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

arXiv: https://arxiv.org/abs/2504.16093 · HTML: https://mlsanity.com/paper/2504.16093/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 6 Apr 2025.

## Builds on (most cited first, 16 of 16)

- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Large Language Models Can Be Used to Estimate the Latent Positions of Politicians](https://mlsanity.com/paper/2303.12057/) (2023)
- [Efficient computation of rankings from pairwise comparisons](https://mlsanity.com/paper/2207.00076/) (2022)
- [MORAL: Aligning AI with Human Norms through Multi-Objective Reinforced Active Learning](https://mlsanity.com/paper/2201.00012/) (2021)
- [Participatory Budgeting: Models and Approaches](https://mlsanity.com/paper/2003.00606/) (2020)
- [Efficient LLM Comparative Assessment: a Product of Experts Framework for Pairwise Comparisons](https://mlsanity.com/paper/2405.05894/) (2024)
- [Properties of Multiwinner Voting Rules](https://mlsanity.com/paper/1506.02891/) (2015)
- [ONEBench to Test Them All: Sample-Level Benchmarking Over Open-Ended Capabilities](https://mlsanity.com/paper/2412.06745/) (2024)
- [Sorting with Predictions](https://mlsanity.com/paper/2311.00749/) (2023)
- [A Bayesian Bradley-Terry model to compare multiple ML algorithms on multiple data sets](https://mlsanity.com/paper/2208.04935/) (2022)
- [Designing Digital Voting Systems for Citizens: Achieving Fairness and Legitimacy in Participatory Budgeting](https://mlsanity.com/paper/2310.03501/) (2023)
- [Parallel Algorithms for Select and Partition with Noisy Comparisons](https://mlsanity.com/paper/1603.04941/) (2016)
- [Leveraging Sub-Optimal Data for Human-in-the-Loop Reinforcement Learning](https://mlsanity.com/paper/2405.00746/) (2024)
- [Generalized Sorting with Predictions](https://mlsanity.com/paper/2011.00172/) (2020)
- [Longest Increasing Subsequence under Persistent Comparison Errors](https://mlsanity.com/paper/1808.03307/) (2018)
- [Organizational Selection of Innovation](https://mlsanity.com/paper/2405.09843/) (2024)

## Abstract (arXiv)

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.