relations (version 0.5-4)

choice: Relation-Based Choices

Description

Choose objects based on an ensemble of relations between these.

Usage

relation_choice(x, method = "symdiff", weights = 1, control = list(), ...)

Arguments

x

an ensemble of endorelations.

method

a character string specifying one of the built-in methods, or a function to be taken as a user-defined method. See Details for available built-in methods.

weights

a numeric vector with non-negative case weights. Recycled to the number of elements in the ensemble given by x if necessary.

control

a list of control parameters. See Details.

...

a list of control parameters (overruling those specified in control).

Value

• A set with the chosen objects, or a list of such sets.

Details

A social choice function is a rule for choosing from a set $D$ of objects, i.e., selecting suitable subsets of $D$. Voting rules used in elections are the most prominent example of such functions, which typically aggregate individual preferences (e.g., of voters).

Choice methods "symdiff" and "CKS" (currently the only ones available) choose a given number $k$ of objects (winners) by determining a relation $R$ minimizing $\sum_b w_b d(R_b, R)$ over all relations for which winners are always strictly preferred to losers, without any further constraints on the relations between pairs of winners or pairs of losers, where $d$ is symmetric difference (symdiff, Kemeny-Snell) or Cook-Kress-Seiford (CKS) dissimilarity, respectively, the $R_b$ are crisp endorelations, and $w_b$ is the case weight given to $R_b$. (Note that this is different from computing consensus preference relations.)

Available control options include: [object Object],[object Object]

Examples

data("SVM_Benchmarking_Classification")
## Determine the three best classification learners in the above sense.
relation_choice(SVM_Benchmarking_Classification, k = 3)