lorenzdominance {ClaimsProblems} | R Documentation |
Lorenz-dominance relation
Description
This function checks whether or not the awards assigned by two rules to a claims problem are Lorenz-comparable.
Usage
lorenzdominance(E, d, Rules, Info = FALSE)
Arguments
E |
The endowment. |
d |
The vector of claims. |
Rules |
The two rules: AA, APRO, CE, CEA, CEL, DT, MO, PIN, PRO, RA, Talmud. |
Info |
A logical value. |
Details
Let be the endowment to be divided and
the vector of claims
with
and such that
the sum of claims exceeds the endowment.
A vector is an awards vector for the claims problem
if
and satisfies the balance requirement, that is,
the sum of its coordinates is equal to
.
Let
be the set of awards vectors for
.
Given a claims problem , in order to compare a pair of awards vectors
with the Lorenz criterion,
first one has to rearrange the coordinates of each allocation in a non-decreasing order. Then we say that
Lorenz-dominates
(or, that
is Lorenz-dominated by
)
if all the cumulative sums of the rearranged coordinates are greater with
than with
. That is,
Lorenz-dominates
if for each
we have that
Let and
be two rules. We say that
Lorenz-dominates
if
Lorenz-dominates
for all
.
Value
If Info = FALSE, the Lorenz-dominance relation between the awards vectors selected by both rules. If both awards vectors are equal then cod = 2. If the awards vectors are not Lorenz-comparable then cod = 0. If the awards vector selected by the first rule Lorenz-dominates the awards vector selected by the second rule then cod = 1; otherwise cod = -1. If Info = TRUE, it also gives the corresponding cumulative sums.
References
Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American statistical association, 9(70), 209-219.
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
Mirás Calvo, M.Á., Núñez Lugilde, I., Quinteiro Sandomingo, C., and Sánchez-Rodríguez, E. (2021). The adjusted proportional and the minimal overlap rules restricted to the lower-half, higher-half, and middle domains. Working paper 2021-02, ECOBAS.
See Also
cumawardscurve, deviationindex, indexgpath, lorenzcurve, giniindex.
Examples
E=10
d=c(2,4,7,8)
Rules=c(AA,CEA)
lorenzdominance(E,d,Rules)