We analyze the relation between strategy-proofness and preference reversal in the case that agents may declare indifference. 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 \mbox{%DIFAUXCMD E Berga and Moreno \mbox{%DIFAUXCMD BM , 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  and at the same time simplify this result. Moreover we show that the difficulties they highlighted relaxing the assumption on the cardinality of the range, disappear under a proper assumption on the domain. We introduce the concept of complete sets of preferences and show that individual strategy-proofness is sufficient to obtain the preference reversal property when the agents' feasible set of orderings is complete. This covers interesting cases like single peaked preferences, rich domains admitting regular social choice functions, and universal domains. The fact that we use individual rather than group strategy-proofness, further allows to get immediately some of the known, and some new, equivalences between individual and group strategy-proofness. Finally, we show that group strategy-proofness is only really needed to obtain preference reversal if there are infinitely many voters.
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 simplify 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). Moreover, we show that the difficulties Berga and Moreno highlighted relaxing the assumption on the cardinality of the range, disappear under a proper assumption on the domain. We introduce the concept of complete sets of preferences and show that individual strategy-proofness is sufficient to obtain the preference reversal property when the agents' feasible set of orderings is complete. This covers interesting cases like single peaked preferences, rich domains admitting regular social choice functions, and universal domains. The fact that we use individual rather than group strategy-proofness, allows to get immediately some of the known, and some new, equivalences between individual and group strategy-proofness. Finally, we show that group strategy-proofness is only really needed to obtain preference reversal if there are infinitely many voters.
R
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 \mbox{%DIFAUXCMD E
Interestingly,
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\mbox{%DIFAUXCMD BM
(2020)
A
this result
R
this result. Moreover
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). Moreover,
R
they
Berga and Moreno
D
further