# PRO: Proportional rule In ClaimsProblems: Analysis of Conflicting Claims

## Description

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

## Usage

 `1` ```PRO(E, d, name = FALSE) ```

## Arguments

 `E` The endowment. `d` The vector of claims. `name` A logical value.

## Details

Let E≥ 0 be the endowment to be divided and d the vector of claims with d≥ 0 and such that D=∑ di ≥ E, the sum of claims D exceeds the endowment.

The proportional rule distributes awards proportional to claims.

PRO(E,d)=(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.

 ```1 2 3``` ```E=10 d=c(2,4,7,8) PRO(E,d) ```