# indexgpath: Index path In ClaimsProblems: Analysis of Conflicting Claims

 indexgpath R Documentation

## 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, 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.

### Details

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.

### 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. (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.

### 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 Jan. 12, 2023, 5:13 p.m.