Entrepreneurs may undertake investments when returns cannot be precisely evaluated: they are decisive. Lenders may require high compensation to place funds in those ventures: they are cautious. We analyze optimal ̄nancing contracts between entrepreneurs and lenders. Decisiveness and cautiousness are characterized using Bewley's (1986) incomplete preferences framework. Preferences are represente...

A. For f > g ∈ ω let c∀f ,g be the minimal number of uniform trees with g-splitting needed to ∀-cover the uniform tree with f -splitting. c∃f ,g is the dual notion for the ∃ cover. Assuming CH and given א1 many (sufficiently different) pairs ( f2 , g2 ) and cardinals κ2 such that κ0 2 = κ2 , we construct a partial order forcing that c∃f2 ,g2 = c ∀ f2 ,g2 = κ2 . For this, we introduce a c...

This paper develops a new approach to the analysis of the underlying power structure when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness, which is weaker than standard decisiveness, and investigate the family of quasi-decisive groups associated an Arrovian collective choice rule. A group is quasi-decisive if for every pair x, y of alternatives, y i...