Eliciting Preference Intensities in Efficient Assignment Design

Abstract

We study the problem of designing a truthful mechanism for allocation problems. Currently, allocation mechanisms typically only take into account an agent's ordinal ranking of items and disregard the intensity of preferences. We show that a mechanism involving preference intensity, known as a cardinal mechanism, can be constructed from an ordinal mechanism by combining modifications which are individually incentive-compatible. Next, we use this procedure to construct a cardinal mechanism for the balanced allocation problem with n=3, using random serial dictatorship (RSD) as a starting point. Finally, we compare the efficiency of this cardinal mechanism against RSD. For the examined settings, the relative efficiency of the constructed mechanism is between 2% and 40% higher than RSD and monotonically increasing in the degree of correlation between agents' ordinal preferences. These results demonstrate the potential of carefully designed cardinal mechanisms for improving allocation outcomes when agents value objects in similar orders, but with varying intensities.