Current approaches to mitigate these representational harms balance the number of retrieved items across population groups defined by a small number of (often binary) attributes. However, most existing methods overlook intersectional groups determined by combinations of group attributes, such as gender, race, and ethnicity.

Location-based vehicular traffic management faces significant challenges in protecting sensitive geographical data while maintaining utility for traffic management and fairness across regions. Existing state-of-the-art solutions often fail to meet the required level of protection against linkage attacks and demographic biases, leading to privacy leakage and inequity in data analysis. In this paper, we propose a novel algorithm designed to address the challenges regarding the balance of privacy, utility, and fairness in location-based vehicular traffic management systems. In this context, utility means providing reliable and meaningful traffic information, while fairness ensures that all regions and individuals are treated equitably in data use and decision-making. Employing differential privacy techniques, we enhance data security by integrating query-based data access with iterative shuffling and calibrated noise injection, ensuring that sensitive geographical data remains protected. We ensure adherence to epsilon-differential privacy standards by implementing the Laplace mechanism. We implemented our algorithm on vehicular location-based data from Norway, demonstrating its ability to maintain data utility for traffic management and urban planning while ensuring fair representation of all geographical areas without being overrepresented or underrepresented. Additionally, we have created a heatmap of Norway based on our model, illustrating the privatized and fair representation of the traffic conditions across various cities. Our algorithm provides privacy in vehicular traffic

In multiwinner approval voting, forming a committee that proportionally represents voters' approval ballots is an essential task. The notion of justified representation (JR) demands that any large "cohesive" group of voters should be proportionally "represented". The "cohesiveness" is defined in different ways; two common ways are the following: (C1) demands that the group unanimously approves a set of candidates proportional to its size, while (C2) requires each member to approve at least a fixed fraction of such a set. Similarly, "representation" have been considered in different ways: (R1) the coalition's collective utility from the winning set exceeds that of any proportionally sized alternative, and (R2) for any proportionally sized alternative, at least one member of the coalition derives less utility from it than from the winning set. Three of the four possible combinations have been extensively studied: (C1)-(R1) defines Proportional Justified Representation (PJR), (C1)-(R2) defines Extended Justified Representation (EJR), (C2)-(R2) defines Full Justified Representation (FJR). All three have merits, but also drawbacks. PJR is the weakest notion, and perhaps not sufficiently demanding; EJR may not be compatible with perfect representation; and it is open whether a committee satisfying FJR can be found efficiently. We study the combination (C2)-(R1), which we call Full Proportional Justified Representation (FPJR). We investigate FPJR's properties and find that it shares PJR's advantages over EJR: several proportionality axioms (e.g. priceability, perfect representation) imply FPJR and PJR but not EJR. We also find that efficient rules like the greedy Monroe rule and the method of equal shares satisfy FPJR, matching a key advantage of EJR over FJR. However, the Proportional Approval Voting (PAV) rule may violate FPJR, so neither of EJR and FPJR implies the other.

Fairness in multi-document summarization (MDS) measures whether a system can generate a summary fairly representing information from documents with different social attribute values. Fairness in MDS is crucial since a fair summary can offer readers a comprehensive view. Previous works focus on quantifying summary-level fairness using Proportional Representation, a fairness measure based on Statistical Parity. However, Proportional Representation does not consider redundancy in input documents and overlooks corpus-level unfairness. In this work, we propose a new summary-level fairness measure, Equal Coverage, which is based on coverage of documents with different social attribute values and considers the redundancy within documents. To detect the corpus-level unfairness, we propose a new corpus-level measure, Coverage Parity. Our human evaluations show that our measures align more with our definition of fairness. Using our measures, we evaluate the fairness of thirteen different LLMs. We find that Claude3-sonnet is the fairest among all evaluated LLMs. We also find that almost all LLMs overrepresent different social attribute values.

We introduce a novel definition for a small set R of k points being "representative" of a larger set in a metric space. Given a set V (e.g., documents or voters) to represent, and a set C of possible representatives, our criterion requires that for any subset S comprising a theta fraction of V, the average distance of S to their best theta*k points in R should not be more than a factor gamma compared to their average distance to the best theta*k points among all of C. This definition is a strengthening of proportional fairness and core fairness, but - different from those notions - requires that large cohesive clusters be represented proportionally to their size. Since there are instances for which - unless gamma is polynomially large - no solutions exist, we study this notion in a resource augmentation framework, implicitly stating the constraints for a set R of size k as though its size were only k/alpha, for alpha > 1. Furthermore, motivated by the application to elections, we mostly focus on the "ordinal" model, where the algorithm does not learn the actual distances; instead, it learns only for each point v in V and each candidate pairs c, c' which of c, c' is closer to v. Our main result is that the Expanding Approvals Rule (EAR) of Aziz and Lee is (alpha, gamma) representative with gamma <= 1 + 6.71 * (alpha)/(alpha-1). Our results lead to three notable byproducts. First, we show that the EAR achieves constant proportional fairness in the ordinal model, giving the first positive result on metric proportional fairness with ordinal information. Second, we show that for the core fairness objective, the EAR achieves the same asymptotic tradeoff between resource augmentation and approximation as the recent results of Li et al., which used full knowledge of the metric. Finally, our results imply a very simple single-winner voting rule with metric distortion at most 44.

Real-life tools for decision-making in many critical domains are based on ranking results. With the increasing awareness of algorithmic fairness, recent works have presented measures for fairness in ranking. Many of those definitions consider the representation of different ``protected groups'', in the top-$k$ ranked items, for any reasonable $k$. Given the protected groups, confirming algorithmic fairness is a simple task. However, the groups' definitions may be unknown in advance. In this paper, we study the problem of detecting groups with biased representation in the top-$k$ ranked items, eliminating the need to pre-define protected groups. The number of such groups possible can be exponential, making the problem hard. We propose efficient search algorithms for two different fairness measures: global representation bounds, and proportional representation. Then we propose a method to explain the bias in the representations of groups utilizing the notion of Shapley values. We conclude with an experimental study, showing the scalability of our approach and demonstrating the usefulness of the proposed algorithms.

This work tackles the issue of fairness in the context of generative procedures, such as image super-resolution, which entail different definitions from the standard classification setting. Moreover, while traditional group fairness definitions are typically defined with respect to specified protected groups -- camouflaging the fact that these groupings are artificial and carry historical and political motivations -- we emphasize that there are no ground truth identities. For instance, should South and East Asians be viewed as a single group or separate groups? Should we consider one race as a whole or further split by gender? Choosing which groups are valid and who belongs in them is an impossible dilemma and being "fair" with respect to Asians may require being "unfair" with respect to South Asians. This motivates the introduction of definitions that allow algorithms to be \emph{oblivious} to the relevant groupings. We define several intuitive notions of group fairness and study their incompatibilities and trade-offs. We show that the natural extension of demographic parity is strongly dependent on the grouping, and \emph{impossible} to achieve obliviously. On the other hand, the conceptually new definition we introduce, Conditional Proportional Representation, can be achieved obliviously through Posterior Sampling. Our experiments validate our theoretical results and achieve fair image reconstruction using state-of-the-art generative models.

Citizens' assemblies need to represent subpopulations according to their proportions in the general population. These large committees are often constructed in an online fashion by contacting people, asking for the demographic features of the volunteers, and deciding to include them or not. This raises a trade-off between the number of people contacted (and the incurring cost) and the representativeness of the committee. We study three methods, theoretically and experimentally: a greedy algorithm that includes volunteers as long as proportionality is not violated; a non-adaptive method that includes a volunteer with a probability depending only on their features, assuming that the joint feature distribution in the volunteer pool is known; and a reinforcement learning based approach when this distribution is not known a priori but learnt online.

We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should have. We look for a set that fits as much as possible the desired distributions on all attributes. Examples of applications include choosing members of a representative committee, where candidates are described by attributes such as sex, age and profession, and where we look for a committee that for each attribute offers a certain representation, i.e., a single committee that contains a certain number of young and old people, certain number of men and women, certain number of people with different professions, etc. With a single attribute the problem collapses to the apportionment problem for party-list proportional representation systems (in such case the value of the single attribute would be a political affiliation of a candidate). We study the properties of the associated subset selection rules, as well as their computation complexity.