SocialRanking {socialranking}R Documentation

SocialRanking object

Description

Create a SocialRanking object.

Usage

SocialRanking(l)

Arguments

l

A list of vectors

Details

Similar to PowerRelation(), SocialRanking expects expects a list to represent a power relation. Unlike PowerRelation() however, this list should not be nested and should only contain vectors, each vector containing elements that are deemed equally preferable.

Use doRanking() to rank elements based on arbitrary score objects.

A social ranking solution, or ranking solution, or solution, maps each power relation between coalitions to a power relation between its elements. I.e., from the power relation :{1,2}{2}{1}\succsim: \{1,2\} \succ \{2\} \succ \{1\}, we may expect the result of a ranking solution RR^\succsim to rank element 2 over 1. Therefore 2R12 R^\succsim 1 will be present, but not 1R21 R^\succsim 2.

Formally, a ranking solution R:T(P)T(N)R: \mathcal{T}(\mathcal{P}) \rightarrow \mathcal{T}(N) is a function that, given a power relation T(P)\succsim \in \mathcal{T}(\mathcal{P}), always produces a power relation R()R(\succsim) (or RR^\succsim) over its set of elements. For two elements i,jNi, j \in N, iRji R^\succsim j means that applying the solution RR on the ranking \succsim makes ii at least as preferable as jj. Often times iIjiI^\succsim j and iPjiP^\succsim j are used to indicate its symmetric and asymmetric part, respectively. As in, iIjiI^\succsim j implies that iRjiR^\succsim j and jRijR^\succsim i, whereas iPjiP^\succsim j implies that iRjiR^\succsim j but not jRijR^\succsim i.

Value

A list of type SocialRanking. Each element of the list contains a vector of elements in powerRelation$elements that are indifferent to one another.

See Also

Function that ranks elements based on their scores, doRanking()

Examples

SocialRanking(list(c("a", "b"), "f", c("c", "d")))
# a ~ b > f > c ~ d


[Package socialranking version 1.2.0 Index]