cumawardscurve {ClaimsProblems}

Cumulative awards curve

Description

The graphical representation of the cumulative curves of a rule (or several rules) with respect to a given rule, for a claims problem.

Usage

cumawardscurve(E, d, Rule = PRO, Rules, col = NULL, legend = TRUE)

Arguments

E

The endowment.

d

The vector of claims.

Rule

Principal Rule: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. By default, Rule = PRO.

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

Rearrange the claims from small to large, 0 \le d_1 \le...\le d_n. The cumulative curve allows us to compare the division recommended by a specific rule R with the division the division recommended by another specific rule S.

The cumulative awards curve of a rule S with respect of a rule R for the claims problem (E,d) is the polygonal path connecting the n+1 points

(0,0), (\frac{R_1}{E},\frac{S_1}{E}),\dots,(\frac{\sum_{i=1}^{n-1}R_i}{E},\frac{\sum_{i=1}^{n-1}S_i}{E}),(1,1).

The cumulative awards curve fully captures the Lorenz ranking of rules: if a rule R Lorenz-dominates a rule S then, for each claims problem, the cumulative curve of R lies above the cumulative curve of S. If R = PRO, the cumulative curve coincides with the cumulative claims-awards curve.

cumulativecurve function of version 0.1.0 returned the cumulative claims-awards curve with respect to the proportional rule.

Value

The graphical representation of the cumulative curves of a rule (or several rules) for a claims problem.

References

Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American statistical association, 9(70), 209-219.

Mirás Calvo, M.Á., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez Rodríguez, E. (2022). Deviation from proportionality and Lorenz-domination for claims problems. Rev Econ Design. doi: 10.1007/s10058-022-00300-y

See Also

deviationindex, indexgpath, lorenzcurve, giniindex, lorenzdominance, allrules.

Examples

E=10
d=c(2,4,7,8)
Rule=PRO
Rules=c(AA,RA,Talmud,CEA,CEL)
cumawardscurve(E,d,Rule,Rules)