| 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 \succsim: \{1,2\} \succ \{2\} \succ \{1\}, we may expect the result of a ranking solution R^\succsim
to rank element 2 over 1. Therefore 2 R^\succsim 1 will be present, but not 1 R^\succsim 2.
Formally, a ranking solution R: \mathcal{T}(\mathcal{P}) \rightarrow \mathcal{T}(N) is a function that,
given a power relation \succsim \in \mathcal{T}(\mathcal{P}), always produces a power relation
R(\succsim) (or R^\succsim) over its set of elements.
For two elements i, j \in N, i R^\succsim j means that applying the solution R on the ranking \succsim
makes i at least as preferable as j.
Often times iI^\succsim j and iP^\succsim j are used to indicate its symmetric and asymmetric part, respectively.
As in, iI^\succsim j implies that iR^\succsim j and jR^\succsim i,
whereas iP^\succsim j implies that iR^\succsim j but not jR^\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