Efficient Portfolio Selection through Preference Aggregation with Quicksort and the Bradley–Terry Model

ArXiv ID: 2504.16093 “View on arXiv”

Authors: Unknown

Abstract

How to allocate limited resources to projects that will yield the greatest long-term benefits is a problem that often arises in decision-making under uncertainty. For example, organizations may need to evaluate and select innovation projects with risky returns. Similarly, when allocating resources to research projects, funding agencies are tasked with identifying the most promising proposals based on idiosyncratic criteria. Finally, in participatory budgeting, a local community may need to select a subset of public projects to fund. Regardless of context, agents must estimate the uncertain values of a potentially large number of projects. Developing parsimonious methods to compare these projects, and aggregating agent evaluations so that the overall benefit is maximized, are critical in assembling the best project portfolio. Unlike in standard sorting algorithms, evaluating projects on the basis of uncertain long-term benefits introduces additional complexities. We propose comparison rules based on Quicksort and the Bradley–Terry model, which connects rankings to pairwise “win” probabilities. In our model, each agent determines win probabilities of a pair of projects based on his or her specific evaluation of the projects’ long-term benefit. The win probabilities are then appropriately aggregated and used to rank projects. Several of the methods we propose perform better than the two most effective aggregation methods currently available. Additionally, our methods can be combined with sampling techniques to significantly reduce the number of pairwise comparisons. We also discuss how the Bradley–Terry portfolio selection approach can be implemented in practice.

Keywords: Project Selection, Bradley-Terry Model, Quicksort, Decision Making Under Uncertainty, Resource Allocation, Project Finance

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper introduces significant mathematical complexity through the Bradley-Terry model and statistical theory, but provides minimal empirical validation with no backtesting or implementation details.

  flowchart TD
    A["Research Goal: Develop efficient methods to rank & select projects under uncertainty"] --> B{"Key Inputs: <br>Set of N Projects <br>Agent Evals & Pairwise Win Probabilities"}
    B --> C["Methodology: <br>Aggregate Probabilities & Apply Quicksort with Bradley-Terry Model"]
    C --> D{"Data Processing: <br>Computational Ranking & Portfolio Selection"}
    D --> E["Validation: <br>Benchmark against existing aggregation methods"]
    E --> F["Key Findings: <br>Higher performance & efficiency achieved <br>Sampling reduces pairwise comparisons"]