View source: R/lorenzdominance.R

lorenzdominance | R Documentation |

This function checks whether or not the awards assigned by two rules to a claims problem are Lorenz-comparable.

lorenzdominance(E, d, Rules, Info = FALSE)

`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. |

Let *E≥ 0* be the endowment to be divided and *d* the vector of claims
with *d≥ 0* and such that the sum of claims exceeds the endowment.

A vector *x=(x1,...,xn)* is an awards vector for the claims problem *(E,d)* if *0≤ x ≤ d*
and satisfies the balance requirement, that is, *x1+…+xn=E* the sum of its coordinates is equal to *E*.
Let *X(E,d)* be the set of awards vectors for *(E,d)*.

Given a claims problem *(E,d)*, in order to compare a pair of awards vectors *x,y in X(E,d)* with the Lorenz criterion,
first one has to rearrange the coordinates of each allocation in a non-decreasing order. Then we say that *x* Lorenz-dominates *y* (or, that *y* is Lorenz-dominated by *x*)
if all the cumulative sums of the rearranged coordinates are greater with *x* than with *y*. That is,
*x* Lorenz-dominates *y* if for each *k=1,…,n-1* we have that

*x1+…+xk ≥ y1+…+yk.*

Let *R* and *R'* be two rules. We say that *R* Lorenz-dominates *R'* if *R(E,d)* Lorenz-dominates *R'(E,d)* for all *(E,d)*.

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.

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.

cumawardscurve, deviationindex, indexgpath, lorenzcurve, giniindex.

E=10 d=c(2,4,7,8) Rules=c(AA,CEA) lorenzdominance(E,d,Rules)

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