von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc

Expert Financial Advice Neurobiologically “Offloads” Financial Decision-Making under Risk

BACKGROUND: Financial advice from experts is commonly sought during times of uncertainty. While the field of neuroeconomics has made considerable progress in understanding the neurobiological basis of risky decision-making, the neural mechanisms through which external information, such as advice, is integrated during decision-making are poorly understood. In the current experiment, we investigated the neurobiological basis of the influence of expert advice on financial decisions under risk. METHODOLOGY/PRINCIPAL FINDINGS: While undergoing fMRI scanning, participants made a series of financial choices between a certain payment and a lottery. Choices were made in two conditions: 1) advice from a financial expert about which choice to make was displayed (MES condition); and 2) no advice was displayed (NOM condition). Behavioral results showed a significant effect of expert advice. Specifically, probability weighting functions changed in the direction of the expert's advice. This was paralleled by neural activation patterns. Brain activations showing significant correlations with valuation (parametric modulation by value of lottery/sure win) were obtained in the absence of the expert's advice (NOM) in intraparietal sulcus, posterior cingulate cortex, cuneus, precuneus, inferior frontal gyrus and middle temporal gyrus. Notably, no significant correlations with value were obtained in the presence of advice (MES). These findings were corroborated by region of interest analyses. Neural equivalents of probability weighting functions showed significant flattening in the MES compared to the NOM condition in regions associated with probability weighting, including anterior cingulate cortex, dorsolateral PFC, thalamus, medial occipital gyrus and anterior insula. Finally, during the MES condition, significant activations in temporoparietal junction and medial PFC were obtained. CONCLUSIONS/SIGNIFICANCE: These results support the hypothesis that one effect of expert advice is to "offload" the calculation of value of decision options from the individual's brain

Salience in decision-making: a neuroeconomic analysis

Attention and the closely related concept of salience play an important role in the complex process of human decision-making. In 2012, Bordalo et al. (2012a) proposed a theory on human decision-making that is based on salience. They suggest that salience differences within a decision problem may explain many decision biases. Concerning decisions under risk, Bordalo and colleagues developed a formula to calculate salience differences that are shaped by bottom-up processes. These salience differences have been experimentally investigated. Reaction times in a dot-probe task served as indicator of attentional biases. Data revealed a significant salience effect after a lottery exposure duration of 150 ms. This supports the salience concept proposed by Bordalo et al. (2012a) and suggests an early attentional orienting towards salient payoffs. In order to further differentiate attentional processes involved in the salience effect EEG has been recorded. Different ERP-components may indicate attentional biases at different stages of attentional processing and give a hint at more detailed reasons behind the salience effect. All investigated components, namely, P1, N1, P3a and P3b, showed no significant salience differences. Part III presents a further experiment that was devoted to nudges. These interventions often work by altering the salience within a decision problem or by directing the attention to the decision task itself. Since these interventions influence decisions at least partly on an unconscious level, nudges are subject to criticism. The experiment aimed at investigating the effect of transparent information accompanying the nudges on their efficacy. In line with previous research adding information on the nudge itself, on its purpose and the combination of both had no significant effect on the efficacy of the nudge, even though this additional information again alters salience ratios within the decision problem

A Bayesian Approach to Recurrence in Neural Networks

We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation; this leads to a Bayesian recurrent unit with a prescribed feedback formulation. We show that introduction of a context indicator leads to a variable feedback that is similar to the forget mechanism in conventional recurrent units. A similar approach leads to a probabilistic input gate. The Bayesian formulation leads naturally to the two pass algorithm of the Kalman smoother or forward-backward algorithm, meaning that inference naturally depends upon future inputs as well as past ones. Experiments on speech recognition confirm that the resulting architecture can perform as well as a bidirectional recurrent network with the same number of parameters as a unidirectional one. Further, when configured explicitly bidirectionally, the architecture can exceed the performance of a conventional bidirectional recurrence

Modeling Risky Choices in Unknown Environments

Decision-theoretic models explain human behavior in choice problems involving uncertainty, in terms of individual tendencies such as risk aversion. However, many classical models of risk require knowing the distribution of possible outcomes (rewards) for all options, limiting their applicability outside of controlled experiments. We study the task of learning such models in contexts where the modeler does not know the distributions but instead can only observe the choices and their outcomes for a user familiar with the decision problems, for example a skilled player playing a digital game. We propose a framework combining two separate components, one for modeling the unknown decision-making environment and another for the risk behavior. By using environment models capable of learning distributions we are able to infer classical models of decision-making under risk from observations of the user's choices and outcomes alone, and we also demonstrate alternative models for predictive purposes. We validate the approach on artificial data and demonstrate a practical use case in modeling risk attitudes of professional esports teams.Peer reviewe

Perceptual Capacities

Despite their importance in the history of philosophy and in particular in the work of Aristotle and Kant, mental capacities have been neglected in recent philosophical work. By contrast, the notion of a capacity is deeply entrenched in psychology and the brain sciences. Driven by the idea that a cognitive system has the capacity it does in virtue of its internal components and their organization, it is standard to appeal to capacities in cognitive psychology. The main benefit of invoking capacities in an account of the mind is that it allows for an elegant counterfactual analysis of mental states: it allows us to analyze mental states on three distinct yet interrelated levels. A first level of analysis pertains to the function of mental capacities. A second level of analysis pertains to the mental capacities employed, irrespective of the context in which they are employed. A third level of analysis pertains to the mental capacities employed, taking into account the context in which they are employed. This paper develops an account of perceptual capacities. This account involves an analysis of their function, their individuation and possession conditions, the relation between perceptual capacities and their employment, as well as their informational and neural base conditions

Machine Learning? In MY Election? It\u27s More Likely Than You Think: Voting Rules via Neural Networks

Impossibility theorems in social choice have represented a barrier in the creation of universal, non-dictatorial, and non-manipulable voting rules, highlighting a key trade-off between social welfare and strategy-proofness. However, a social planner may be concerned with only a particular preference distribution and wonder whether it is possible to better optimize this trade-off. To address this problem, we propose an end-to-end, machine learning-based framework that creates voting rules according to a social planner\u27s constraints, for any type of preference distribution. After experimenting with rank-based social choice rules, we find that automatically-designed rules are less susceptible to manipulation than most existing rules, while still attaining high social welfare

Selected Topics of Social Physics: Equilibrium Systems

The present review is based on the lectures that the author had been giving during several years at the Swiss Federal Institute of Technology in Zurich (ETH Zurich). Being bounded by lecture frames, the selection of the material, by necessity, is limited and is motivated by the author's research interests. The paper gives an introduction to the physics of social systems, providing the main definitions and notions used in the modeling of these systems. The behavior of social systems is illustrated by several simple typical models. The present part considers equilibrium systems. Nonequilibrium systems will be presented in the second part of the lectures. The style of the paper combines the features of a tutorial and a survey, which, from one side, makes it easy to read for nonspecialists aiming at grasping the basics of social physics, and from the other side, describes several rather recent original models containing new ideas that could be of interest to experienced researchers in the field.Comment: Revie