In Defense of Randomization: A Subjectivist Bayesian Approach

• Activity Number: 458
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Fernando Vieira Bonassi*+ and Raphael Nishimura and Rafael Bassi Stern
• Companies: Duke University and University of Michigan and Carnegie Mellon University
• Keywords: Bayesian Statistics ; Decision Theory ; Game Theory ; Intersubjectivism ; Randomization

Abstract

In research situations usually approached by Decision Theory, it is only considered one researcher who collects a sample and makes a decision based on it. It can be shown that randomization of the sample does not improve the utility of the obtained results. Nevertheless, we present situations in which this approach is not satisfactory. First, we present a case in which randomization can be an important tool in order to achieve agreement between people with different opinions. Next, we present another situation in which there are two agents: the researcher - a person who collects the sample; and the decision-maker - a person who makes decisions based on the sample collected. We show that problems emerge when the decision-maker allows the researcher to arbitrarily choose a sample. We also show that the decision-maker maximizes his expected utility requiring that the sample is collected randomly.