The expected number of pairwise comparisons needed to learn a partial order on n elements is shown to be at least /4 − (), and an algorithm is given that needs only /4 + () comparisons on average. In addition, the optimal strategy for learning a poset with four elements is presented

It is shown that each continuous transformation from Euclidean -space ( > 1) into Euclidean -space that preserves the equality of distances (that is, fulfils the implication is a similarity map. The case of equal dimensions already follows from the Beckman-Quarles Theorem

Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for representability probabilities are produced by...

Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of “indifference” in individual preferences is misleading and should be...

We present typical scenarios and general insights from a novel dynamic model of farsighted climate coalition formation involving market linkage and cap coordination, using a simple analytical model of the underlying cost-benefit structure. In our model, the six major emitters of CO2 can link...

We consider games where individual contributions are costly but beneficial to other players, so that contributing nothing is a dominant strategy. Considering that players may be unable to write binding agreements but may make binding unilateral commitments that are conditional on others'...

Standard macroeconomic models assume that households are rational in the sense that they are perfect utility maximizers, and explain economic dynamics in terms of shocks that drive the economy away from the steady-state. Here we build on a standard macroeconomic model in which a single rational...