Beliefs in Decision-Making Cascades

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.Comment: final version, to appear in IEEE Transactions on Signal Processin

Beliefs and expertise in sequential decision making

This work explores a sequential decision making problem with agents having diverse expertise and mismatched beliefs. We consider an N-agent sequential binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on previous agents’ decisions. In addition, the agents have their own beliefs instead of the true prior, and have varying expertise in terms of the noise variance in the private signal. We focus on the risk of the last-acting agent, where precedent agents are selfish. Thus, we call this advisor(s)-advisee sequential decision making. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The impact of diverse noise levels (which means diverse expertise levels) in the two-agent case is also considered and the analytical properties of the optimal belief curves are given. These curves, for certain cases, resemble probability weighting functions from cumulative prospect theory, and so we also discuss the choice of Prelec weighting functions as an approximation for the optimal beliefs, and the possible psychophysical optimality of human beliefs. Next, we consider an advisor selection problem where in the advisee of a certain belief chooses an advisor from a set of candidates with varying beliefs. We characterize the decision region for choosing such an advisor and argue that an advisee with beliefs varying from the true prior often ends up selecting a suboptimal advisor, indicating the need for a social planner. We close with a discussion on the implications of the study toward designing artificial intelligence systems for augmenting human intelligence.https://arxiv.org/abs/1812.04419First author draf

An information-theoretic approach to the gravitational-wave burst detection problem

The observational era of gravitational-wave astronomy began in the Fall of 2015 with the detection of GW150914. One potential type of detectable gravitational wave is short-duration gravitational-wave bursts, whose waveforms can be difficult to predict. We present the framework for a new detection algorithm for such burst events -- \textit{oLIB} -- that can be used in low-latency to identify gravitational-wave transients independently of other search algorithms. This algorithm consists of 1) an excess-power event generator based on the Q-transform -- \textit{Omicron} --, 2) coincidence of these events across a detector network, and 3) an analysis of the coincident events using a Markov chain Monte Carlo Bayesian evidence calculator -- \textit{LALInferenceBurst}. These steps compress the full data streams into a set of Bayes factors for each event; through this process, we use elements from information theory to minimize the amount of information regarding the signal-versus-noise hypothesis that is lost. We optimally extract this information using a likelihood-ratio test to estimate a detection significance for each event. Using representative archival LIGO data, we show that the algorithm can detect gravitational-wave burst events of astrophysical strength in realistic instrumental noise across different burst waveform morphologies. We also demonstrate that the combination of Bayes factors by means of a likelihood-ratio test can improve the detection efficiency of a gravitational-wave burst search. Finally, we show that oLIB's performance is robust against the choice of gravitational-wave populations used to model the likelihood-ratio test likelihoods

Ordering effects and strategic response in discrete choice experiments

This study explores ordering effects and response strategies in repeated binary discrete choice experiments (DCE). Mechanism design theory and empirical evidence suggest that repeated choice tasks per respondent introduce strategic behavior. We find evidence that the order in which choice sets are presented to respondents may provide strategic opportunities that affect choice decisions (‘strategic response’). The findings propose that the ‘strategic response’ does not follow strong cost-minimization but other strategies such as weak cost-minimization or good deal/ bad deal heuristics. Evidence further suggests that participants, as they answer more choice questions, not only make more accurate choices (‘institutional learning’) but may also become increasingly aware of and learn to take advantage of the order in which choice sets are presented to them (‘strategic learning’).discrete choice experiments, incentive compatibility, mixed logit models, ordering effects, repeated binary choice task, response strategies, Environmental Economics and Policy,

Augmented Human Machine Intelligence for Distributed Inference

With the advent of the internet of things (IoT) era and the extensive deployment of smart devices and wireless sensor networks (WSNs), interactions of humans and machine data are everywhere. In numerous applications, humans are essential parts in the decision making process, where they may either serve as information sources or act as the final decision makers. For various tasks including detection and classification of targets, detection of outliers, generation of surveillance patterns and interactions between entities, seamless integration of the human and the machine expertise is required where they simultaneously work within the same modeling environment to understand and solve problems. Efficient fusion of information from both human and sensor sources is expected to improve system performance and enhance situational awareness. Such human-machine inference networks seek to build an interactive human-machine symbiosis by merging the best of the human with the best of the machine and to achieve higher performance than either humans or machines by themselves. In this dissertation, we consider that people often have a number of biases and rely on heuristics when exposed to different kinds of uncertainties, e.g., limited information versus unreliable information. We develop novel theoretical frameworks for collaborative decision making in complex environments when the observers may include both humans and physics-based sensors. We address fundamental concerns such as uncertainties, cognitive biases in human decision making and derive human decision rules in binary decision making. We model the decision-making by generic humans working in complex networked environments that feature uncertainties, and develop new approaches and frameworks facilitating collaborative human decision making and cognitive multi-modal fusion. The first part of this dissertation exploits the behavioral economics concept Prospect Theory to study the behavior of human binary decision making under cognitive biases. Several decision making systems involving humans\u27 participation are discussed, and we show the impact of human cognitive biases on the decision making performance. We analyze how heterogeneity could affect the performance of collaborative human decision making in the presence of complex correlation relationships among the behavior of humans and design the human selection strategy at the population level. Next, we employ Prospect Theory to model the rationality of humans and accurately characterize their behaviors in answering binary questions. We design a weighted majority voting rule to solve classification problems via crowdsourcing while considering that the crowd may include some spammers. We also propose a novel sequential task ordering algorithm to improve system performance for classification in crowdsourcing composed of unreliable human workers. In the second part of the dissertation, we study the behavior of cognitive memory limited humans in binary decision making and develop efficient approaches to help memory constrained humans make better decisions. We show that the order in which information is presented to the humans impacts their decision making performance. Next, we consider the selfish behavior of humans and construct a unified incentive mechanism for IoT based inference systems while addressing the selfish concerns of the participants. We derive the optimal amount of energy that a selfish sensor involved in the signal detection task must spend in order to maximize a certain utility function, in the presence of buyers who value the result of signal detection carried out by the sensor. Finally, we design a human-machine collaboration framework that blends both machine observations and human expertise to solve binary hypothesis testing problems semi-autonomously. In networks featuring human-machine teaming/collaboration, it is critical to coordinate and synthesize the operations of the humans and machines (e.g., robots and physical sensors). Machine measurements affect human behaviors, actions, and decisions. Human behavior defines the optimal decision-making algorithm for human-machine networks. In today\u27s era of artificial intelligence, we not only aim to exploit augmented human-machine intelligence to ensure accurate decision making; but also expand intelligent systems so as to assist and improve such intelligence

Probability Weighting as Evolutionary Second-best

The economic concept of the second-best involves the idea that multiple simultaneous deviations from a hypothetical first-best optimum may be optimal once the first-best itself can no longer be achieved, since one distortion may partially compensate for another. Within an evolutionary framework, we translate this concept to behavior under uncertainty. We argue that the two main components of prospect theory, the value function and the probability weighting function, are complements in the second-best sense. Previous work has shown that an adaptive S-shaped value function may be evolutionary optimal if decision-making is subject to cognitive or perceptive constraints. We show that distortions in the way probabilities are perceived can further enhance fitness. The second-best optimum involves overweighting of small and underweighting of large probabilities. Behavior as described by prospect theory might therefore be evolution's second-best solution to the fitness maximization problem. We discuss under which circumstance our model makes empirically testable predictions about the relation between individuals' value and probability weighting functions.Probability Weighting, Prospect Theory, Evolution of Preferences

Decisions under Risk, Uncertainty and Ambiguity: Theory and Experiments

I combine theory, experiments and econometrics to undertake the task of disentangling the subtleties and implications of the distinction between risk, uncertainty and ambiguity. One general conclusion is that the elements of this methodological trilogy are not equally advanced. For example, new experimental tools must be developed to adequately test the predictions of theory. My dissertation is an example of this dynamic between theoretical and applied economics