Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms -- one based on column generation and one based on random sampling -- for estimating such models from data. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms both rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25, 2021

Portfolio selection models: A review and new directions

Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean-risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a risk value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We revisit these risk measures and the resulting mean-risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance

Success from Satisficing and Imitation: Entrepreneurs’ Location Choice and Implications of Heuristics for Local Economic Development

Decisions about location choice provide an opportunity to compare the predictions of optimization models, which require exhaustive search through very large choice sets, against the actual decision processes used by entrepreneurs choosing where to allocate investment capital. This paper presents new data on entrepreneurs’ self-described decision processes when choosing where to locate, based on scripted interviews with 49 well-placed business owners and senior managers in charge of location choice. Consideration sets are surprisingly small, especially among those who are successful. According to entrepreneurs’ own accounts, locations are frequently discovered by chance rather than systematic search. Few describe decision processes that bear any resemblance to equating marginal benefit with marginal cost as prescribed by standard optimization theory. Nearly all interviewees describe location choice decisions based on threshold conditions, providing direct evidence of satisficing rather than optimization. Imitation is beneficial for small investment projects. Decision process data collected here suggests a need to rethink standard policy tools used to stimulate local economic development.Process Model, Bounded Rationality, Interview Data, Ethnic, Discrimination, Low income, Neighborhood, Lexicographic, Non-compensatory, Business Owners