# Quantifying Availability and Discovery in Recommender Systems via Stochastic Reachability

arXiv: https://arxiv.org/abs/2107.00833 · HTML: https://mlsanity.com/paper/2107.00833/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Top-K Off-Policy Correction for a REINFORCE Recommender System](https://mlsanity.com/paper/1812.02353/) (2018)
- [How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility](https://mlsanity.com/paper/1710.11214/) (2017)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [Boltzmann Exploration Done Right](https://mlsanity.com/paper/1705.10257/) (2017)
- [A Troubling Analysis of Reproducibility and Progress in Recommender Systems Research](https://mlsanity.com/paper/1911.07698/) (2019)
- [Auditing Radicalization Pathways on YouTube](https://mlsanity.com/paper/1908.08313/) (2019)
- [On the Difficulty of Evaluating Baselines: A Study on Recommender Systems](https://mlsanity.com/paper/1905.01395/) (2019)
- [Exploring Author Gender in Book Rating and Recommendation](https://mlsanity.com/paper/1808.07586/) (2018)
- [Do Offline Metrics Predict Online Performance in Recommender Systems?](https://mlsanity.com/paper/2011.07931/) (2020)
- [Recommendations and User Agency: The Reachability of Collaboratively-Filtered Information](https://mlsanity.com/paper/1912.10068/) (2019)
- [Measuring Recommender System Effects with Simulated Users](https://mlsanity.com/paper/2101.04526/) (2021)
- [Exploring Artist Gender Bias in Music Recommendation](https://mlsanity.com/paper/2009.01715/) (2020)
- [How the Design of YouTube Influences User Sense of Agency](https://mlsanity.com/paper/2101.11778/) (2021)
- [The Impact of Popularity Bias on Fairness and Calibration in Recommendation](https://mlsanity.com/paper/1910.05755/) (2019)
- [A Longitudinal Analysis of YouTube's Promotion of Conspiracy Videos](https://mlsanity.com/paper/2003.03318/) (2020)

## Built on by (most cited first, 8 of 8)

- [Modeling Content Creator Incentives on Algorithm-Curated Platforms](https://mlsanity.com/paper/2206.13102/) (2022)
- [The Minority Matters: A Diversity-Promoting Collaborative Metric Learning Algorithm](https://mlsanity.com/paper/2209.15292/) (2022)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Rewiring What-to-Watch-Next Recommendations to Reduce Radicalization Pathways](https://mlsanity.com/paper/2202.00640/) (2022)
- [CTRL-Rec: Controlling Recommender Systems With Natural Language](https://mlsanity.com/paper/2510.12742/) (2025)
- [Datasets for Navigating Sensitive Topics in Recommendation Systems](https://mlsanity.com/paper/2509.07269/) (2025)
- [A Unified Causal Framework for Auditing Recommender Systems for Ethical Concerns](https://mlsanity.com/paper/2409.13210/) (2024)
- [The User Asks, Platforms Compete: How Agentic Recommendation Markets Take Shape](https://mlsanity.com/paper/2607.25253/) (2026)

## Abstract (arXiv)

In this work, we consider how preference models in interactive recommendation systems determine the availability of content and users' opportunities for discovery. We propose an evaluation procedure based on stochastic reachability to quantify the maximum probability of recommending a target piece of content to an user for a set of allowable strategic modifications. This framework allows us to compute an upper bound on the likelihood of recommendation with minimal assumptions about user behavior. Stochastic reachability can be used to detect biases in the availability of content and diagnose limitations in the opportunities for discovery granted to users. We show that this metric can be computed efficiently as a convex program for a variety of practical settings, and further argue that reachability is not inherently at odds with accuracy. We demonstrate evaluations of recommendation algorithms trained on large datasets of explicit and implicit ratings. Our results illustrate how preference models, selection rules, and user interventions impact reachability and how these effects can be distributed unevenly.