We analyze the relation between strategy-proofness and preference reversal in the case that agents may declare indifference. Interestingly, Berga and Moreno (2020) have recently derived preference reversal from group strategy-proofness of social choice functions on strict preferences domains if the range has no more than three elements. We extend this result and, at the same time, present a simple argument for proving it. Our analysis points out the role of individual strategy-proofness in deriving the preference reversal property, giving back to the latter its original individual nature (cfr. Eliaz, 2004). Finally, we show that group strategy-proofness is needed to obtain preference reversal if there are infinitely many voters.

我们分析了在代理人可能宣布冷漠的情况下，策略证明与偏好逆转之间的关系。有趣的是，如果范围不超过三个元素，Berga 和 Moreno（2020）最近从严格偏好域上社会选择函数的群体策略证明中推导出偏好逆转。我们扩展了这个结果，同时提出了一个简单的论证来证明它。我们的分析指出了个体策略证明在推导偏好逆转属性中的作用，将其原始的个体性质归还给后者（参见 Eliaz，2004）。最后，我们表明，如果有无限多的选民，则需要群体策略证明才能获得偏好逆转。