🤖 AI Summary
This paper addresses proportional representation in multi-round sequential decision-making: ensuring that any α%-consensus voter group receives representation in approximately α% of rounds under sequential approval voting. It systematically adapts proportional representation axioms—previously defined for multi-winner elections—to the sequential setting, introducing three novel rule families: online (Sequential Phragmén), semi-online (Method of Equal Shares), and offline (Proportional Approval Voting), each satisfying distinct strength levels of proportionality axioms. Leveraging load-balancing, resource-allocation, and global-optimization mechanisms, the rules are evaluated on synthetic data, U.S. election data, and Moral Machine ethical preference data. Results demonstrate that, compared to conventional global aggregation methods, the proposed rules significantly improve equality in utility distribution across demographic groups. This confirms proportional aggregation as a critical pathway toward fair sequential decision-making.
📝 Abstract
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, using axioms inspired by the multi-winner voting literature. The axioms require that every group of α% of the voters, if it agrees in every round (i.e., approves a common alternative), then those voters 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 Phragmén) 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.
