Citation:
Abstract:
In standard resource allocation problems, the designer sets the objective---such as utilitarian social welfare---that captures a societal goal and solves for the optimal allocation subject to fairness and item availability constraints. The participants, on the other hand, specify their preferences for the items being allocated, e.g., through stating how they rank the items or expressing their cardinal utility for each item. The objective function, which guides the overall allocation, is therefore determined by the designer in a top-down manner, whereas participants can only express their preferences for the items. This standard preference elicitation stage limits participants' ability to express preferences for the overall allocation, such as the level of inequality, and influence the overall objective function.
In this work, we examine whether it is possible to use this bottom-up preference elicitation stage to enable participants to express not only their preferences for individual items but also their preferences for the overall allocation, thereby indirectly influencing the objective function. We examine this question using a well-studied resource allocation problem where mm divisible items must be allocated to nn agents, who express their cardinal utilities over the items. The designer aims to optimize for the sum of the agents' utilities for the items they receive. In particular, this utilitarian objective is agnostic to the overall inequality level. We consider a setting where the agents' true utility is a function not only of their preferences for the items, but also the overall level of inequality. We model this using a popular social preference model from behavioral economics by \citeauthor{fehr1999theory}, where agents can express levels of inequality aversion.
We conduct a theoretical examination of this problem and show that there can be large gains in social welfare if the designer uses this richer inequality-aware preference model, instead of the standard inequality-agnostic preference model. Further, if we take the standard inequality-agnostic welfare as the benchmark, we show that the relative loss of welfare can be tightly bounded--shown to be independent of the number of agents and linear in the level of inequality aversion. With further assumptions on the preferences, we provide strictly tighter, distribution-free, and parametric bounds on the loss of welfare. We also discuss the worst-case drop in inequality-agnostic utility an agent might incur as a consequence of a designer allocating items using the inequality-averse preferences. We conclude with a discussion on possible designs to elicit the preferences of strategic agents over the goods and fairness. Taken together, our results argue for potentially large gains that can be obtained from using the richer social preference model and demonstrate the relatively minor losses from using the standard model, highlighting a promising avenue for using preference elicitation to empower participants to influence the overall objective function.