R: Relation-Based Choices

choice {relations} | R Documentation

## 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`).

### 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 ∑_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.

### Value

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

### Examples

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

[Package relations version 0.6-7 Index]