Dominance — dominates • socialranking

Check if one element dominates the other.

Usage

dominates(powerRelation, e1, e2, strictly = FALSE, includeEmptySet = TRUE)

Arguments

powerRelation: A PowerRelation object created by PowerRelation() or as.PowerRelation()
e1, e2: Elements in powerRelation$elements
strictly: If TRUE, check if p1 strictly dominates p2
includeEmptySet: If TRUE, check $\lbrace i \rbrace \succsim \lbrace j \rbrace$ even if empty set is not part of the power relation.

Value

Logical value TRUE if e1 dominates e2, else FALSE.

Details

$i$ is said to dominate $j$ if $S \cup \lbrace i \rbrace \succsim S \cup \lbrace j \rbrace$ for all $S \in 2^{N \setminus \lbrace i,j \rbrace}$.

$i$ strictly dominates $j$ if there also exists an $S \in 2^{N \setminus \lbrace i,j \rbrace}$ such that $S \cup \lbrace i \rbrace \succ S \cup \lbrace j \rbrace$.

Examples

pr <- as.PowerRelation("12 > 1 > 2")

# TRUE
d1 <- dominates(pr, 1, 2)

# FALSE
d2 <- dominates(pr, 2, 1)

# TRUE (because it's not strict dominance)
d3 <- dominates(pr, 1, 1)

# FALSE
d4 <- dominates(pr, 1, 1, strictly = TRUE)

stopifnot(all(d1, !d2, d3, !d4))