The Distortion of Cardinal Preferences in Voting

The theoretical guarantees provided by voting have distinguished it as a prominent method of preference aggregation among autonomous agents. However, unlike humans, agents usually assign each candidate an exact utility, whereas an election is resolved based solely on each voter’s linear ordering of candidates. In essence, the agents’ cardinal (utility-based) preferences are embedded into the space of ordinal preferences. This often gives rise to a distortion in the preferences, and hence in the social welfare of the outcome. In this paper, we formally define and analyze the concept of distortion. We fully characterize the distortion under different restrictions imposed on agents’ cardinal preferences; both possibility and strong impossibility results are established. We also tackle some computational aspects of calculating the distortion. Ultimately, we argue that, whenever voting is applied in a multiagent system, distortion must be a pivotal consideration.