In
social choice theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Soci ...
, Anonymity is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different voters. In other words, the rule returns the same outcome (whatever this outcome may be) if the vector of votes is permuted arbitrarily.
[{{Cite book, last=Felix Brandt, chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&dq=multiwinner++voting+a+new+challenge&pg=PA27, title=Trends in Computational Social Choice, date=2017-10-26, publisher=Lulu.com, isbn=978-1-326-91209-3, editor-last=Endriss, editor-first=Ulle, language=en, chapter=Roling the Dice: Recent Results in Probabilistic Social Choice]
Anonymous rules
Most voting rules are anonymous by design. For example,
plurality voting
Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per ...
is anonymous, since only counts the number of votes received by each candidates, regardless of who cast these votes. Similarly, the
utilitarian rule
In social choice and operations research, the utilitarian rule (also called the max-sum rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''sum of the utilities'' of all individual ...
and
egalitarian rule In social choice and operations research, the egalitarian rule (also called the max-min rule or the Rawlsian rule) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the ''minimum utility'' of ...
are both anonymous, since the only consider the set of utilities, regardless of who these utilities belong to.
All rules using a
secret ballot
The secret ballot, also known as the Australian ballot, is a voting method in which a voter's identity in an election or a referendum is anonymous. This forestalls attempts to influence the voter by intimidation, blackmailing, and potential vo ...
are anonymous, since they do not know which voter cast which vote. But the opposite is not true: a committee can use non-secret ballot, and still use an anonymous voting rule.
Non-anonymous rules
Weighted voting
Weighted voting can exist in a policy or law making body in which each representative has a variable voting power (weighted vote) as determined by the number principals who have made that person their proxy, or the population or the electorate t ...
rules are non-anonymous, as they give some voters a higher weight than others, for example, due to their expertise or entitlement.
Another example of a non-anonymous voting rule is plurality voting with the additional rule that, in case of a tie, the option preferred by the chair is selected.
In general, whenever different agents may have different
entitlements, a non-anonymous rule makes sense.
See also
*
Neutrality (social choice) In social choice theory, Neutrality is a basic requirement of a social choice rule. It says that the rule does not discriminate apriori between different candidates. In other words, if the vector of candidates is permuted arbitrarily, then the retur ...
- a related requirement, saying that the rule does not discriminate apriori between different ''candidates''.
References
Social choice theory