# Abductive and Contrastive Explanations for Scoring Rules in Voting

arXiv: https://arxiv.org/abs/2408.12927 · HTML: https://mlsanity.com/paper/2408.12927/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 23 Aug 2024.

## Builds on (most cited first, 14 of 14)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback](https://mlsanity.com/paper/2404.10271/) (2024)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [Proportional Participatory Budgeting with Additive Utilities](https://mlsanity.com/paper/2008.13276/) (2020)
- [On Relating 'Why?' and 'Why Not?' Explanations](https://mlsanity.com/paper/2012.11067/) (2020)
- [A unified logical framework for explanations in classifier systems](https://mlsanity.com/paper/2105.14452/) (2021)
- [Putting a Compass on the Map of Elections](https://mlsanity.com/paper/2105.07815/) (2021)
- [Learning to Elect](https://mlsanity.com/paper/2108.02768/) (2021)
- [Sample Complexity for Winner Prediction in Elections](https://mlsanity.com/paper/1502.04354/) (2015)
- [Diversity, Agreement, and Polarization in Elections](https://mlsanity.com/paper/2305.09780/) (2023)
- [Understanding Political Divisiveness using Online Participation data from the 2022 French and Brazilian Presidential Elections](https://mlsanity.com/paper/2211.04577/) (2022)
- [Computational Complexity Characterization of Protecting Elections from Bribery](https://mlsanity.com/paper/2007.02533/) (2020)

## Built on by (most cited first, 3 of 3)

- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [Explaining Tournament Solutions with Minimal Supports](https://mlsanity.com/paper/2509.09312/) (2025)
- [Characterizing Necessary Losers to Explain Tournaments Solutions](https://mlsanity.com/paper/2608.23446/) (2026)

## Abstract (arXiv)

We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to identify minimal subsets of a preference profile that either imply the current winner or explain why a different candidate was not elected. Formal explanations turn out to have strong connections with classical problems studied in computational social choice such as bribery, possible and necessary winner identification, and preference learning. We design algorithms for computing abductive and contrastive explanations for scoring rules. For the Borda rule, we find a lower bound on the size of the smallest abductive explanations, and we conduct simulations to identify correlations between properties of preference profiles and the size of their smallest abductive explanations.