In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation.

Recent constraint satisfaction models of explanation, analogy, and decision making claim that these processes are influenced by bidirectional constraints that promote coherence. College students were asked to reach a verdict in a complex legal case involving multiple conflicting arguments, including alternative analogies to the target case. Participants rated agreement with the individual arguments both in isolation before seeing the case and again after reaching a verdict. Assessments of the individual arguments shifted so as to cohere with their emerging verdict. A cascade of spreading coherence influenced decisions made about a subsequent case involving different legal issues. Participants' memory for their initial positions also shifted so as to cohere with their final positions. The results demonstrate that constraint satisfaction can transform ambiguous inputs into coherent decisions. One of the most deep-rooted assumptions about human reasoning is that the flow of inference is inherently unidirectional, moving from premises to be accepted as given to inferred conclusions. Unidirectionality is most apparent in deductive inference, but it is generally assumed to hold also for inductive inference. For example, Bayesian inference uses prior odds and likelihood ratios (premises) to derive posterior odds (conclusions). The direction of inference may vary depending on what is initially known (e.g., people may use known causes to infer potential effects or else use known effects to diagnose possible causes), but it is generally assumed that in any reasoning episode certain information constitutes the fixed premises from which certain other information can be derived as a (perhaps tentative) conclusion. The Unidirectionality assumption rules out reverse inferences, that is, those that move from conclusions to premises. Within this unidirectional framework, any inferences that

The authors suggest that decisions made from multiple pieces of evidence are performed hy mechanisms of parallel constraint satisfaction, which are related to cognitive consistency theories. Such reasoning processes are bidirectional--decisions follow from evidence, and evaluations of the evidence shift toward coherence with the emerging decision. Using a factually complex legal case, the authors observed patterns of coherence shifts that persisted even when the distribution of decisions was manipulated (Study 1) and influenced by the participants' attitudes (Study 2). The evaluations of the evidence cohered with the preferred decision even when participants changed their preference (Study 3). Supporting the bidirectionality of reasoning. Study 4 showed that assigning participants to a verdict affected their evaluation of the evidence. Coherence shifts were observed also in related background knowledge. This research suggests that cognitive consistency theories should play a greater role in the understanding of human reasoning and decision making.

Previous research has indicated that decision making is accompanied by an increase in the coherence of assessments of the factors related to the decision alternatives. In the present study, the authors investigated whether this coherence shift is obtained before people commit to a decision, and whether it is obtained in the course of a number of other processing tasks. College students were presented with a complex legal case involving multiple conflicting arguments. Participants rated agreement with the individual arguments in isolation before seeing the case and after processing it under various initial sets, including playing the role of a judge assigned to decide the case. Coherence shifts were observed when participants were instructed to delay making the decision (Experiment 1), to memorize the case (Experiment 2), and to comprehend the case (Experiment 3). The findings support the hypothesis that a coherence-generating mechanism operates in a variety of processing tasks, including decision making.Many decisions people are faced with require the integration of multiple inferences. Tasks such as deciding which job offer to accept, or what candidate to support in an election, involve sets of inferences that tend to be ambiguous, contradictory, and complex. Holyoak and Simon (1999) examined such inference-based decision making in a laboratory analog of judicial decision making, in which college students were asked to render a verdict in a complex legal case. The principal finding was that the decision-making process was accompanied by a systematic change in the evaluation of the inferences toward a pattern of coherence with the emerging decision. Assessments of inferences spread apart increasingly, with those supporting the chosen decision growing stronger as those supporting the rejected alternative waned. This shifting of inferences suggests that the participants' reasoning processes operated bidirectionally: The decisions seemed to be based on the inferences made from the provided information, and at the same time, the emerging decisions worked backwards to alter the strength of the inferences, yielding even stronger support for the decision. Evidence of this bidirectional influence was provided by a manipulation of the favorability of 1 of the 12 inferences inDan Simon, School of Law, University of Southern California; Lien B. Pham, Quang A. Le, and Keith J. Holyoak, Department of Psychology, University of California, Los Angeles.A preliminary report of the findings was presented at the 40th Annual Meeting of the Psychonomic Society, Los Angeles, November 1999. This research was supported by National Science Foundation Grants SES-0080424 and SES-0080375.This article benefited from the comments of Tom Lyon, Steve Read, David Boninger, and Jay Russo. We thank Andre Der-Avakian, Mercedes Barajas, Vera Cha, Humberto Iglesias, Mimi Lin, Diana Lucero, Annahita Palar, Suzette Viemes, and Kristine Vuong for assisting in running the experiments and Sean McAuliffe for preparing figures.Correspondence concerning thi...

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HERE are many people that I would like to thank for their help and support to help me become the person that I am today. Foremost, I must acknowledge my adviser Dr. Simon for always leading by example, through his hard work and ethical and optimal decision making skills. I am forever grateful to him for his mentoring style of encouraging investigative thinking and allowing us the freedom to do research. It gives me great pleasure in acknowledging the support and help of all my committee members, Dr. Hizlan, Dr. Richter, Dr. Sikder and Dr. Shao for all their suggestions and recommendations. Special thanks to Dawei Du, Rick Rarick, George Thomas, Berney Montavon, Paul Lozovyy and all of the remaining past and present members of the Embedded Controls Lab. Being part of a team that solves real-world problems has been one of the most rewarding experiences of my life. Also, many thanks to our industrial partners, including Jeff Abell from General Motors, Nick Mastandrea from Innovative Developments and Arun Venkatesan from Cleveland Medical Polymers, for working with us on these projects. I consider it an honor to work with my fellow engineers at ARCON Corporation. I am indebted to them for encouraging me the complete my research. Last, but not least, I owe a debt of gratitude to my family, especially my parents Güngör and Dr. Yalçın Ergezer. I could not achieve this without their unconditional love, encouragement and guidance. I must also thank Slava and her parents for welcoming me and tolerating me through this long adventure and for providing me with the much needed relief from the technical world.

Participants were given a choice between two multiattribute alternatives (job offers). Preferences for the attributes were measured before, during, and after the choices were made. We found that over the course of decision making, the preferences shifted to cohere with the choice: The attributes of the option that was eventually chosen came to be rated more favorably than they had been rated initially, while the attributes of the rejected option received lower preference ratings than before. These coherence shifts were triggered by a single attribute that decisively favored one option (Experiment 1), and occurred spontaneously in the absence of a decisive attribute (Experiment 2). The coherence shift preceded commitment to choice. These findings favor constraint-satisfaction models of decision making.

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