In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans.

In algorithmically fair prediction problems, a standard goal is to ensure the equality of fairness metrics across multiple overlapping groups simultaneously.

We thank the reviewers for their insightful comments. We have done experiments showing that the Sortition Foundation's greedy algorithm gives Thanks for suggesting Banaszczyk's result: an algorithmic version is in [2,Thm 5.3]. Additionally, in Appendix D.4, we provide several pieces of

In algorithmically fair prediction problems, a standard goal is to ensure the equality of fairness metrics across multiple overlapping groups simultaneously.

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans.

This paper describes the construction of a dataset and the evaluation of training methods to improve generative large language models' (LLMs) ability to answer queries on sensitive topics with a Neutral Point of View (NPOV), i.e., to provide significantly more informative, diverse and impartial answers. The dataset, the SHQ-NPOV dataset, comprises 300 high-quality, human-written quadruplets: a query on a sensitive topic, an answer, an NPOV rating, and a set of links to source texts elaborating the various points of view. The first key contribution of this paper is a new methodology to create such datasets through iterative rounds of human peer-critique and annotator training, which we release alongside the dataset. The second key contribution is the identification of a highly effective training regime for parameter-efficient reinforcement learning (PE-RL) to improve NPOV generation. We compare and extensively evaluate PE-RL and multiple baselines-including LoRA finetuning (a strong baseline), SFT and RLHF. PE-RL not only improves on overall NPOV quality compared to the strongest baseline ($97.06\%\rightarrow 99.08\%$), but also scores much higher on features linguists identify as key to separating good answers from the best answers ($60.25\%\rightarrow 85.21\%$ for presence of supportive details, $68.74\%\rightarrow 91.43\%$ for absence of oversimplification). A qualitative analysis corroborates this. Finally, our evaluation finds no statistical differences between results on topics that appear in the training dataset and those on separated evaluation topics, which provides strong evidence that our approach to training PE-RL exhibits very effective out of topic generalization.

In representative democracy, a redistricting map is chosen to partition an electorate into a collection of districts each of which elects a representative. A valid redistricting map must satisfy a collection of constraints such as being compact, contiguous, and of almost equal population. However, these imposed constraints are still loose enough to enable an enormous ensemble of valid redistricting maps. This fact introduces a difficulty in drawing redistricting maps and it also enables a partisan legislature to possibly gerrymander by choosing a map which unfairly favors it. In this paper, we introduce an interpretable and tractable distance measure over redistricting maps which does not use election results and study its implications over the ensemble of redistricting maps. Specifically, we define a central map which may be considered as being "most typical" and give a rigorous justification for it by showing that it mirrors the Kemeny ranking in a scenario where we have a committee voting over a collection of redistricting maps to be drawn. We include run-time and sample complexity analysis for our algorithms, including some negative results which hold using any algorithm. We further study outlier detection based on this distance measure. More precisely, we show gerrymandered maps that lie very far away from our central maps in comparison to a large ensemble of valid redistricting maps. Since our distance measure does not rely on election results, this gives a significant advantage in gerrymandering detection which is lacking in all previous methods.