Commutativity, comonotonicity, and Choquet integration of self-adjoint operators

In this work, we propose a definition of comonotonicity for elements of [Formula: see text], i.e. bounded self-adjoint operators defined over a complex Hilbert space [Formula: see text]. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of [Formula: see text] that generalizes quantum expectations. We characterize Choquet expectations as the real-valued functionals over [Formula: see text] which are comonotonic additive, [Formula: see text]-monotone, and normalized

Divergent platforms

Models of electoral competition between two opportunistic, office-motivated parties typically predict that both parties become indistinguishable in equilibrium. I show that this strong connection between the office motivation of parties and their equilibrium choice of identical platforms depends on two—possibly false—assumptions: (1) Issue spaces are uni-dimensional and (2) Parties are unitary actors whose preferences can be represented by expected utilities. I provide an example of a two-party model in which parties offer substantially different equilibrium platforms even though no exogenous differences between parties are assumed. In this example, some voters’ preferences over the 2-dimensional issue space exhibit non-convexities and parties evaluate their actions with respect to a set of beliefs on the electorate

Selection of climate policies under the uncertainties in the Fifth Assessment Report of the IPCC

Analysis of uncertainty decision making criteria