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In social choice theory, a function satisfies voter anonymity, neutrality, or symmetry if the rule does not discriminate between different voters ahead of time; in other words, it does not matter who casts which vote. Formally, this is defined as saying the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily.[1][2]
Similarly, candidate anonymity (neutrality, symmetry) says that the rule does not discriminate between different candidates ahead of time. Formally, if the labels assigned to each candidate are permuted arbitrarily, the returned result is permuted in the same way.[1][2]
Some authors reserve the term anonymity for voter symmetry and neutrality for candidate symmetry,[1][2] but this pattern is not perfectly consistent.[3]: 75
Examples
editMost voting rules are anonymous and neutral by design, or else only violate anonymity and neutrality in some very limited circumstance like a perfect tie. For example, plurality voting is anonymous and neutral, since only counts the number of votes received by each candidate, regardless of who cast these votes. Similarly, the utilitarian rule and egalitarian rule are both anonymous and neutral, since the only consider the utility given to each candidate, regardless of the candidate's name or index.
All rules using a secret ballot are voter-anonymous, since they do not know which voter cast which vote. However, the converse is not true (as in e.g. roll call votes).
Non-examples
editAn example of a non-neutral rule is a rule which says that, in case of a tie, the alternative X is selected. This is particularly prominent in cases where X is the status quo option: parliamentary procedures often specify that the status quo unless there is a strict majority against it. Other rules are non-anonymous in the case of a tied vote, e.g. when a chairman is allowed to break ties.
However, not all violations of anonymity and neutrality are due to tied votes. For example, many motions require a supermajority to pass, and other rules can give certain stakeholders a veto. The United States' electoral college is a well-known example of a non-anonymous voting rule, as the results of the election depend not just on the votes for each candidate, but also on their physical arrangement across space.
Weighted voting rules are non-anonymous, as they give some voters a higher weight than others, for example, due to their expertise or entitlement.
See also
editReferences
edit- ^ a b c Bogomolnaia, Anna; Moulin, Hervé; Stong, Richard (2005-06-01). "Collective choice under dichotomous preferences" (PDF). Journal of Economic Theory. 122 (2): 165–184. doi:10.1016/j.jet.2004.05.005. ISSN 0022-0531.
- ^ a b c Felix Brandt (2017-10-26). "Roling the Dice: Recent Results in Probabilistic Social Choice". In Endriss, Ulle (ed.). Trends in Computational Social Choice. Lulu.com. ISBN 978-1-326-91209-3.
- ^ Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.), "Divisor Methods of Apportionment: Divide and Round", Proportional Representation: Apportionment Methods and Their Applications, Cham: Springer International Publishing, pp. 71–93, doi:10.1007/978-3-319-64707-4_4, ISBN 978-3-319-64707-4, retrieved 2021-09-01