# indexpath: Proportionality index path In ClaimsProblems: Analysis of Conflicting Claims

## Description

The function returns the proportionality deviation index path of a rule for a vector of claims.

## Usage

 `1` ```indexpath(d, Rules, col = NULL, points = 201, legend = TRUE) ```

## Arguments

 `d` The vector of claims. `Rules` The rules: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. `col` The colors. If col = NULL then the sequence of default colors 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 color legend is shown if legend = TRUE.

## Details

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

Given a rule R, consider the function J that assigns to each 0<E≤ D the value J(E)=I(R,E,d), that is, the proportionality deviation index of the rule R for the problem (E,d). The graph of J is the index path of R for the vector of claims d.

The index path is a simple tool to visualize the discrepancy of the divisions recommended by a rule for a vector of claims with respect to the proportional distribution and to compare it with other rules.

## Value

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

## References

Mirás Calvo, M.A., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2021). Deviation from proportionality and Lorenz-dominance between the average of awards and the standard rules for claims problems. Working paper 2021-01, ECOBAS.

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.

 ```1 2 3 4``` ```d=c(2,4,7,8) Rules=c(Talmud,RA,AA) col=c("red","green","blue") indexpath(d,Rules,col) ```