socialranking (version 1.2.0)

dominates: Dominance

Description

Check if one element dominates the other.

Usage

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

Value

Logical value TRUE if e1 dominates e2, else FALSE.

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.

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))