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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".
The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1). The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a ...
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.
If A, B and C are the candidates, then '1' will vote A-B-C, '2' will vote B-C-A, and '3' will vote C-A-B, giving a Condorcet cycle. This is the subject of the McKelvey–Schofield theorem. Proof. See the diagram, in which the grey disc represents the voter distribution as uniform over a circle and M is the median in all directions.
For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule.
Android phones, like this Nexus S running Replicant, allow installation of apps from the Play Store, F-Droid store or directly via APK files.. This is a list of notable applications (apps) that run on the Android platform which meet guidelines for free software and open-source software.
Black proved that by replacing unrestricted domain with single-peaked preferences in Arrow's theorem removes the impossibility: there are Pareto-efficient non-dictatorships that satisfy the "independence of irrelevant alternatives" criterion. However, Black's 1948 proof was published before Arrow's impossibility theorem was published in 1950 ...