Two Statements

Two statements of the Duggan-Schwartz theorem

The Duggan-Schwartz theorem [Duggan and Schwartz, 1992] is a famous result concerning strategy-proof social choice correspondences, often stated as “A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak dictator”. However, this formulation is actually due to Taylor [2002], and the original theorem, at face value, looks rather different. In this...

Two statements on the Bouvia case.

Two Statements about Infinite Products that Are Not Quite True

The first half of this note concerns modules; so let R be a nonzero associative ring with unit. A countably infinite direct product of copies of R, which we will usually regard as a left R-module, will be written R (ω denoting the set of natural numbers); the corresponding direct sum, i.e., the free left R-module of countably infinite rank, will be written ⊕ ω R. Here, now, are the two not-alwa...

Quranic Statements

“The state of being plain” is one of the features of the Holy Quran, taken as indicative of Quran’s expressiveness and clearness regarding its intentions. However, one of the aspects of Quranic miracles is its expressive miracle based on which verses have been revealed according to suitability and appropriateness of situation in an explicit and succinct form. In order to have a desirable unders...

Position Statements