Calculate cumulative score vectors for each element.

e1, e2

Elements in powerRelation$elements strictly If TRUE, check if p1 strictly dominates p2 ## Value Score function returns a list of type CumulativeScores and length of powerRelation$elements

(unless parameter elements is specified). Each index contains a vector of length powerRelation\$eqs, cumulatively counting up the number of times the given element appears in each equivalence class.

cumulativelyDominates() returns TRUE if e1 cumulatively dominates e2, else FALSE.

## Details

An element's cumulative score vector is calculated by cumulatively adding up the amount of times it appears in each equivalence class in the powerRelation. I.e., in a linear power relation with eight coalitions, if element 1 appears in coalitions placed at 1, 3, and 6, its score vector is [1, 1, 2, 2, 2, 3, 3, 3].

## Dominance

$$i$$ dominates $$j$$ if, for each index $$x, \textrm{Score}(i)_x \geq \textrm{Score}(j)_x$$.

$$i$$ strictly dominates $$j$$ if there exists an $$x$$ such that $$\textrm{Score}(i)_x > \textrm{Score}(j)_x$$.

Moretti S (2015). “An axiomatic approach to social ranking under coalitional power relations.” Homo Oeconomicus, 32(2), 183--208.

Moretti S, Öztürk M (2017). “Some axiomatic and algorithmic perspectives on the social ranking problem.” In International Conference on Algorithmic Decision Theory, 166--181. Springer.