indexgpath | R Documentation |

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.

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

`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. |

`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", "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. |

Let *d* be a vector of claims rearranged from small to large, *
0 ≤ d1 ≤...≤ dn*.

Given two rules *R* and *S*, consider the function *J* that assigns to each *0<E≤ D*
the value *J(E)=I(R(E,d),S(E,d))*, that is, the signed deviation index of the rules *R* and *S* for the problem *(E,d)*.
The graph of *J* is the signed index path of *S* in function of the rule *R* for the vector of claims *d*.

Given two rules *R* and *S*, consider the function *J+* that assigns to each *0<E≤ D*
the value *J+(E)=I+(R(E,d),S(E,d))*, that is, the deviation index of the rules *R* and *S* for the problem *(E,d)*.
The graph of *J+* is the index path of *S* in function of the rule *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 R = PRO, the function draws the proportionality deviation index path or the signed proportionality deviation index path.

*indexpath* function of version 0.1.0 returned the signed proportionality deviation index path.

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

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. (2022). Deviation from proportionality and Lorenz-domination for claims problems. Rev Econ Design. doi: 10.1007/s10058-022-00300-y

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.

deviationindex, cumawardscurve, giniindex, lorenzcurve, lorenzdominance, allrules.

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)

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