indexgpath {ClaimsProblems} | 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, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud. By default, |
Rules |
The rules: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud. |
signed |
A logical value. If |
col |
The colours. If |
points |
The number of endowment values to be drawn. |
legend |
A logical value. The legend is shown if |
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)