In
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
and
social choice
Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures ( social welfare functions) used to combine i ...
, a
function satisfies anonymity, neutrality, or symmetry 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.
{{Rp, 75
Examples
Most voting rules are anonymous and neutral by design. For example,
plurality voting
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other (that is, receive a plurality) are elected.
Under single-winner plurality voting, and in systems based on single-member ...
is anonymous and neutral, since only counts the number of first-preferences for each candidate, regardless of who cast these votes.
Any rule that uses 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 vote ...
must be 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
An 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
is a Latin phrase meaning the existing state of affairs, particularly with regard to social, economic, legal, environmental, political, religious, scientific or military issues. In the sociological sense, the ''status quo'' refers to the curren ...
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
The chair, also chairman, chairwoman, or chairperson, is the presiding officer of an organized group such as a board, committee, or deliberative assembly. The person holding the office, who is typically elected or appointed by members of the gro ...
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
A supermajority is a requirement for a proposal to gain a specified level of support which is greater than the threshold of one-half used for a simple majority. Supermajority rules in a democracy can help to prevent a majority from eroding fun ...
to pass, and other rules can give certain stakeholders a
veto
A veto is a legal power to unilaterally stop an official action. In the most typical case, a president (government title), president or monarch vetoes a bill (law), bill to stop it from becoming statutory law, law. In many countries, veto powe ...
. 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
*
One man, one vote
"One man, one vote" or "one vote, one value" is a slogan used to advocate for the principle of equal representation in voting. This slogan is used by advocates of democracy and political equality, especially with regard to electoral reforms like ...
*
Fair election
References
Social choice theory