We study a simple variant of the house allocation problem (one-sided matching). We demonstrate that agents with recursive preferences may systematically prefer one allocation mechanism to the other, even among mechanisms that are considered to be the same in standard models, in the sense that they induce the same probability distribution over successful matchings. Using this, we propose a new Priority Groups mechanism and provide conditions under which it is preferred to two popular mechanisms, Random Top Cycle and Random Serial Dictatorship.