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When allocating indivisible items to agents, it is known that the onlystrategyproof mechanisms that satisfy a set of rather mild conditions areconstrained serial dictatorships: given a fixed order over agents, at each stepthe designated agent chooses a given number of items (depending on her positionin the sequence). With these rules, also known as non-interleaving pickingsequences, agents who come earlier in the sequence have a larger choice ofitems. However, this advantage can be compensated by a higher number of itemsreceived by those who come later. How to balance priority in the sequence andnumber of items received is a nontrivial question. We use a previous model,parameterized by a mapping from ranks to scores, a social welfare functional,and a distribution over preference profiles. For several meaningful choices ofparameters, we show that the optimal sequence can be computed in polynomialtime. Last, we give a simple procedure for eliciting scoring vectors and westudy the impact of the assignment from agents to positions on the ex-postsocial welfare.

Thou Shalt not Pick all Items if Thou are First: of Strategyproof and Fair Picking Sequences