May's theorem

May's theorem

In social choice theory, May's theorem states that simple majority voting is the only anonymous, neutral, and monotone choice function between two alternatives. Further, this procedure is resolute when there are an odd number of voters and ties (indecision) are not allowed. Kenneth May first published this theory in 1952.[1] Various modifications have been suggested by others since the original publication; in particular, Mark Fey[2] extended the proof to an infinite number of voters.

Arrow's theorem in particular does not apply to the case of two candidates, so this possibility result can be seen as a mirror analogue of that theorem. (Note that anonymity is a stronger form of non-dictatorship.)

Another way of explaining the fact that simple majority voting can successfully deal with at most two alternatives is to cite Nakamura's theorem. The theorem states that the number of alternatives that a rule can deal with successfully is less than the Nakamura number of the rule. The Nakamura number of simple majority voting is 3, except in the case of four voters. Supermajority rules may have greater Nakamura numbers.

Formal statement

  • Condition 1. The group decision function sends each set of preferences to a unique winner. (resolute, unrestricted domain)
  • Condition 2. The group decision function treats each voter identically. (anonymity)
  • Condition 3. The group decision function treats both outcomes the same, in that reversing each preferences reverses the group preference. (neutrality)
  • Condition 4. If the group decision was 0 or 1 and a voter raises a vote from −1 to 0 or 1 or from 0 to 1, the group decision is 1.

Theorem: A group decision function with an odd number of voters meets conditions 1, 2, 3, and 4 if and only if it is the simple majority method.

Notes

  1. ^ May, Kenneth O. 1952. "A set of independent necessary and sufficient conditions for simple majority decisions", Econometrica, Vol. 20, Issue 4, pp. 680–684.
  2. ^ Mark Fey, "May’s Theorem with an Infinite Population", Social Choice and Welfare, 2004, Vol. 23, issue 2, pages 275–293.

References


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • May 2004 — May 2004: January – February – March – April – May – June – July – August – September – October – November – December Events …   Wikipedia

  • Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements …   Wikipedia

  • Arrow's impossibility theorem — In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives (options), no voting system can convert the ranked preferences of… …   Wikipedia

  • Kenneth May — Kenneth O. May (July 8, 1915 December 1977) was an American mathematician and historian of mathematics, who developed May s theorem. The Kenneth O. May Prize is awarded for outstanding contributions to the history of mathematics.External links*… …   Wikipedia

  • Noether's theorem — This article discusses Emmy Noether s first theorem, which derives conserved quantities from symmetries. For her related theorem on infinite dimensional Lie algebras and differential equations, see Noether s second theorem. For her unrelated… …   Wikipedia

  • De Bruijn–Erdős theorem (graph theory) — This article is about coloring infinite graphs. For the number of lines determined by a finite set of points, see De Bruijn–Erdős theorem (incidence geometry). In graph theory, the De Bruijn–Erdős theorem, proved by Nicolaas Govert de Bruijn and… …   Wikipedia

  • Miller theorem — refers to the process of creating equivalent circuits. It asserts that a floating impedance element supplied by two voltage sources connected in series may be split into two grounded elements with corresponding impedances. There is also a dual… …   Wikipedia

  • Pythagorean theorem — See also: Pythagorean trigonometric identity The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c) …   Wikipedia

  • Four color theorem — Example of a four colored map A four colori …   Wikipedia

  • Nyquist–Shannon sampling theorem — Fig.1: Hypothetical spectrum of a bandlimited signal as a function of frequency The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”