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.
Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga’s rebuttal to Belot’s analysis, which focuses attention on the role that the assumption of countable additivity plays in Belot’s criticisms.
The Sleeping Beauty problem has spawned a debate between "thirders" and "halfers" who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard "Bayesian" account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment.
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