Editing Majority rule (section)

== Properties ==
=== May's theorem ===
{{main|May's theorem}}

[[Kenneth May]] proved that the simple majority rule is the only "fair" [[Ordinal utility|ordinal]] decision rule, in that majority rule does not let some votes count more than others or privilege an alternative by requiring fewer votes to pass. Formally, majority rule is the only decision rule that has the following properties:<ref name="May2">{{cite journal |last1=May |first1=Kenneth O. |year=1952 |title=A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision |journal=Econometrica |volume=20 |issue=4 |pages=680–684 |doi=10.2307/1907651 |jstor=1907651}}</ref><ref name="Fey2">Mark Fey, "[https://web.archive.org/web/20030806231803/http://troi.cc.rochester.edu/~markfey/papers/May.pdf May's Theorem with an Infinite Population]", ''Social Choice and Welfare'', 2004, Vol. 23, issue 2, pages 275–293.</ref>

* [[Anonymity (social choice)|'''Anonymity''']]: the decision rule treats each voter identically ([[one vote, one value]]). Who casts a vote makes no difference; the voter's identity need not be disclosed.
* [[Neutrality (social choice)|'''Neutrality''']]: the decision rule treats each ''alternative'' or ''candidate'' equally (a [[free and fair election]]).
* [[Resolvability criterion|'''Decisiveness''']]: if the vote is tied, adding a single voter (who expresses an opinion) will break the tie.
* '''[[Positive response]]''': If a voter changes a preference, MR never switches the outcome against that voter. If the outcome the voter now prefers would have won, it still does so.
* [[Ranked voting|'''Ordinality''']]: the decision rule relies only on ''which'' of two outcomes a voter prefers, not ''how much''.<!--<!--While not as clearly desirable as the other principles are, this condition is needed for strategyproofness, and can also be helpful in situations where cardinal information is unavailable.--&gt;-->
** This can be replaced by [[strategyproofness]], i.e. every person's [[dominant strategy]] is to honestly disclose their preferences.

=== Agenda manipulation ===
{{Main|McKelvey–Schofield chaos theorem}}
If voter's preferences are defined over a multidimensional option space, then choosing options using pairwise majority rule is unstable. In most cases, there will be no [[Condorcet winner criterion|Condorcet winner]] and any option can be chosen through a sequence of votes, regardless of the original option. This means that adding more options and changing the order of votes ("agenda manipulation") can be used to arbitrarily pick the winner.<ref>{{Cite book |last1=Cox |first1=Gary W. |author-link=Gary W. Cox |title=Positive Changes in Political Science |last2=Shepsle |first2=Kenneth A. |author-link2=Kenneth Shepsle |pages=20–23 |chapter=Majority Cycling and Agenda Manipulation: Richard McKelvey's Contributions and Legacy |date=2007 |publisher=University of Michigan Press |isbn=978-0-472-06986-6 |editor-last=Aldrich |editor-first=John Herbert |series=Analytical perspectives on politics |location=Ann Arbor, Michigan |editor-last2=Alt |editor-first2=James E. |editor-last3=Lupia |editor-first3=Arthur}}</ref>

=== Other properties ===
In group decision-making [[Voting paradox|voting paradoxes]] can form. It is possible that alternatives a, b, and c exist such that a majority prefers a to b, another majority prefers b to c, and yet another majority prefers c to a. Because majority rule requires an alternative to have majority support to pass, majority rule is vulnerable to rejecting the majority's decision.