Balancing Fairness, Efficiency and Strategy-Proofness in Voting and Facility Location Problems

In the field of computational social choice, researchers seek mechanisms that fulfil the notion of strategy-proofness, so that it is optimal for agents to simply report their truthful preferences. This notion can be very difficult to achieve, and mechanisms that satisfy this strict constraint often sacrifice ideal properties such as fairness and efficiency. For example, a surjective voting rule satisfying strategyproofness must be dictatorial, which may be considered unfair and wasteful to the voters, as it only takes into account one voter's preference. Strategy-proof facility location mechanisms are also known to be sub-optimal in terms of fairness, and in some scenarios, efficiency. Focussing on these two areas, we question if strategy-proofness is too strict of a constraint, and to what extent are mechanisms satisfying weaker variations of the property more fair and efficient.