CEA {ClaimsProblems}

Constrained equal awards rule

Description

This function returns the awards vector assigned by the constrained equal awards rule (CEA) to a claims problem.

Usage

CEA(E, d, name = FALSE)

Arguments

E

The endowment.

d

The vector of claims.

name

A logical value.

Details

Let E\ge 0 be the endowment to be divided and let d\in \mathcal{R}^n be the vector of claims with d\ge 0 and such that \sum_{i=1}^{n} d_i\ge E, the sum of claims exceeds the endowment.

The constrained equal awards rule (CEA) equalizes awards under the constraint that no individual's award exceeds his/her claim. Then, claimant i receives the minimum of the claim and a value \lambda \ge 0 chosen so as to achieve balance.

CEA_i(E,d)=\min\{d_i,\lambda\},\ i=1,\dots,n, \ such \ that \ \sum_{i=1}^{n} CEA_i(E,d)=E.

The constrained equal awards rule corresponds to the Dutta-Ray solution to the associated (pessimistic) coalitional game. The CEA and CEL rules are dual.

Value

The awards vector selected by the CEA rule. If name = TRUE, the name of the function (CEA) as a character string.

References

Maimonides, Moses, 1135-1204. Book of Judgements, Moznaim Publishing Corporation, New York, Jerusalem (Translated by Rabbi Elihahu Touger, 2000).

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, CE, CEL, PIN, Talmud

Examples

E=10
d=c(2,4,7,8)
CEA(E,d)
# CEA and CEL are dual: CEA(E,d)=d-CEL(D-E,d)
D=sum(d)
d-CEL(D-E,d)