Random priority item allocation
Random priority item allocation
- Random priority (RP), also called random serial dictatorship** (RSD), is a procedure for [[fair-random-assignment]] - dividing indivisible items fairly among people.
Suppose <math>n</math> partners have to divide <math>n</math> (or fewer) different items among them. Since the items are indivisible, some partners will necessarily get the less-preferred items (or no items at all). RSD attempts to insert fairness into this situation in the following way. Draw a random permutation of the agents from the uniform distribution. Then, let them successively choose an object in that order (so the first agent in the ordering gets first pick and so on).
Properties RSD is a truthful mechanism when the number of items is at most the number of agents, since you only have one opportunity to pick an item, and the obviously dominant strategy in this opportunity is to pick the best available item.
RSD always yields an ex-post Pareto efficient (PE) outcome. Moreover, in an assignment problem, every deterministic PE assignment is the outcome of SD for some ordering of the agents.
An alternative rule, the probabilistic-serial rule, is sd-efficient (which implies ex-post PE) and sd-envy-free (which implies ex-ante envy-freeness), but it is not truthful. It is impossible to enjoy the advantages of both mechanisms:
- With cardinal additive utility functions, no mechanism is symmetric, truthful and ex-ante PE.
- With ordinal utility functions, no mechanism is sd-efficient, strategyproof, and treats equals equally. When agents can have weak preferences, however, no procedure that extends RD (which includes RSD) satisfies both efficiency and strategyproofness.