Symmetry (social choice)
quirement of a social choice rule
In economics and social choice, a function satisfies symmetry, neutrality, or anonymity if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time. Formally, this is defined by saying the rule returns the same outcome (whatever this may be) if the votes are "relabeled" arbitrarily, e.g. by swapping votes #1 and #2. Similarly, outcome-neutrality says the rule does not discriminate between different outcomes (e.g. candidates) ahead of time. Formally, if the labels assigned to each outcome are permuted arbitrarily, the returned result is permuted in the same way.
Some authors reserve the term anonymity for agent symmetry and neutrality for outcome-symmetry, but this pattern is not perfectly consistent.
Examples
Most voting rules are anonymous and neutral by design.
Begin with the source’s own compact description: “Symmetry (social choice)” is quirement of a social choice rule. The dossier treats that line as a proposition to test through Symmetry, social and choice, not as a finished interpretation.
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The phrase “quirement of a social choice rule” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Jun 23, 2026. The linked authority identifier is Q108443775. None of the 0 selected statements returned an explicit reference.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The source lead contains qualifying language; that uncertainty should survive quotation, summary and reuse. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
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This entry incorporates text from “Symmetry (social choice)” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.