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Single-peaked preferences are a class of preference relations. A group has single-peaked preferences over a set of outcomes if the outcomes can be ordered along a line such that: Each agent has a "best outcome" in the set, and; For each agent, outcomes that are further from his or her best outcome are preferred less.
In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal".
More formally, Black's theorem assumes preferences are single-peaked: a voter's happiness with a candidate goes up and then down as the candidate moves along some spectrum. For example, in a group of friends choosing a volume setting for music, each friend would likely have their own ideal volume; as the volume gets progressively too loud or ...
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
A rule is anonymous and strategyproof for all single-peaked preferences if it is equivalent to a median rule with at most n+1 phantoms. A rule is strategyproof for all single-peaked preferences iff it is equivalent to a minmax rule of the following form. There are 2 n parameters, b S for any subset S of voters.
In political science and social choice, the median voter theorem states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single-peaked preferences, any voting method that is compatible with majority-rule will elect the candidate preferred by the median voter.
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Single-peaked preferences are star-shaped preferences in the special case in which the set of possible distributions is a (one-dimensional) line. Metric-based preferences . There is a metric d on the Euclidean space, and every agent prefers a point q to a point r iff d( p , q ) ≤ d( p , r ).