PRO {ClaimsProblems}

Proportional rule

Description

This function returns the awards vector assigned by the proportional rule (PRO) to a claims problem.

Usage

PRO(E, d, name = FALSE)

Arguments

E

The endowment.

d

The vector of claims.

name

A logical value.

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 D=\sum_{i=1}^{n} d_i\ge E, the sum of claims D exceeds the endowment.

The proportional rule distributes awards proportional to claims.

PRO(E,d)=\frac{E}{D}d

Value

The awards vector selected by the PRO rule. If name = TRUE, the name of the function (PRO) as a character string.

References

Aristotle, Ethics, Thompson, J.A.K., tr. 1985. Harmondsworth: Penguin.

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

allrules, APRO

Examples

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