makePowerRelationMonotonic {socialranking}R Documentation

Make Power Relation monotonic

Description

Given a powerRelation object, make its order monotonic.

Usage

makePowerRelationMonotonic(powerRelation, addMissingCoalitions = TRUE)

Arguments

powerRelation

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

addMissingCoalitions

If TRUE, also include all coalitions in the power set of powerRelation$elements that are not present in the current power relation.

Details

A power relation is monotonic if

TSST.T \subset S \Leftrightarrow S \succsim T.

for every coalition SNS \subseteq N.

Calling makePowerRelationMonotonic() on some PowerRelation object moves or adds coalitions to certain equivalence classes so that the power relation becomes monotonic.

Value

PowerRelation object containing the following values:

See Also

Other helper functions for transforming power relations: appendMissingCoalitions()

Examples

pr <- as.PowerRelation("ab > ac > abc > b > a > {} > c > bc")
makePowerRelationMonotonic(pr)
# (abc ~ ab) > ac > (bc ~ b) > a > (c ~ {})

# notice that missing coalitions are automatically added,
# except for the empty set
pr <- as.PowerRelation("a > b > c")
makePowerRelationMonotonic(pr)
# (abc ~ ab ~ ac ~ a) > (bc ~ b) > c

# setting addMissingCoalitions to FALSE changes this behavior
pr <- as.PowerRelation("a > ab > c ~ {} > b")
makePowerRelationMonotonic(pr, addMissingCoalitions = FALSE)
# (ab ~ a) > (b ~ c ~ {})

# notice that an equivalence class containing an empty coalition
# automatically moves all remaining coalitions to that equivalence class.
pr <- as.PowerRelation("a > {} > b > c")
makePowerRelationMonotonic(pr)
# (abc ~ ab ~ ac ~ a) > (bc ~ b ~ c ~ {})


[Package socialranking version 1.2.0 Index]