# Fair mixing: the case of dichotomous preferences

arXiv: https://arxiv.org/abs/1712.02542 · HTML: https://mlsanity.com/paper/1712.02542/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2017.

## Built on by (most cited first, 14 of 14)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Proportionally Representative Clustering](https://mlsanity.com/paper/2304.13917/) (2023)
- [Strategyproof and Proportionally Fair Facility Location](https://mlsanity.com/paper/2111.01566/) (2021)
- [Method of Equal Shares with Bounded Overspending](https://mlsanity.com/paper/2409.15005/) (2024)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism](https://mlsanity.com/paper/2205.14798/) (2022)
- [Proportional Fairness in Obnoxious Facility Location](https://mlsanity.com/paper/2301.04340/) (2023)
- [Maxmin Participatory Budgeting](https://mlsanity.com/paper/2204.13923/) (2022)
- [Indivisible Participatory Budgeting under Weak Rankings](https://mlsanity.com/paper/2207.07981/) (2022)
- [Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences](https://mlsanity.com/paper/2207.07984/) (2022)
- [Nash Welfare and Facility Location](https://mlsanity.com/paper/2310.04102/) (2023)
- [Generating Fair Consensus Statements with Social Choice on Token-Level MDPs](https://mlsanity.com/paper/2510.14106/) (2025)
- [Fair Transit Stop Placement: A Clustering Perspective and Beyond](https://mlsanity.com/paper/2602.06776/) (2026)
- [Aggregating Correlated Estimations with (Almost) no Training](https://mlsanity.com/paper/2309.02005/) (2023)

## Abstract (arXiv)

Agents vote to choose a fair mixture of public outcomes; each agent likes or dislikes each outcome. We discuss three outstanding voting rules. The Conditional Utilitarian rule, a variant of the random dictator, is Strategyproof and guarantees to any group of like-minded agents an influence proportional to its size. It is easier to compute and more efficient than the familiar Random Priority rule. Its worst case (resp. average) inefficiency is provably (resp. in numerical experiments) low if the number of agents is low. The efficient Egalitarian rule protects similarly individual agents but not coalitions. It is Excludable Strategyproof: I do not want to lie if I cannot consume outcomes I claim to dislike. The efficient Nash Max Product rule offers the strongest welfare guarantees to coalitions, who can force any outcome with a probability proportional to their size. But it fails even the excludable form of Strategyproofness.