allrules | R Documentation |

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.

allrules(E, d, draw = TRUE, col = NULL)

`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"). |

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.

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.

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.

AA, APRO, CD, CE, CEA, CEL , DT, MO, PIN, PRO, RA, Talmud, verticalruleplot

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

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