relations (version 0.6-13)

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(), ...)

Value

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

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).

Details

A social choice function is a rule for choosing from a set \(X\) of objects, i.e., selecting suitable subsets of \(X\). 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", "PC" and "euclidean" choose a given number \(k\) of objects (“winners”) by determining a relation \(R\) minimizing \(\sum_b w_b d(R_b, R)^e\) 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), generalized paired comparison, or Euclidean dissimilarity, respectively, and \(w_b\) is the case weight given to \(R_b\). For symdiff, CKS and PC choice, the \(R_b\) must be crisp endorelations, and \(e = 1\); for Euclidean choice, the \(R_b\) can be crisp or fuzzy endorelations, and \(e = 2\). (Note that solving such a choice problem is different from computing consensus preference relations.) See relation_dissimilarity() for more information about these dissimilarities.

Available control options include:

k

an integer giving the number of objects/winners to be chosen.

n

the maximal number of optimal choices to be obtained, with NA constants or "all" indicating to obtain all optimal choices. By default, only a single optimal choice is computed.

For the general PC case, the discrepancies can be specified via the delta control option.

Choice method "Schulze" implements the Schulze method for selecting winners from (votes expressing) preferences. See e.g. https://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)