# PIN: Piniles' rule In ClaimsProblems: Analysis of Conflicting Claims

## Description

This function returns the awards vector assigned by the Piniles' rule (PIN) to a claims problem.

## Usage

 `1` ```PIN(E, d, name = FALSE) ```

## Arguments

 `E` The endowment. `d` The vector of claims. `name` A logical value.

## Details

Let E≥ 0 be the endowment to be divided and d the vector of claims with d≥ 0 and such that D=∑ di ≥ E, the sum of claims D exceeds the endowment.

The Piniles' rule 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 it assigns to each claimant i half of the claim, di/2 and, then, it distributes the remainder with the CEA rule. Therefore:

If E≤ D/2 then:

PIN(E,d)=CEA(E,d/2).

If E≥ D/2 then:

PIN(E,d)=d/2+CEA(E-D/2,d/2).

## Value

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

## References

Piniles, H.M. (1861). Darkah shel Torah. Forester, Vienna.

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.

 ```1 2 3``` ```E=10 d=c(2,4,7,8) PIN(E,d) ```