allrules: Summary of the division rules

In ClaimsProblems: Analysis of Conflicting Claims

Summary of the division rules

Description

This function returns the awards vectors selected, for a given claims problem, by the rules: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, and RTalmud.

Usage

allrules(E, d, draw = TRUE, col = NULL)

Arguments

E	The endowment.
d	The vector of claims.
draw	A logical value.
col	The colours (useful only if draw=TRUE). If col=NULL then the sequence of default colours is: c("red", "blue", "green", "yellow", "pink", "orange", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet","darkgreen").

Details

Let N=\{1,\ldots,n\} be the set of claimants, E\ge 0 the endowment to be divided and d\in \mathbb{R}_+^N the vector of claims such that \sum_{i \in N} d_i\ge E.

A vector x=(x_1,\dots,x_n) is an awards vector for the claims problem (E,d) if 0\le x \le d and satisfies the balance requirement, that is, \sum_{i=1}^{n}x_i=E.

A rule is a function that assigns to each claims problem (E,d) an awards vector. The formal definitions of the main rules are given in the corresponding function help.

Value

A data-frame with the awards vectors selected by the main division rules. If draw = TRUE, it displays a mosaic plot representing the data-frame.

References

Mirás Calvo, M.A., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2022). The average-of-awards rule for claims problems. Social Choice and Welfare 59, 863-888.

Thomson, W. (2019). How to divide when there isn't enough. From Aristotle, the Talmud, and Maimonides to the axiomatics of resource allocation. Cambridge University Press.

See Also

AA, APRO, axioms, CD, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud, verticalruleplot.

Examples

E=10
d=c(2,4,7,8)
allrules(E,d)

ClaimsProblems documentation built on April 4, 2025, 2:21 a.m.