cumawardscurve: Cumulative awards curve

In ClaimsProblems: Analysis of Conflicting Claims

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, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud. By default, Rule = PRO.
Rules	The rules: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud.
col	The colours. If col = NULL then the sequence of default colours is: c("red", "blue", "green", "yellow", "pink","orange", "coral4", "darkgray", "burlywood3", "black", "darkorange", "darkviolet").
legend	A logical value. The colour legend is shown if legend = TRUE.

Details

Let N=\{1,\ldots,n\} be the set of claimants, E\ge 0 the endowment to be divided and d\in \mathbb{R}_+^N the vector of claims such that \sum_{i \in N} d_i\ge E.

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 \mathcal{R} with the division the division recommended by another specific rule \mathcal{S}.

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

(0,0), \Bigl(\frac{\mathcal{R}_1}{E},\frac{\mathcal{S}_1}{E}\Bigr),\dots,\Bigl(\frac{\sum_{i=1}^{n-1}\mathcal{R}_i}{E},\frac{\sum_{i=1}^{n-1}\mathcal{S}_i}{E}\Bigr),(1,1).

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

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. (2023). Deviation from proportionality and Lorenz-domination for claims problems. Review of Economic Design 27, 439-467.

See Also

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

Examples

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

ClaimsProblems documentation built on April 4, 2025, 2:21 a.m.