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

 verticalruleplot R Documentation

## Vertical rule plot

### Description

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

### Usage

```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 colours. If col=NULL then the sequence of default colours is: c("red", "blue", "green", "yellow", "pink", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet"). `legend` A logical value. The colour 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.

### See Also

allrules, pathawards, pathawards3, schedrule, schedrules

### Examples

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

ClaimsProblems documentation built on Jan. 12, 2023, 5:13 p.m.