# allrules: Summary of the division rules In ClaimsProblems: Analysis of Conflicting Claims

 allrules R Documentation

## 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≥ 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

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.

```E=10