CEL {ClaimsProblems} | R Documentation |
Constrained equal losses rule
Description
This function returns the awards vector assigned by the constrained equal losses rule (CEL) to a claims problem.
Usage
CEL(E, d, name = FALSE)
Arguments
E |
The endowment. |
d |
The vector of claims. |
name |
A logical value. |
Details
Let N=\{1,\ldots,n\}
be the set of claimants, E\ge 0
the endowment to be divided and d\in \mathbb{R}_+^N
the vector of claims
such that \sum_{i \in N} d_i\ge E
.
The constrained equal losses rule (CEL) equalizes losses under the constraint that no award
is negative. Then, claimant i
receives the maximum of zero and the claim minus a number \lambda \ge 0
chosen so as to achieve balance. That is, for each i\in N
,
\text{CEL}_i(E,d)=\max\{0,d_i-\lambda\},
where \lambda\geq 0
is chosen such that \sum_{i\in N} \text{CEL}_i(E,d)=E.
CEA and CEL are dual rules.
Value
The awards vector selected by the CEL rule. If name = TRUE
, the name of the function (CEL) as a character string.
References
Maimonides, Moses, [1135-1204], Book of Judgements (translated by Rabbi Elihahu Touger, 2000), New York and Jerusalem: Moznaim Publishing Corporation, 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, axioms, CE, CEA, AV, PIN, Talmud, RTalmud.
Examples
E=10
d=c(2,4,7,8)
CEL(E,d)
# CEL and CEA are dual: CEL(E,d)=d-CEA(D-E,d)
D=sum(d)
d-CEA(D-E,d)