On the relation between preference reversal and strategy-proofness

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.