# Proportional Aggregation of Preferences for Sequential Decision Making

arXiv: https://arxiv.org/abs/2306.14858 · HTML: https://mlsanity.com/paper/2306.14858/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 74 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 30 of 32)

- [Cooperative Inverse Reinforcement Learning](https://mlsanity.com/paper/1606.03137/) (2016)
- [Fine-tuning language models to find agreement among humans with diverse preferences](https://mlsanity.com/paper/2211.15006/) (2022)
- [Reward Uncertainty for Exploration in Preference-based Reinforcement Learning](https://mlsanity.com/paper/2205.12401/) (2022)
- [A Voting-Based System for Ethical Decision Making](https://mlsanity.com/paper/1709.06692/) (2017)
- [Justified Representation in Approval-Based Committee Voting](https://mlsanity.com/paper/1407.8269/) (2014)
- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Proportional Participatory Budgeting with Additive Utilities](https://mlsanity.com/paper/2008.13276/) (2020)
- [Adapting a Kidney Exchange Algorithm to Align with Human Values](https://mlsanity.com/paper/2005.09755/) (2020)
- [Proportional Justified Representation](https://mlsanity.com/paper/1611.09928/) (2016)
- [Robust and Verifiable Proportionality Axioms for Multiwinner Voting](https://mlsanity.com/paper/2302.01989/) (2023)
- [Moral Machine or Tyranny of the Majority?](https://mlsanity.com/paper/2305.17319/) (2023)
- [Fair Public Decision Making](https://mlsanity.com/paper/1611.04034/) (2016)
- [Proportionality and the Limits of Welfarism](https://mlsanity.com/paper/1911.11747/) (2019)
- [Properties of Multiwinner Voting Rules](https://mlsanity.com/paper/1506.02891/) (2015)
- [Fairness and Welfare Quantification for Regret in Multi-Armed Bandits](https://mlsanity.com/paper/2205.13930/) (2022)
- [The Core of the Participatory Budgeting Problem](https://mlsanity.com/paper/1610.03474/) (2016)
- [Fair mixing: the case of dichotomous preferences](https://mlsanity.com/paper/1712.02542/) (2017)
- [A Computational Model of Commonsense Moral Decision Making](https://mlsanity.com/paper/1801.04346/) (2018)
- [Phragm'en's Voting Methods and Justified Representation](https://mlsanity.com/paper/2102.12305/) (2021)
- [Computational Aspects of Multi-Winner Approval Voting](https://mlsanity.com/paper/1407.3247/) (2014)
- [Proportional Rankings](https://mlsanity.com/paper/1612.01434/) (2016)
- [What Do Multiwinner Voting Rules Do? An Experiment Over the Two-Dimensional Euclidean Domain](https://mlsanity.com/paper/1901.09217/) (2019)
- [Online Approval Committee Elections](https://mlsanity.com/paper/2202.06830/) (2022)
- [Proportionally Fair Online Allocation of Public Goods with Predictions](https://mlsanity.com/paper/2209.15305/) (2022)
- [Approval-Based Apportionment](https://mlsanity.com/paper/1911.08365/) (2019)
- [Proportionality Degree of Multiwinner Rules](https://mlsanity.com/paper/1810.08799/) (2018)
- [Phragm'en's and Thiele's election methods](https://mlsanity.com/paper/1611.08826/) (2016)
- [Strategyproofness and Proportionality in Party-Approval Multiwinner Elections](https://mlsanity.com/paper/2211.13567/) (2022)
- [Privacy-preserving Crowd-guided AI Decision-making in Ethical Dilemmas](https://mlsanity.com/paper/1906.01562/) (2019)
- [Proportionality and Strategyproofness in Multiwinner Elections](https://mlsanity.com/paper/2104.08594/) (2021)

## Built on by (most cited first, 17 of 17)

- [Temporal Elections: Welfare, Strategyproofness, and Proportionality](https://mlsanity.com/paper/2408.13637/) (2024)
- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Multiwinner Temporal Voting with Aversion to Change](https://mlsanity.com/paper/2408.11017/) (2024)
- [Strengthening Proportionality in Temporal Voting](https://mlsanity.com/paper/2505.22513/) (2025)
- [Online Fair Division with Additional Information](https://mlsanity.com/paper/2505.24503/) (2025)
- [Not in My Backyard! Temporal Voting Over Public Chores](https://mlsanity.com/paper/2508.08810/) (2025)
- [Approximate Proportionality in Online Fair Division](https://mlsanity.com/paper/2508.03253/) (2025)
- [The Price of Proportional Representation in Temporal Voting](https://mlsanity.com/paper/2605.11157/) (2026)
- [Fairness in Repeated Matching: A Maximin Perspective](https://mlsanity.com/paper/2510.04624/) (2025)
- [Artificial Delegates Resolve Fairness Issues in Perpetual Voting with Partial Turnout](https://mlsanity.com/paper/2506.21186/) (2025)
- [Learning the Value Systems of Agents with Preference-based and Inverse Reinforcement Learning](https://mlsanity.com/paper/2602.04518/) (2026)
- [The End Justifies the Mean: A Linear Ranking Rule for Proportional Sequential Decisions](https://mlsanity.com/paper/2605.12717/) (2026)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [Efficient Algorithms for Electing Successive Committees](https://mlsanity.com/paper/2505.18287/) (2025)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [Rules Before Oracles: Auditable, User-Configurable Argument Selection for Deliberative Polling](https://mlsanity.com/paper/2608.23979/) (2026)
- [Proportional Representation in Temporal Voting with Ranked Preferences](https://mlsanity.com/paper/2609.30555/) (2026)

## Abstract (arXiv)

We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of going with the most popular choice in each round, we aim for proportional representation across rounds, using axioms inspired by the multi-winner voting literature. The axioms require that every group of α% of the voters that agrees in every round (i.e., approves a common alternative), must approve at least α% of the decisions. A stronger version of the axioms requires that every group of α% of the voters that agrees in a β fraction of rounds must approve β·α% of the decisions. We show that three attractive voting rules satisfy axioms of this style. One of them (Sequential Phragm'en) makes its decisions online, and the other two satisfy strengthened versions of the axioms but make decisions semi-online (Method of Equal Shares) or fully offline (Proportional Approval Voting). We present empirical results for these rules based on synthetic data and U.S. political elections. We also run experiments using the moral machine dataset about ethical dilemmas: We train preference models on user responses from different countries and let the models cast votes. We find that aggregating these votes using our rules leads to a more equal utility distribution across demographics than making decisions using a single global preference model.