Ignorance and indifference

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the 'principle of invariance of ignorance' (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution. Copyright 2008 by the Philosophy of Science Association. All rights reserved

Algebraic boundaries among typical ranks for real binary forms of arbitrary degree

We show that the algebraic boundaries of the regions of real binary forms with fixed typical rank are always unions of dual varieties to suitable coincident root loci.Comment: Accepted for publication in Foundations of Computational Mathematic

Automated Macro-scale Causal Hypothesis Formation Based on Micro-scale Observation

This book introduces new concepts at the intersection of machine learning, causal inference and philosophy of science: the macrovariable cause and effect. Methods for learning such from microvariable data are introduced. The learning process proposes a minimal number of guided experiments that recover the macrovariable cause from observational data. Mathematical definitions of a micro- and macro- scale manipulation, an observational and causal partition, and a subsidiary variable are given. These concepts provide a link to previous work in causal inference and machine learning. The main theoretical result is the Causal Coarsening Theorem, a new insight into the measure-theoretic structure of probability spaces and structural equation models. The theorem provides grounds for automatic causal hypothesis formation from data. Other results concern the minimality and sufficiency of representations created in accordance with the theorem. Finally, this book proposes the first algorithms for supervised and unsupervised causal macrovariable discovery. These algorithms bridge large-scale, multidimensional machine learning and causal inference. In an application to climate science, the algorithms re-discover a known causal mechanism as a viable causal hypothesis. In a psychophysical experiment, the algorithms learn to minimally change visual stimuli to achieve a desired effect on human perception.</p

Political Mergers as Coalition Formation

Political coalition formation games can describe the formation and dissolution of nations, as well as the creation of coalition governments, the establishment of political parties, and other similar phenomena. These games have been studied from a theoretical perspective, but the resulting models have not been used extensively in empirical work. This paper presents a method of estimating political coalition formation models with many-player coalitions, and then illustrates this method by estimating structural coefficients that describe the behaviour of municipalities during a recent set of municipal mergers in Japan. The method enables counterfactual analysis, which in the Japanese case shows that the national government could increase welfare via a counter-intuitive policy involving transfers to richer municipalities conditional on their participation in a merger.computational techniques, coalitions, municipalities