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The single-peaked recognition problem is the following decision problem: given a set of preferences on a set of outcomes, decide if there is a common order of the outcomes for which the preferences are single-peaked. Usually, it is required to also find this common order, if it exists.
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".
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
A further restriction of the single-peaked domain is that agents have single-peaked preferences with L1 metric on the probability density function. That is: for each agent i, there is an "ideal" probability distribution p i, and his utility from a selected probability distribution p* is minus the L1 distance between p i and p*.
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 ).
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 ...
Since he became CEO in April 2018, the energy drink company's stock has soared by more than 6,300% at its peak. Nonetheless, the stock has lost 75% from its 2024 high amid lower purchases by a key ...
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.