Preserving Dependent Choice

State dependent choice

We propose a theory of choices that are influenced by the psychological state of the agent. The central hypothesis is that the psychological state controls the urgency of the attributes sought by the decision maker in the available alternatives. While state dependent choice is less restricted than rational choice, our model does have empirical content, expressed by simple ‘revealed preference’ ...

6 - Dependent Random Choice

If F is a family of graphs containing a bipartite graph, then for some δ > 0, ex(n,F) < n2−δ by the Kövari-Sós-Turán Theorem. Erdős and Simonovits [5] conjectured that for every finite family graph F of graphs, there exists α = α(F) such that ex(n,F) = Θ(nα). This α is called the exponent of F . If F is a bipartite graph containing a cycle, then in general it is not known if F = {F} has an expo...

Dependent random choice

We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this survey we discuss so...

Sophie’s Choice: Preserving Patient Autonomy in Organ Donation

Fixed point theories and dependent choice

In this paper we establish the proof-theoretic equivalence of (i) ATR and c