Item-side group fairness (IGF) requires a recommendation model to treat different item groups similarly, and has a crucial impact on information diffusion, consumption activity, and market equilibrium. Previous IGF notions only focus on the direct utility of the item exposures, i.e., the exposure numbers across different item groups. Nevertheless, the item exposures also facilitate utility gained from the neighboring users via social influence, called social utility, such as information sharing on the social media. To fill this gap, this paper introduces two social attribute-aware IGF metrics, which require similar user social attributes on the exposed items across the different item groups. In light of the trade-off between the direct utility and social utility, we formulate a new multi-objective optimization problem for training recommender models with flexible trade-off while ensuring controllable accuracy. To solve this problem, we develop a gradient-based optimization algorithm and theoretically show that the proposed algorithm can find Pareto optimal solutions with varying trade-off and guaranteed accuracy.

Previous IGF notions only focus on the direct utility of the item exposures, i.e., the exposure numbers across different item groups.

Value trade-offs are an integral part of human decision-making and language use, however, current tools for interpreting such dynamic and multi-faceted notions of values in LLMs are limited. In cognitive science, so-called "cognitive models" provide formal accounts of such trade-offs in humans, by modeling the weighting of a speaker's competing utility functions in choosing an action or utterance. Here we use a leading cognitive model of polite speech to systematically evaluate value trade-offs in two encompassing model settings: degrees of reasoning "effort" in frontier black-box models, and RL post-training dynamics of open-source models. Our results highlight patterns of higher informational utility than social utility in reasoning models' default behavior, and demonstrate that these patterns shift in predictable ways when models are prompted to prioritize certain goals over others. Our findings from LLMs' training dynamics suggest large shifts in utility values early on in training with persistent effects of the choice of base model and pretraining data, compared to feedback dataset or alignment method. Our framework offers a flexible tool for probing value trade-offs across diverse model types, providing insights for generating hypotheses about other social behaviors such as sycophancy and for shaping training regimes that better control trade-offs between values during model development.

Item-side group fairness (IGF) requires a recommendation model to treat different item groups similarly, and has a crucial impact on information diffusion, consumption activity, and market equilibrium. Previous IGF notions only focus on the direct utility of the item exposures, i.e., the exposure numbers across different item groups. Nevertheless, the item exposures also facilitate utility gained from the neighboring users via social influence, called social utility, such as information sharing on the social media. To fill this gap, this paper introduces two social attribute-aware IGF metrics, which require similar user social attributes on the exposed items across the different item groups. In light of the trade-off between the direct utility and social utility, we formulate a new multi-objective optimization problem for training recommender models with flexible trade-off while ensuring controllable accuracy.

We study the mechanism design problem of a social planner for locating two facilities on a line interval [0, 1], where a set of n strategic agents report their locations and a mechanism determines the locations of the two facilities. We consider the requirement of a minimum distance 0 ≤ d ≤ 1 between the two facilities. Given the two facilities are heterogeneous, we model the cost/utility of an agent as the sum of his distances to both facilities. In the heterogeneous two-facility location game to minimize the social cost, we show that the optimal solution can be computed in polynomial time and prove that carefully choosing one optimal solution as output is strategyproof. We also design a strategyproof mechanism minimizing the maximum cost. Given the two facilities are homogeneous, we model the cost/utility of an agent as his distance to the closer facility. In the homogeneous two-facility location game for minimizing the social cost, we show that any deterministic strategyproof mechanism has unbounded approximation ratio. Moreover, in the obnoxious heterogeneous two-facility location game for maximizing the social utility, we propose new deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound (7 − d)/6 for any deterministic strategyproof mechanism. We also design a strategyproof mechanism maximizing the minimum utility. In the obnoxious homogeneous two-facility location game for maximizing the social utility, we propose deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound 4/3. Besides, in the two-facility location game with triple-preference, where each facility may be favorable, obnoxious, indifferent for any agent, we further motivate agents to report both their locations and preferences towards the two facilities truthfully, and design a deterministic group strategyproof mechanism with an approximation ratio 4.

In this paper, we propose a fractional preference model for the facility location game with two facilities that serve the similar purpose on a line where each agent has his location information as well as fractional preference to indicate how well they prefer the facilities. The preference for each facility is in the range of [0, L] such that the sum of the preference for all facilities is equal to 1. The utility is measured by subtracting the sum of the cost of both facilities from the total length L where the cost of facilities is defined as the multiplication of the fractional preference and the distance between the agent and the facilities. We first show that the lower bound for the objective of minimizing total cost is at least Ω(n^1/3). Hence, we use the utility function to analyze the agents' satification. Our objective is to place two facilities on [0, L] to maximize the social utility or the minimum utility. For each objective function, we propose deterministic strategy-proof mechanisms. For the objective of maximizing the social utility, we present an optimal deterministic strategy-proof mechanism in the case where agents can only misreport their locations. In the case where agents can only misreport their preferences, we present a 2-approximation deterministic strategy-proof mechanism. Finally, we present a 4-approximation deterministic strategy-proof mechanism and a randomized strategy-proof mechanism with an approximation ratio of 2 where agents can misreport both the preference and location information. Moreover, we also give a lower-bound of 1.06. For the objective of maximizing the minimum utility, we give a lower-bound of 1.5 and present a 2-approximation deterministic strategy-proof mechanism where agents can misreport both the preference and location.

We study hybrid online-batch matching problems, where agents arrive continuously, but are only matched in periodic rounds, when many of them can be considered simultaneously. Agents not getting matched in a given round remain in the market for the next round. This setting models several scenarios of interest, including many job markets as well as kidney exchange mechanisms. We consider the social utility of two commonly used mechanisms for such markets: one that aims for stability in each round (greedy), and one that attempts to maximize social utility in each round (max-weight). Surprisingly, we find that in the long term, the social utility of the greedy mechanism can be higher than that of the max-weight mechanism. We hypothesize that this is because the greedy mechanism behaves similarly to a soft threshold mechanism, where all connections below a certain threshold are rejected by the participants in favor of waiting until the next round. Motivated by this observation, we propose a method to approximately calculate the optimal threshold for an individual agent to use based on characteristics of the other agents participating, and demonstrate experimentally that social utility is high when all agents use this strategy. Thresholding can also be applied by the mechanism itself to improve social welfare; we demonstrate this with an example on graphs that model pairwise kidney exchange.