Randomness in Limited Information Based Decisionmaking

Abstract

Standard decision-making theory assumes that an agent considers all possible alternatives when determining their final choice. However, in reality, agents do not truly consider all options but rather a select subset. Previous literature lays a framework for decision making theory based on such an assumption. This paper explores and develops two extensions. First, this paper recognizes that the order in which a user is presented with choices can affect their choice due to the dependency of the elements that are considered upon the ordering of elements. Second, this paper recognizes that the ordering that a user faces is random and subject to some probability distribution. Using these two assumptions, this paper develops a number of results that provide conditions under which an analyst may view the final choice of a user for any given permutation of elements from which the underlying preferences can be deduced. This paper then develops a plausible model for the manner in which humans pay attention to elements and demonstrates how the earlier results in the manuscript can be used to deduce underlying preferences based on observational data.