RTalmud: Reverse Talmud rule

In ClaimsProblems: Analysis of Conflicting Claims

Reverse Talmud rule

Description

This function returns the awards vector assigned by the reverse Talmud rule to a claims problem.

Usage

RTalmud(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 D=\sum_{i \in N} d_i\ge E.

The reverse Talmud rule (RTalmud) coincides with the constrained equal losses rule (CEL) applied to the problem (E, d/2) if the endowment is less or equal than the half-sum of the claims, D/2. Otherwise, the reverse Talmud rule assigns d/2 and the remainder, E-D/2, is awarded with the constrained equal awards rule with claims d/2. Therefore, for each i\in N,

\text{RTalmud}_i(E,d) = \begin{cases} \max\{\frac{d_i}{2}-\lambda,0\} & \text{if } E\leq \tfrac{1}{2}D\\[3pt] \frac{d_i}{2}+\min\{\frac{d_i}{2},\lambda\} & \text{if } E \geq \tfrac{1}{2}D \end{cases},

where \lambda \geq 0 is chosen such that \underset{i\in N}{\sum} \text{RTalmud}_i(E,d)=E.

Value

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

References

Chun, Y., Schummer, J., and Thomson, W. (2001). Constrained egalitarianism: a new solution for claims problems. Seoul Journal of Economics 14, 269-297.

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

AA, allrules, APRO, Talmud, CEA, CEL, CD, RA.

Examples

E=10
d=c(2,4,7,8)
RTalmud(E,d)

ClaimsProblems documentation built on April 4, 2025, 2:21 a.m.