verticalruleplot {ClaimsProblems}

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\ge 0 be the endowment to be divided and d\in \mathcal{R}^n the vector of claims with d\ge 0 and such that \sum_{i=1}^{n} d_i\ge E,\ the sum of claims exceeds the endowment.

A vector x=(x_1,\dots,x_n) is an awards vector for the claims problem (E,d) if: no claimant is asked to pay (0\le x); no claimant receives more than his claim (x\le d); and the balance requirement is satisfied, that is, the sum of the awards is equal to the endowment (\sum_{i=1}^{n} x_i= 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)