Optimizing Expected Utility in a Multinomial Logit Model with Position Bias and Social Influence

Motivated by applications in retail, online advertising, and cultural markets, this paper studies how to find the optimal assortment and positioning of products subject to a capacity constraint. We prove that the optimal assortment and positioning can be found in polynomial time for a multinomial logit model capturing utilities, position bias, and social influence. Moreover, in a dynamic market, we show that the policy that applies the optimal assortment and positioning and leverages social influence outperforms in expectation any policy not using social influence

Variable Selection in General Multinomial Logit Models

The use of the multinomial logit model is typically restricted to applications with few predictors, because in high-dimensional settings maximum likelihood estimates tend to deteriorate. In this paper we are proposing a sparsity-inducing penalty that accounts for the special structure of multinomial models. In contrast to existing methods, it penalizes the parameters that are linked to one variable in a grouped way and thus yields variable selection instead of parameter selection. We develop a proximal gradient method that is able to efficiently compute stable estimates. In addition, the penalization is extended to the important case of predictors that vary across response categories. We apply our estimator to the modeling of party choice of voters in Germany including voter-specific variables like age and gender but also party-specific features like stance on nuclear energy and immigration

Assortment and Pricing Optimisation under non-conventional customer choice models

Nowadays, extensive research is being done in the area of revenue management, with applications across industries. In the center of this area lays the assortment problem, which amounts to find a subset of products to offer in order to maximise revenue, provided that customers follow a certain model of choice. Most studied models satisfy the following property: whenever the offered set is enlarged, then the probability of selecting a specific product decreases. This property is called regularity in the literature. However, customer behaviour often shows violations of this condition such as the decoy effect, where adding extra options sometimes leads to a positive effect for some products, whose probabilities of being selected increase relative to other products (e.g., including a medium size popcorn slightly cheaper than the large one, with the purpose of making the latter more attractive by comparison). We study two models of customer choice where regularity violations can be accommodated (hence the non-conventionality), and show that the assortment optimisation problem can still be solved in polynomial time. First we analyse the Sequential Multinomial Logit (SML). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products on the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al.(2018). It can explain many behavioural phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the Multinomial Logit (MNL) model or any discrete choice model based on random utility. We show that the concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, we show that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable Secondly, the Two-Stage Luce model (2SLM), is a discrete choice model introduced by Echenique and Saito (2018) that generalizes the standard multinomial logit model (MNL). The 2SLM does not satisfy the Independence of Irrelevant Alternatives (IIA) property nor regularity, and to model customer behaviour, each product has an intrinsic utility, and uses a dominance relation between products. Given a proposed assortment S, consumers first discard all dominated products in S before using an MNL model on the remaining products. As a result, the model can capture behaviour that cannot be replicated by any discrete choice model based on random utilities. We show that the assortment problem under the 2SLM is polynomially-solvable. Moreover, we prove that the capacitated assortment optimization problem is NP-hard and present polynomial-time algorithms for the cases where (1) the dominance relation is attractiveness correlated and (2) its transitive reduction is a forest. The proofs exploit a strong connection between assortments under the 2SLM and independent sets in comparability graphs. The third and final contribution is an in-depth study of the pricing problem under the 2SLM. We first note that changes in prices should be reflected in the dominance relation if the differences between the resulting attractiveness are large enough. This is formalised by solving the joint assortment and pricing problem under the Threshold Luce model, where one product dominates another if the ratio between their attractiveness is greater than a fixed threshold. In this setting, we show that this problem can be solved in polynomial time

Parties, Committees, and Rules in the U.S. House of Representatives

This dissertation project aims to build upon the literature of positive theories of legislative politics, and provide three more nuanced stories about various stages in the U.S. House of Representatives: rules making, committee composition, and floor voting. The chapter, Conditional Nature of Rules Changes, examines why the U.S. House of Representatives has changed its standing rules regarding the principle of majority rule and minority rights. I begin by taking a critical look at previous studies on this subject, after which I propose an alternative theory on the conditional nature of rules changes. The empirical findings reveal that different combinations of factors are required for the two distinct types of rules changes. In particular, the size and homogeneity of the majority party are the main factors for promoting majority rule while the size of the majority party and the dimensionality of policy space are the main factors for creating minority rights. The chapter, Minority Party Members on Committees, questions why a generic legislature allows minority party members on committees. If the majority party considers the minority a burden, then it could choose to exclude minority party members entirely from the committee system. This has, however, rarely happened in history. This chapter provides one possible explanation to this puzzle via a simple signaling game. In equilibrium, I show that the majority party has an incentive to include the minority party delegation on the committee. By allowing the minority to make a public speech on the uncertainty, the majority leadership can constrain the majority committee delegation in a way to serve the party in general: the majority committee delegation, in equilibrium, moderates the bill proposal in order to respond to the minority\u27s public speech. The chapter, Special Rules and Dimensionality, is one of the first attempts to investigate the determinants for dimensionality of individual bills. I first develop a theory on partisan manipulation of dimensionality by focusing especially on the role of restrictive special rules in the House of Representatives: party leaders try to reduce the dimensionality of individual bills in order to have clear party image and to avoid ugly defeats. I collect every piece of major legislation identified by Clinton and Lapinski: 2006), and record the contents of their special rules. Ultimately, the data demonstrate that restrictive rules contribute to lower dimensionality

Multinomial logit processes and preference discovery: inside and outside the black box

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation. Our axiomatic analysis provides a behavioural foundation of softmax (also known as Multinomial Logit Model). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behaviour. Jointly, the two approaches provide a thorough understanding of softmaximization in terms of internal causes (neuro-physiological mechanisms) and external effects (testable implications)

Changing with the tide: Semi-parametric estimation of preference dynamics

We contrast the discovered preference hypothesis against the theory of coherent arbitrariness in a split-sample stated choice experiment on flood-risk exposure. A semiparametric local multinomial logit model is developed as an alternative to the Swait and Louviere (1993) test procedure controlling for preference dynamics within and between samples. The proposed model supports the discovered preference hypothesis by means of a decaying starting point bias. The Swait and Louviere (1993) test procedure reaches a different conclusion. It rejects the assumption of stable preferences, but most preference dynamics tend to be smoothed out, causing a more erratic pattern of preference dynamics