Create a `SocialRanking`

object.

## 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.

## 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 \(jR^\succsim i\).

## See also

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