Test relation between two elements

On a given PowerRelation object pr, check if e1 relates to e2 based on the given social ranking solution.

Usage

testRelation(powerRelation, e1)

powerRelation %:% e1

pr_e1 %>=dom% e2

pr_e1 %>dom% e2

pr_e1 %>=cumuldom% e2

pr_e1 %>cumuldom% e2

pr_e1 %>=cp% e2

pr_e1 %>cp% e2

pr_e1 %>=banz% e2

pr_e1 %>banz% e2

pr_e1 %>=cop% e2

pr_e1 %>cop% e2

pr_e1 %>=ks% e2

pr_e1 %>ks% e2

pr_e1 %>=lex% e2

pr_e1 %>lex% e2

pr_e1 %>=duallex% e2

pr_e1 %>duallex% e2

pr_e1 %>=L1% e2

pr_e1 %>L1% e2

pr_e1 %>=L2% e2

pr_e1 %>L2% e2

pr_e1 %>=LP% e2

pr_e1 %>LP% e2

pr_e1 %>=LPS% e2

pr_e1 %>LPS% e2

Arguments

powerRelation

A PowerRelation object created by PowerRelation() or as.PowerRelation()

e1, e2

Elements in powerRelation$elements

pr_e1

PowerRelation and e1 element, packed into a list using pr %:% e1

Value

testRelation() and %:% returns list(powerRelation, e1).

Followed by a %>=comparison% or %>comparison% it returns TRUE or FALSE, depending on the relation between e1 and e2.

Details

The function testRelation is somewhat only used to make the offered comparison operators in the package better discoverable.

testRelation(pr, e1) is equivalent to pr %:% e1 and list(pr, e1). It should be used together with one of the comparison operators listed in the usage section.

See also

Comparison function: dominates(), cumulativelyDominates(), cpMajorityComparison().

Score Functions: ordinalBanzhafScores(), copelandScores(), kramerSimpsonScores(), lexcelScores().

Examples

pr <- as.PowerRelation("123 > 12 ~ 13 ~ 23 > 3 > 1 ~ 2 > {}")

# Dominance
stopifnot(pr %:% 1 %>=dom% 2)

# Strict dominance
stopifnot((pr %:% 1 %>dom% 2) == FALSE)

# Cumulative dominance
stopifnot(pr %:% 1 %>=cumuldom% 2)

# Strict cumulative dominance
stopifnot((pr %:% 1 %>cumuldom% 2) == FALSE)

# CP-Majority relation
stopifnot(pr %:% 1 %>=cp% 2)

# Strict CP-Majority relation
stopifnot((pr %:% 1 %>cp% 2) == FALSE)

# Ordinal banzhaf relation
stopifnot(pr %:% 1 %>=banz% 2)

# Strict ordinal banzhaf relation
# (meaning 1 had a strictly higher positive contribution than 2)
stopifnot((pr %:% 1 %>banz% 2) == FALSE)

# Copeland-like method
stopifnot(pr %:% 1 %>=cop% 2)
stopifnot(pr %:% 2 %>=cop% 1)

# Strict Copeland-like method
# (meaning pairwise winning minus pairwise losing comparison of
# 1 is strictly higher than of 2)
stopifnot((pr %:% 1 %>cop% 2) == FALSE)
stopifnot((pr %:% 2 %>cop% 1) == FALSE)
stopifnot(pr %:% 3 %>cop% 1)

# Kramer-Simpson-like method
stopifnot(pr %:% 1 %>=ks% 2)
stopifnot(pr %:% 2 %>=ks% 1)

# Strict Kramer-Simpson-like method
# (meaning ks-score of 1 is actually higher than 2)
stopifnot((pr %:% 2 %>ks% 1) == FALSE)
stopifnot((pr %:% 1 %>ks% 2) == FALSE)
stopifnot(pr %:% 3 %>ks% 1)

# Lexicographical and dual lexicographical excellence
stopifnot(pr %:% 3 %>=lex% 1)
stopifnot(pr %:% 3 %>=duallex% 1)

# Strict lexicographical and dual lexicographical excellence
# (meaning their lexicographical scores don't match)
stopifnot(pr %:% 3 %>lex% 1)
stopifnot(pr %:% 3 %>duallex% 1)

# L^(1) and L^(2)
stopifnot(pr %:% 1 %>=L1% 2)
stopifnot(pr %:% 1 %>=L2% 2)

# Strict L^(1) and L^(2)
stopifnot((pr %:% 1 %>L1% 2) == FALSE)
stopifnot(pr %:% 3 %>L1% 1)

stopifnot((pr %:% 1 %>L2% 2) == FALSE)
stopifnot(pr %:% 3 %>L2% 1)

# L^p and L^p*
stopifnot(pr %:% 1 %>=LP% 2)
stopifnot(pr %:% 1 %>=LPS% 2)

# Strict L^(1) and L^(2)
stopifnot((pr %:% 1 %>LP% 2) == FALSE)
stopifnot(pr %:% 3 %>LP% 1)

stopifnot((pr %:% 1 %>LPS% 2) == FALSE)
stopifnot(pr %:% 3 %>LPS% 1)