Definition
Manipulation ( COMSOC)
Manipulation is a false preference report that gives the reporting voter a strictly preferred outcome, holding all other reports fixed. For a social choice function
and a truthful profile , voter can manipulate if Here
contains the other voters’ reports, and is the set of strict rankings. The improvement over truthful voting is evaluated using the voter’s true preference , not the reported ranking . It is a successful instance of strategic voting. Coalitional manipulation
A group of voters coordinates false reports, keeping outsiders’ reports fixed, so that every member strictly prefers the resulting winner to the truthful winner. The plurality example uses this form.
Set-valued outcomes
For a social choice correspondence, the definition additionally needs a way to compare winner sets, or a specified tie-breaking rule. Rankings of individual alternatives alone do not determine whether one winner set is better than another.