Modelling the expected probability of correct assignment under uncertainty

TL;DR

This paper analyzes how decision uncertainty affects the probability of correct matching in attribute-based choices, providing analytical expressions and exploring implications for policy and resource allocation.

Contribution

It introduces a Voronoi tessellation framework to quantify the probability of correct matches under uncertainty and examines optimal allocation strategies.

Findings

Significant mismatch occurs even at low uncertainty levels.

The probability of correct match depends on individuals' location relative to Voronoi boundaries.

Allocating service resources near decision boundaries improves matching outcomes.

Abstract

When making important decisions such as choosing health insurance or a school, people are often uncertain what levels of attributes will suit their true preference. After choice, they might realize that their uncertainty resulted in a mismatch: choosing a sub-optimal alternative, while another available alternative better matches their needs. We study here the overall impact, from a central planner's perspective, of decisions under such uncertainty. We use the representation of Voronoi tessellations to locate all individuals and alternatives in an attribute space. We provide an expression for the probability of correct match, and calculate, analytically and numerically, the average percentage of matches. We test dependence on the level of uncertainty and location. We find overall considerable mismatch even for low uncertainty - a possible concern for policy makers. We further explore a commonly used practice - allocating service representatives to assist individuals' decisions. We show that within a given budget and uncertainty level, the effective allocation is for individuals who are close to the boundary between several Voronoi cells, but are not right on the boundary.