criticism

The present paper analyzes the presence of the axiom of the rationality of the political actors in theories of International Relations and traces considerations about the concept of rationality as a whole, its theoretical limits and the main criticisms about it. Aiming to overcome the absence of an in-depth conceptualization for the idea of rationality, the paper base itself on the literature of rational choice theory of Political Science to define the concept in question. It questions the validity of considering the states as rational actors and the limits of explanation offered by the axiom of rationality, addressing the criticisms originated from the constructivist current of International Relations. It concludes that considering states as rational actors is a valid theoretical simplification in cases where subnational actors with decision-making power behave as a cohesive unit and argues that rationalist theories and approaches such as constructivism are potentially reconcilable, considering that they are two analytical lenses whose nature is more complementary than contradictory.

Patented intelligence: Cloning human decision models for Industry 4.0

Industry 4.0 is a trend related to smart factories, which are cyber-physical spaces populated and controlled by the collective intelligence for the autonomous and highly flexible manufacturing purposes. Artificial Intelligence (AI) embedded into various planning, production, and management processes in Industry 4.0 must take the initiative and responsibility for making necessary real-time decisions in many cases. In this paper, we suggest the Pi-Mind technology as a compromise between completely human-expert-driven decision-making and AI-driven decision-making. Pi-Mind enables capturing, cloning and patenting essential parameters of the decision models from a particular human expert making these models transparent, proactive and capable of autonomic and fast decision-making simultaneously in many places. The technology facilitates the human impact (due to ubiquitous presence) in smart manufacturing processes and enables human-AI shared responsibility for the consequences of the decisions made. It also benefits from capturing and utilization of the traditionally human creative cognitive capabilities (sometimes intuitive and emotional), which in many cases outperform the rational decision-making. Pi-Mind technology is a set of models, techniques, and tools built on principles of value-based biased decision-making and creative cognitive computing to augment the axioms of decision rationality in industry.