We show lower bounds on the number of sample points and on the number of coin tosses used by general sampling algorithms for estimating the average value of functions over a large domain. The bounds depend on the desired precision and on the error probability of the estimate. Our lower bounds match upper bounds established by known algorithms, up to a mul-tiplicative constant. Furthermore, we g...

This paper presents an application of voting geometry to individual decision making. We demonstrate that a number of decision anomalies can arise as a natural consequence of the aggregation of preferences of different neural systems. We present a proof of existence of a set of voting procedures that can account for the attraction effect, the similarity effect and the compromise effect, and prov...

THIS SUPPLEMENTAL MATERIAL contains the proofs of all the lemmas that do not appear in the printed Appendix to the paper. It also contains the statements of all these lemmas and details of the intervening arguments in the proofs of the propositions. These arguments appeared in the printed Appendix. It also contains a proof of existence for a more general model that implies Proposition 3(ii). Th...

Abstract That certain paper bills have monetary value, that Vladimir Putin is the president of Russia, and Prince Philip husband Queen Elizabeth II: such facts are commonly called ‘institutional facts’ (IFF). IFF are, by definition, exist virtue collective recognition (where can be direct or indirect). The standard view tacit belief really exist. In this we argue, however, they do not—they just...