Information Aggregation, with Application to Monotone Ordering, Advocacy, and Conviviality

Citation

Klemens, Ben (2003) Information Aggregation, with Application to Monotone Ordering, Advocacy, and Conviviality. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JB45-Z027. https://resolver.caltech.edu/CaltechETD:etd-06022003-155827

Abstract

I. Chapter 1 presents a convenient notation for describing methods of aggregating information to form posterior distributions, allowing a description of Bayesian updating and many of the cognitive errors people commit in the lab. Chapter 2 looks at the monotone ordering problem: if the prior distributions are ordered in some manner, what updating operations will preserve that ordering? Bayesian updating is a member of a small class of operators which preserve the monotone likelihood ratio property, but is not in the class of functions which preserve first-order stochastic dominance. It also considers ordering distributions by their medians, which is useful for Political Science and other decisionmaking applications.

II. Chapter 3 presents a literature review of existing models of information aggregation from one party, and gives the very weak conditions under which one or two biased advocates will always reveal full information. Chapter 4 then presents a model of a trial, in which events are grouped into causal stories. Each story may point to a specific verdict, but the judge has leeway in selecting a verdict when multiple stories are shown to simultaneously be sufficient to explain an event. Two judges may be `perfect Bayesians', share the same priors, and still arrive at different verdicts for the same trial. Unlike the information revelation literature to date, there may be apropos stories and facts that neither party will want to reveal in equilibrium.

III. Chapter 5 presents a simultaneous model of goods or actions which demonstrate conformity effects. Previous models of such goods universally describe people as acting in sequence; actors in the model here act simultaneously, so they must decide what to do based only on prior information about the distribution of tastes in the society. The shape of this distribution (e.g., centered around zero, skewed upward, or fat-tailed) predicts the number of people who will act in some systematic ways, which I catalog here.

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