On the manipulability of equitable voting rules ✩

We consider the equity-manipulability trade-off when voting over two alternatives. Pairwise equity is a weakening of anonymity requiring certain permutations of the voters' identities to preserve the outcome of the election. B-robust group strategy-proofness (t-RGSP) and fine robust group strategy-proofness (FRGSP) are notions of group strategy-proofness that allow voters to have different beliefs about players' types (Kivinen and Tumennasan, 2021). Our main results show that, under mild conditions, for pairwise equitable voting rules anonymity is equivalent to 2-RGSP, 3-RGSP, and FRGSP. In this way, anonymity is special in its equity and non-manipulability. These results follow from several preliminary results, one of which equates 2-RGSP to comonotonicity and swap-robustness. Finally, we consider the manipulability of k-unanimous rules, and 2-RGSP when agents can be indifferent and abstain.& COPY; 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).