On the safety of group manipulation. (English) Zbl 1529.91038
Summary: Groups of voters have more possibilities to influence the voting result than separate individuals. However, there is a problem with coordinating their actions. This paper considers manipulation by groups of voters who have the same preferences. If a voting result is more preferable for voters of a particular group provided that all its members use the same strategy (report the same insincere preference), then each of these members has an incentive to manipulate. If there is a chance that they will become worse off in case only a subset of the whole group manipulates, then manipulation is unsafe. For several voting rules we study conditions on the numbers of voters and alternatives which allow for an unsafe manipulation or which make manipulation always safe.
References:
| [1] | Aleskerov F, Kurbanov E (1999) Degree of manipulability of social choice procedures. Curr Trends Econ 13-27 · Zbl 0959.91014 |
| [2] | Elkind E, Grandi U, Rossi F, Slinko A (2015) Gibbard-satterthwaite games. In: IJCAI · Zbl 1426.91007 |
| [3] | Gibbard, A., Manipulation of voting schemes: a general result, Econometrica, 41, 587-601 (1973) · Zbl 0325.90081 · doi:10.2307/1914083 |
| [4] | Grandi, U.; Hughes, D.; Rossi, F.; Slinko, A., Gibbard-Satterthwaite games for \(k\)-approval voting rules, Math Soc Sci, 99, 24-35 (2019) · Zbl 1426.91007 · doi:10.1016/j.mathsocsci.2019.03.001 |
| [5] | Hazon N, Elkind E (2010) Complexity of safe strategic voting. In: International symposium on algorithmic game theory, Springer, 210-221 · Zbl 1310.91062 |
| [6] | Ianovski, E.; Yu, L.; Elkind, E.; Wilson, MC, The complexity of safe manipulation under scoring rules, IJCAI, 11, 246-251 (2011) |
| [7] | Kelly, JS, 4. minimal manipulability and local strategy-proofness, Soc Choice Welf, 5, 81-85 (1988) · doi:10.1007/BF00435499 |
| [8] | Maus, S.; Peters, H.; Storcken, T., Anonymous voting and minimal manipulability, J Econ Theory, 135, 533-544 (2007) · Zbl 1186.91082 · doi:10.1016/j.jet.2006.04.002 |
| [9] | Nitzan, S., The vulnerability of point-voting schemes to preference variation and strategic manipulation, Public Choice, 47, 349-370 (1985) · doi:10.1007/BF00127531 |
| [10] | Peters, H.; Roy, S.; Storcken, T., On the manipulability of approval voting and related scoring rules, Soc Choice Welf, 39, 399-429 (2012) · Zbl 1287.91070 · doi:10.1007/s00355-011-0621-7 |
| [11] | Satterthwaite, MA, Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions, J Econ Theory, 10, 187-217 (1975) · Zbl 0315.90088 · doi:10.1016/0022-0531(75)90050-2 |
| [12] | Slinko A (2019) Beyond Gibbard and Satterthwaite: Voting ma- nipulation games. Fut Econ Design, Springer, 131-138 |
| [13] | Slinko, A.; White, S., Is it ever safe to vote strategically?, Soc Choice Welf, 43, 403-427 (2014) · Zbl 1297.91064 · doi:10.1007/s00355-013-0785-4 |
| [14] | Wilson M, Reyhani Shokat Abad R (2010) The probability of safe manipulation. COMSOC 2010 |
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