relations (version 0.6-2)

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", "CKS" and "euclidean" choose a given number $k$ of objects (winners) by determining a relation $R$ minimizing $\sum_b w_b d(R_b, R)^p$ 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), Cook-Kress-Seiford (CKS), or Euclidean dissimilarity, respectively, and $w_b$ is the case weight given to $R_b$. For symdiff and CKS choice, the $R_b$ must be crisp endorelations, and $p = 1$; for Euclidean choice, the $R_b$ can be crisp or fuzzy endorelations, and $p = 2$. (Note that solving such a choice problem is different from computing consensus preference relations.)

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

Choice method "Schulze" implements the Schulze method for selecting winners from (votes expressing) preferences. See e.g. http://en.wikipedia.org/wiki/Schulze_method for details. Currently, the Schulze heuristic is used, and the set of all possible winners is returned.

Examples

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