indexgpath: Index path

In ClaimsProblems: Analysis of Conflicting Claims

Index path

Description

The function returns the deviation index path or the signed deviation index path for a rule with respect to another rule for a vector of claims.

Usage

indexgpath(
  d,
  Rule = PRO,
  Rules,
  signed = TRUE,
  col = NULL,
  points = 201,
  legend = TRUE
)

Arguments

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.
signed	A logical value. If signed = FALSE, it draws the deviation index path and, if signed = TRUE it draws the signed deviation index path. By default, signed = TRUE.
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").
points	The number of endowment values to be drawn.
legend	A logical value. The legend is shown if legend = TRUE.

Details

Let N=\{1,\ldots,n\} be the set of claimants, d\in \mathbb{R}^N a vector of claims rearranged from small to large, 0 \le d_1 \le...\le d_n and D=\sum_{i\in N}d_i.

Given two rules \mathcal{R} and \mathcal{S}, consider the function J that assigns to each E\in (0,D] the value J(E)=I\Bigl(\mathcal{R}(E,d),\mathcal{S}(E,d)\Bigr), that is, the signed deviation index of the rules \mathcal{R} and \mathcal{S} for the problem (E,d). The graph of J is the signed index path of \mathcal{S} in function of the rule \mathcal{R} for the vector of claims d.

Given two rules \mathcal{R} and \mathcal{S}, consider the function J^{+} that assigns to each E\in (0,D] the value J^{+}(E)=I^{+}\Bigl(\mathcal{R}(E,d),\mathcal{S}(E,d)\Bigr), that is, the deviation index of the rules \mathcal{R} and \mathcal{S} for the problem (E,d). The graph of J^{+} is the index path of \mathcal{S} in function of the rule \mathcal{R} for the vector of claims d.

The signed index path and the index path are simple tools to visualize the discrepancy of the divisions recommended by a rule for a vector of claims with respect to the divisions recommended by another rule. If \mathcal{R} = \text{PRO}, the function draws the proportionality deviation index path or the signed proportionality deviation index path.

Value

This function returns the deviation index path of a rule (or several rules) for a vector of claims.

References

Ceriani, L. and Verme, P. (2012). The origins of the Gini index: extracts from Variabilitá e Mutabilitá (1912) by Corrado Gini. The Journal of Economic Inequality 10(3), 421-443.

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.

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, cumawardscurve, deviationindex, giniindex, lorenzcurve, lorenzdominance.

Examples

d=c(2,4,7,8)
Rule=PRO
Rules=c(Talmud,RA,AA)
col=c("red","green","blue")
indexgpath(d,Rule,Rules,signed=TRUE,col)

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