School Choice and Loss Aversion

Abstract

Extensive evidence suggests that participants in the direct student-proposing deferred-acceptance mechanism (DSPDA) play dominated strategies. In particular, students with low priority tend to misrepresent their preferences for popular schools. To explain the observed data, we introduce expectationbased loss aversion into a school-choice setting and characterize choiceacclimating personal equilibria in DSPDA. Truthful equilibria can fail to exist, and DSPDA might implement unstable and more inefficient allocations in both small and large markets. Specifically, it discriminates against students who are more loss averse or less overconfident than their peers, and amplifies already existing (or perceived) discrimination. To level the playing field, we propose serial dictatorship mechanisms as a strategyproof and stable alternative that is robust to these biases.

Report-Dependent Utility and Strategy-Proofness

“…If a market designer desires to implement allocations that are e cient or stable with respect to report-independent preferences, report-dependent payo↵s may obstruct this goal. If misrepresentations are caused by disappointment aversion, it might be beneficial to tell participants that rejections are common in order to reduce the weight of gain-loss utility, parameter ⌘ in Dreyfuss et al (2019) or Meisner and von Wangenheim (2021). Here, the e↵ect of such an announcement is ambiguous.…”

“…However, informing participants about rejections from options they did not even apply to may seem unnecessarily mean. In settings with a non-strategic market side with homogeneous preferences over participants, sequential serial dictatorship could reduce misrepresentations by letting participants choose sequentially in order of their priority as suggested by Li (2017) or Meisner and von Wangenheim (2021). When participants only select from a pool of options left once it is their turn to choose, the unattainability of preferred options does not influence their choice, and they can also credibly brag that they obtained their most-preferred option.…”

“…3 Consequently, both theories can be disentangled. In contrast to Meisner and von Wangenheim (2021), who find that only top-choice monotone ROLs can be rationalized, we can for each ROL construct environments, in which this ROL is optimal.…”

“…While Antler (2015) considers preferences that directly depend on the reported preferences of others, we consider preferences that directly depend on the own report. Dreyfuss et al (2019) and Meisner and von Wangenheim (2021) study DA with expectation-based loss aversion, where proposers use the ROL to manage their expectations, which become their reference point. As in this paper, beliefs become crucial while they generically do not a↵ect behavior in the classical framework.…”

“…Meisner and von Wangenheim (2021) introduce this terminology in their Lemma 1, which holds for all strategy-proof mechanisms.6 Our model has strictly decreasing functions ⇢. If, for instance, ⇢(r) = ⇢(n) for all r r, it is always weakly optimal to rank options in their true order from rank r onward.…”