Partial knowledge restrictions on the two-stage threshold model of choice

What is it about?

In a two-stage threshold model of choice, a decision maker makes choices in two phases: first pre-selecting their choices according to a criterion, and then narrowing their selection further to maximize a second criterion. This paper uses this decision making procedure to look closely at the limitations of the decision maker’s choices in the presence of endogenous variables, which are known but not explained by the model. This paper therefore explores the difficulties of testing that the model is consistent under partial knowledge with three structural variables g, f, and using a broad framework that can be adapted to different situations and examples. To begin with, the paper considers situations where exactly one of the three structural variables is known and extrapolates information about the unknown variables from the decision maker’s choices. The paper looks first at the case of multi-valued choice functions where the primary criterion f is known, then at the case where the threshold map is known and lastly at the case where the secondary criterion g is known. Next it considers situations where exactly two structural variables are known; whether that be and , and or and Finally, the model briefly adapts its findings to the case of single-valued choice functions. By determining the logical relationships between the three structural variables through propositions and axioms, the paper summarizes the characterization results in both the case of multi-valued choice and single-valued choice.

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