Shivika Narang

Haris Aziz, Shivika Narang, Mashbat Suzuki

We propose a new model for aggregating preferences over a set of indivisible items based on a quantile value. In this model, each agent is endowed with a specific quantile, and the value of a given bundle is defined by the corresponding quantile of the individual values of the items within it. Our model captures the diverse ways in which agents may perceive a bundle, even when they agree on the values of individual items. It enables richer behavioral modeling that cannot be easily captured by additive valuation functions. We study the problem of maximizing utilitarian and egalitarian welfare within the quantile-based valuation setting. For each of the welfare functions, we analyze the complexity of the objectives. Interestingly, our results show that the complexity of both objectives varies significantly depending on whether the allocation is required to be balanced. We provide near-optimal approximation algorithms for utilitarian welfare, and for egalitarian welfare, we present exact algorithms whenever possible.

Haris Aziz, Nicholas Mattei, Shivika Narang et al.

We introduce a novel collective decision making problem that captures the ubiquitous issue of ordering food to cater for varied dietary preferences and requirements. Our settings involve agents with diverse dietary requirements over menu options with varied serving sizes. The goal is to select a menu where everyone has enough food they can consume and wastage of food is minimized. We introduce two different consumption models: optimistic and pessimistic. Optimistic consumption assumes a situation when a central planner can optimally allocate the food ordered among the agents to maximize the number of people who get enough to eat. Pessimistic considers the worst case guarantee on consumption when agents fill their own plates in an arbitrary order. Under either consumption model, we seek valid menus (under which all agents are sufficiently fed) of minimum size. Our work provides two sets of characterizations: (1) we characterize valid menus under either consumption model and (2) we characterize the space of instances that admit polynomial-time algorithms to find minimum sized menus. Our results also help us design Integer Linear Programs to find minimum sized menus in general settings. Furthermore, we present polynomial-time algorithms for important special cases. We then consider the worst case discrepancy between the size of minimum sized optimistic and pessimistic menus. We call this the waste of pessimism, captured by the ratio of the minimum sized pessimistic menu to that of the minimum sized optimistic menu. We show tight upper bounds on this ratio. Our results also provide additional insights on the problem of finding a minimum sized maximal matching, which may be of independent interest.