An introduction to and an overview of various work in progress. Created 2005/01/26 Last Changed Date: 2010-01-25 13:11:02 http://www.rbjones.com/rbjpub/www/papers/p000.pdf Id: p000.tex,v 1.11 2010-01-25 13:11:02 rbj Exp c © Roger Bishop Jones; Licenced under Gnu LGPL p000.tex; 8/08/2010; 20:35; p.1

The“giant component” has remained a guiding theme in the theory of random graphs ever since the seminal paper of Erdős and Rényi [Magayar Tud. Akad. Mat. Kutato Int. Kozl. 5 (1960) 17–61]. Because for any k ≥ 3 the k-core, defined as the (unique) maximal subgraph of minimum degree k, is identical to the largest kconnected subgraph of the random graph w.h.p., the k-core is perhaps the most natur...

This paper contrasts two approaches to analyzing transitivity of preference and other behavioral properties in choice data. The approach of Regenwetter, Dana, and Davis-Stober (2011) assumes that on each choice, a decision maker samples randomly from a mixture of preference orders in order to determine whether A is preferred to B. In contrast, Birnbaum and Gutierrez (2007) assumed that within e...