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Is it ever safe to vote strategically?

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  • Arkadii Slinko

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  • Shaun White

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Abstract

There are many situations in which mis-coordinated strategic voting can leave strategic voters worse off than they would have been had they not tried to strategise. We analyse the simplest of such scenarios, in which a set of strategic voters all have the same sincere preferences and all contemplate casting the same strategic vote, while all other voters are not strategic. Most mis-coordinations in this framework can be classified as instances of either strategic overshooting (too many voted strategically) or strategic undershooting (too few). If mis-coordination can result in strategic voters ending up worse off than they would have been had they all just voted sincerely, we call the strategic vote unsafe. We show that under every onto and non-dictatorial social choice rule there exist circumstances where a voter has an incentive to cast a safe strategic vote. We extend the Gibbard–Satterthwaite Theorem by proving that every onto and non-dictatorial social choice rule can be individually manipulated by a voter casting a safe strategic vote. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Arkadii Slinko & Shaun White, 2014. "Is it ever safe to vote strategically?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 403-427, August.
  • Handle: RePEc:spr:sochwe:v:43:y:2014:i:2:p:403-427 DOI: 10.1007/s00355-013-0785-4
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    References listed on IDEAS

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    1. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    2. Slinko, Arkadii, 2004. "How large should a coalition be to manipulate an election?," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 289-293, May.
    3. Pattanaik, Prasanta K., 1973. "On the stability of sincere voting situations," Journal of Economic Theory, Elsevier, vol. 6(6), pages 558-574, December.
    4. Pritchard, Geoffrey & Wilson, Mark C., 2009. "Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 35-57, July.
    5. Arkadii Slinko & Shaun White, 2010. "Proportional Representation and Strategic Voters," Journal of Theoretical Politics, , vol. 22(3), pages 301-332, July.
    6. Prasanta K. Pattanaik, 1976. "Counter-threats and Strategic Manipulation under Voting Schemes," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 11-18.
    7. Arkadii Slinko, 2006. "How the size of a coalition affects its chances to influence an election," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 143-153, January.
    8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    9. Pattanaik, Prasanta K, 1976. "Threats, Counter-Threats, and Strategic Voting," Econometrica, Econometric Society, vol. 44(1), pages 91-103, January.
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