allrules {ClaimsProblems}

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, DT, MO, PIN, PRO, RA, and Talmud.

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", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet").

Details

Let E\ge 0 be the endowment to be divided and d\in \mathcal{R}^n the vector of claims with d\ge 0 and such that \sum_{i=1}^{n} d_i\ge E,\ the sum of claims exceeds the endowment.

A vector x=(x_1,\dots,x_n) is an awards vector for the claims problem (E,d) if: no claimant is asked to pay (0\le x); no claimant receives more than his claim (x\le d); and the balance requirement is satisfied, that is, the sum of the awards is equal to the endowment (\sum_{i=1}^{n} x_i= E).

A rule is a function that assigns to each claims problem (E,d) an awards vector for (E,d), that is, a division between the claimants of the amount available.

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.Á., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2022). The average-of-awards rule for claims problems. Soc Choice Welf. doi: 10.1007/s00355-022-01414-6

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, CD, CE, CEA, CEL , DT, MO, PIN, PRO, RA, Talmud, verticalruleplot

Examples

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