# verticalruleplot: Vertical rule plot In ClaimsProblems: Analysis of Conflicting Claims

## Description

For each claimant, it plots a vertical line with his claim and a point on the awards vector of the chosen rules.

## Usage

 `1` ```verticalruleplot(E, d, Rules, col = NULL, legend = TRUE) ```

## Arguments

 `E` The endowment. `d` The vector of claims `Rules` The rules: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. `col` The colors. If col=NULL then the sequence of default colors is: c("red", "blue", "green", "yellow", "pink", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet"). `legend` A logical value. The color legend is shown if legend=TRUE.

## Details

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

A vector x=(x1,...,xn) is an awards vector for the claims problem (E,d) if: no claimant is asked to pay (0≤ x); no claimant receives more than his claim (x≤ d); and the balance requirement is satisfied, that is, the sum of the awards is equal to the endowment (x1+...+xn=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

This function represents the claims vector and the awards vector assigned by several rules as vertical segments.

## References

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 4 5``` ```E=10 d=c(2,4,7,8) Rules=c(Talmud,RA,AA) col=c("red","green","blue") verticalruleplot(E,d,Rules,col) ```