Participatory Objective Design via Preference Elicitation
Abstract: In standard resource allocation problems, the designer sets the objective function, which captures the central allocation goal, in a top-down manner. The agents primarily participate in the allocation mechanism by reporting their preferences over the items; they cannot influence the objective once the designer sets it. Implicitly, this approach presumes that standard ways of eliciting the agents’ preferences adequately represent their true preferences—an assumption which does not hold if agents have preferences not just over the items they receive but also over the objective being optimized. For instance, agents may also have social preferences, such as inequality-aversion, altruism, or similar other-regarding behavior. We cannot express such preferences through standard cardinal utilities or ordinal rankings over the items the designer would typically elicit from the agents. This work examines how we can use this bottom-up preference elicitation stage to enable participants to express preferences over the objectives. We present a versatile framework that elicits agents’ preferences over a possible set of objectives and then minimally alters the underlying optimization problem to solve for a new objective that combines both the standard benchmark objective and the agents’ preferences for other objectives. We show how to evaluate this new participatory approach against the standard approach, using our notions of loss and gain in social welfare as well as individual tradeoffs. We illustrate the potency of this framework using a well-studied fair division problem where the designer aims to allocate m divisible items to n agents. In the standard setting, the designer optimizes for utilitarian social welfare, i.e., the sum of the agents’ cardinal utilities. We assume that some agents are also inequality-averse and may, therefore, have preferences for objectives that minimize inequality. Using the popular Fehr and Schmidt [31] model, we demonstrate how to map this fair division question to our framework, where the participatory approach optimizes both the standard utilitarian social welfare objective and the agents’ heterogeneous preferences over the level of inequality. We examine this problem theoretically to show that there can be large gains in social welfare if the designer uses this participatory approach. Further, we show that the loss in social welfare is linear in the level of inequality aversion and independent of the number of agents. We present a tighter bound in both cases under further natural assumptions on the preferences. We also examine the worst-case cost an individual agent might incur. Our results indicate that the loss in social welfare (measured by the standard objective) and gain in social welfare (measured by the participatory one) can favor the participatory approach in several natural settings. Throughout the work, we highlight various promising avenues for examining this participatory approach in the specific case study tackled in this paper and a broader range of resource allocation problems.
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