ClaimsProblems (version 1.0.0)

schedrule: Schedules of awards of a rule

Description

This function returns the graphical representation of the schedules of awards of any rule for a claims vector.

Usage

schedrule(d, claimants, Rule, col = NULL, points = 201, legend = TRUE)

Value

The graphical representation of the schedules of awards of a rule for a claims vector and a group of claimants.

Arguments

d

A vector of claims.

claimants

A subset of claimants.

Rule

The rule: AA, APRO, CE, CEA, CEL, AV, DT, MO, PIN, PRO, RA, Talmud, RTalmud.

col

The colours. If col = NULL then the sequence of default colours is chosen randomly.

points

The number of values of the endowment to draw the path.

legend

A logical value. The colour legend is shown if legend = TRUE.

Details

Let \(N=\{1,\ldots,n\}\) be the set of claimants, \(d\in \mathbb{R}_+^N\) a vector of claims and denote by \(D=\sum_{i\in N} d_i\) the sum of the claims.

The schedules of awards of a rule \(\mathcal{R}\) for claimant \(i\) is the function \(S\) that assigns to each \(E\in [0,D]\) the value: \(S(E)=\mathcal{R}_i(E,d)\in \mathbb{R}\). Therefore, the schedules of awards of a rule plots each claimants's award as a function of \(E\).

References

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

pathawards, pathawards3, schedrules, verticalruleplot.

Examples

d=c(2,4,7,8)
Rule=Talmud
claimants=c(1,2,3,4)
col=c("red","green","yellow","blue")
schedrule(d,claimants,Rule,col)
# The schedules of awards of the concede-and-divide rule.
schedrule(c(2,4),c(1,2),CD)