Approval methods
Approval Methods are voting methods that require each voter to separate alternatives in a given election into two complimentary sets, A and -A. Whichever alternative occurs the most (or least) in A sets of voters wins the election.* Such voting methods are called approval methods because they are all very similar to the most famous example of this type of voting, namely approval voting. Other examples of approval methods include acceptability voting, consensus voting, disapproval voting, happiness voting, and utilitarian voting.
The goals of different approval methods vary. For example, consensus voting seeks to elect the alternative that the greatest number of voters express the desire to form a consensus around. Happiness voting seeks to maximize the number of voters who are happy with the result of the election.
Even if the goals of two distinct approval methods are the same, the A set may differ. For example, in both approval voting and disapproval voting, voters are requested to separate alternatives into two complementary sets: approved and disapproved. However, with approval voting, the A set is approved alternatives and the -A set is disapproved alternatives, while in disapproval voting, the A set is disapproved alternatives and the -A set is approved alternatives. The winner of approval voting occurs in the most A sets, while the winner of disapproval voting occurs in the least A sets. In theory, both voting systems should elect the same alternatives. However, because of limitations on human rationality, it is likely that the way the question is posed to the voter will affect who s/he approves and disapproves. Thus, one might arrive at different winning alternatives in the same election, dependent upon whether approval or disapproval voting is used.
Similarly, one might get different results in the same election depending on whether or not acceptability, or approval, or consensus, or disapproval, or any other approval method is used.
- An "A set" consists of the alternatives that have the trait that is requested in the election. For example, in approval voting, voters are asked which alternatives they approve. Thus, the A set contains approved alternatives. In disapproval voting, voters are asked which alternatives they disapproved, thus the A set contains disapproved alternatives.