Is it ever safe to vote strategically?

• Published in: Social choice and welfare Vol. 43; no. 2; pp. 403 - 427
• Main Authors: Slinko, Arkadii, White, Shaun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer 01.08.2014; Springer Berlin Heidelberg; Springer Nature B.V
• Subjects: Coordinate systems; Coordination; Dictators; Economic incentives; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Election results; Elections; Game Theory; Incentives; International Political Economy; Mathematics; Original Paper; Other things equal assumption; Plurality voting; Political candidates; Preferences; Presidential elections; Public choice; Public Finance; Social and Behav. Sciences; Social Choice; Social Policy; Social welfare; Strategic Voting; Studies; Voter behavior; Voters; Voting; Voting behavior; Voting Rules
• ISSN: 0176-1714; 1432-217X
• DOI: 10.1007/s00355-013-0785-4

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.