Decision Theory, Epistemology (esp. Formal and Social), Philosophy of Science, Philosophical Logic
American Pragmatism, Logic, Philosophy of the Social Sciences
Aggregation is an important topic in economics (e.g., social choice theory) and statistics (e.g., opinion pooling), but it also finds application throughout decision theory and epistemology. Aggregation methods can be and often are interpreted as delivering a “consensus” position among sets of probabilities, beliefs, or preferences. Consensus between points of view is central to any developed account of rationality. While it may be obvious that common ground or consensus matters in settings of group decision-making and joint inquiry, such notions are also crucial for single agents. A rational agent can have multiple goals or values that come into conflict or she may suspend judgment between various ways of evaluating events with respect to subjective probability, for example. I propose general frameworks for aggregating probabilities, full beliefs, and preferences, and I investigate their philosophical and mathematical properties. Drawing on work in the theory of imprecise probabilities, I make a case for employing sets of probability functions and sets of preference relations for identifying common ground among candidate ways of evaluating events and options, respectively. Among other things, I prove that many of the famous “impossibility” results afflicting standard models of aggregation (like Arrow’s Impossibility Theorem or Sen’s Impossibility of the Paretian Liberal in preference aggregation and similar limitative results in probability pooling) do not apply. In other words, certain very attractive constraints on aggregation are simultaneously satisfiable in the generalized aggregation frameworks that I develop. I look at some applications and consequences of this proposal for the social sciences.
“Probabilistic Opinion Pooling with Imprecise Probabilities” (with Ignacio Ojea Quintana), Journal of Philosophical Logic, Forthcoming.
“Conditional Choice with a Vacuous Second Tier,” Synthese.