Advancements In the elicitation, aggregation, and forecasting of probability distributions under time constraints

Includes bibliographical references (p. 141-144).Opinion pooling involves the process of combining the beliefs of multiple individuals into a single consensus which best represents the beliefs of the group. Instances where these methods are often applied occur when historical data is difficult or even impossible to collect. The elicitation of individual beliefs, aggregation into a consensus, and forecasting from the consensus distribution are all important processes in the field of opinion pooling. This thesis develops new techniques in each of these areas, increasing the possibility for more accurate decision making under uncertainty. Currently accepted elicitation techniques have yet to incorporate technological advancements made in the field of visual computing. To help experts exhibit their beliefs more accurately, new visually aided computer software is developed and tested. Individual opinions are expressed as probability distributions constructed with help from a moderator. An experiment is conducted to test whether the newly developed software aids in the ability to better predict the outcome of unknown events across different probability distributions. Constructing a consensus probability distribution relies not only on accurate individual elicitations, but also on the formulaic algorithm used to combine the multiple probability distributions. Popular techniques used today to combine these distributions suffer from some debilitating drawbacks. Investigating the problem through probability distance and divergence measures, new consensus pooling operators are proposed as opposed to the currently used Kullback-Leibler distance measure. Finally, new theory on applying opinion pooling methodology under time constraints is developed. Often decisions need to be made before a specific deadline arrives. In these instances, opinions are not only influenced by available evidence, but also by the amount of time remaining before the decision must be made. With very little research completed in this area, new algorithms and theory are proposed to better incorporate the time dimension into the opinion pooling framework. A thorough example of elicitations and predictions made through prediction markets implements the newly developed theory