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Kenneth May proved that the simple majority rule is the only "fair" 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: [9] [10]
Some proponents of consensus decision-making view procedures that use majority rule as undesirable for several reasons. Majority voting is regarded as competitive, rather than cooperative, framing decision-making in a win/lose dichotomy that ignores the possibility of compromise or other mutually beneficial solutions. [59]
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory.The result implies that it is logically impossible for any voting system to guarantee a winner will have support from a majority of voters: for example there can be rock-paper-scissors scenario where a majority of voters will prefer A to ...
Consensus democracy [1] is the application of consensus decision-making and supermajority to the process of legislation in a democracy.It is characterized by a decision-making structure that involves and takes into account as broad a range of opinions as possible, as opposed to majoritarian democracy systems where minority opinions can potentially be ignored by vote-winning majorities. [2]
The first set of methods studied by economists are the majority-rule, or Condorcet, methods. These rules limit spoilers to situations where majority rule is self-contradictory, called Condorcet cycles, and as a result uniquely minimize the possibility of a spoiler effect among ranked rules. (Indeed, many different social welfare functions can ...
^May, Kenneth O. 1952. "A set of independent necessary and sufficient conditions for simple majority decisions", Econometrica, Vol. 20, Issue 4, pp. 680–684. JSTOR 1907651; ^ Mark Fey, "May’s Theorem with an Infinite Population", Social Choice and Welfare, 2004, Vol. 23, issue 2, pages 275–293.; ^ Goodin, Robert and Christian List (2006). "A conditional defense of plurality rule ...
The Smith criterion guarantees an even stronger kind of majority rule. It says that if there is no majority-rule winner, the winner must be in the top cycle, which includes all the candidates who can beat every other candidate, either directly or indirectly. Most, but not all, Condorcet systems satisfy the top-cycle criterion.
Each majority is counted using a combination, n items taken k at a time, where n is the jury size, and k is the size of the majority. Probabilities range from 0 (= the vote is always wrong) to 1 (= always right). Each person decides independently, so the probabilities of their decisions multiply. The probability of each correct decision is p.