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Abstract A particular adaptation of Gale's top trading cycles (TTC) procedure applied to school choice, the so‐called TTC mechanism, has attracted much attention both in theory and practice due to its superior efficiency and incentive features. We discuss and introduce alternative adaptations of Gale's original procedure that can offer improvements over TTC in terms of equity, along with various other distributional considerations. Instead of giving all the trading power to those students with the highest priority for a school, we argue for the distribution of the trading rights of all slots of each school: This allows them to trade in a thick market where additional constraints can be accommodated by choosing an appropriate pointing rule. We propose a particular mechanism of this kind, the equitable top trading cycle (ETTC) mechanism, which is also Pareto efficient and group strategy‐proof just like TTC and eliminates avoidable justified envy situations. ETTC generates significantly fewer justified envy situations than TTC both in simulations and the lab.
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