Abstract
We study a problem of individual manipulation in an impartial culture (IC) framework using computer modeling. We estimate the degree of manipulability of ten positional voting rules in the case of multiple choice for 3 and 4 alternatives.
Highlights
Gibbard (1973) and Satterthwaite (1975) showed that for at least 3 alternatives and any single-valued choice rule every non-dictatorial voting rule is individually manipulable
SERIEs (2011) 2:431–446 every social choice rule is manipulable, how can we find the least manipulable one? A non-exhaustive list of papers studying to which extent known social choice rules are manipulable includes Chamberlin (1985), Nitzan (1985), Kelly (1993), Aleskerov and Kurbanov (1999), Smith (1999), Favardin and Lepelley (2006), Pritchard and Wilson (2007) and Aleskerov et al (2011a,b)
Nitzan (1985) introduces the following index, which was used by Kelly (1993). We call this index as Nitzan–Kelly’s index and denote as NK, to measure the degree of manipulability of social choice rules d0 (m!)n
Summary
Gibbard (1973) and Satterthwaite (1975) showed that for at least 3 alternatives and any single-valued choice rule every non-dictatorial voting rule is individually manipulable. A non-exhaustive list of papers studying to which extent known social choice rules are manipulable includes Chamberlin (1985), Nitzan (1985), Kelly (1993), Aleskerov and Kurbanov (1999), Smith (1999), Favardin and Lepelley (2006), Pritchard and Wilson (2007) and Aleskerov et al (2011a,b). All those papers differ in main assumptions about profile probability distributions, a measure of manipulability, tie-breaking assumptions and sets of rules under study. Most of the papers use alphabetical tie-breaking rules: in the case of tie first alternative in alphabetical order is chosen (for example, see Nitzan 1985, Aleskerov and Kurbanov 1999, Favardin and Lepelley 2006).
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