CE: Constrained egalitarian rule
In ClaimsProblems: Analysis of Conflicting Claims
CE R Documentation
Constrained egalitarian rule
Description
This function returns the awards vector assigned by the constrained egalitarian rule (CE) rule to a claims problem.
Usage
CE(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.
Rearrange the claims from small to large, 0 \le d_1 \le...\le d_n.
The constrained egalitarian rule (CE) coincides with the constrained equal awards rule (CEA) applied to
the problem (E, d/2) if the endowment is less or equal than the half-sum of the claims, D/2.
Otherwise, any additional unit is assigned to claimant 1 until she/he receives the minimum
of the claim and half of d_2. If this minimun is d_1, she/he stops there. If it is not, the
next increment is divided equally between claimants 1 and 2 until claimant 1 receives
d_1 (in this case she drops out) or they reach d_3/2.
If claimant 1 leaves, claimant 2 receives any additional increment until she/he reaches d_2
or d_3/2. In the case that claimant 1 and 2 reach d_3/2, any additional unit is
divided between claimants 1, 2, and 3 until the first one receives d_1 or they
reach d_4/2, and so on. Therefore, for each i\in N,
\text{CE}_i(E,d)=\begin{cases}
\min\{\frac{d_i}{2},\lambda\} & \text{if } E\leq \tfrac{1}{2}D\\[3pt]
\max \bigl\{ \frac{d_i}{2},\min\{d_i,\lambda \} \bigr\} & \text{if } E \geq \tfrac{1}{2}D
\end{cases},
where \lambda \geq 0 is chosen such that \underset{i\in N}{\sum} \text{CE}_i(E,d)=E.
Value
The awards vector selected by the CE rule. If name = TRUE, the name of the function (CE) as a character string.
References
Chun, Y., Schummer, J., 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
allrules, axioms, CEA, PIN, Talmud.
Examples
E=10
d=c(2,4,7,8)
CE(E,d)
ClaimsProblems documentation built on April 4, 2025, 2:21 a.m.
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| CE | R Documentation |
Constrained egalitarian rule
Description
This function returns the awards vector assigned by the constrained egalitarian rule (CE) rule to a claims problem.
Usage
CE(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.
Rearrange the claims from small to large, 0 \le d_1 \le...\le d_n.
The constrained egalitarian rule (CE) coincides with the constrained equal awards rule (CEA) applied to
the problem (E, d/2) if the endowment is less or equal than the half-sum of the claims, D/2.
Otherwise, any additional unit is assigned to claimant 1 until she/he receives the minimum
of the claim and half of d_2. If this minimun is d_1, she/he stops there. If it is not, the
next increment is divided equally between claimants 1 and 2 until claimant 1 receives
d_1 (in this case she drops out) or they reach d_3/2.
If claimant 1 leaves, claimant 2 receives any additional increment until she/he reaches d_2
or d_3/2. In the case that claimant 1 and 2 reach d_3/2, any additional unit is
divided between claimants 1, 2, and 3 until the first one receives d_1 or they
reach d_4/2, and so on. Therefore, for each i\in N,
\text{CE}_i(E,d)=\begin{cases}
\min\{\frac{d_i}{2},\lambda\} & \text{if } E\leq \tfrac{1}{2}D\\[3pt]
\max \bigl\{ \frac{d_i}{2},\min\{d_i,\lambda \} \bigr\} & \text{if } E \geq \tfrac{1}{2}D
\end{cases},
where \lambda \geq 0 is chosen such that \underset{i\in N}{\sum} \text{CE}_i(E,d)=E.
Value
The awards vector selected by the CE rule. If name = TRUE, the name of the function (CE) as a character string.
References
Chun, Y., Schummer, J., 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
allrules, axioms, CEA, PIN, Talmud.
Examples
E=10
d=c(2,4,7,8)
CE(E,d)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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