Aggregation and Consensus Methods for Preference-Approvals

Tools for aggregating ordinal preference data into a group consensus. The package implements DIVA (Divide and Conquer for Preference-Approvals), a distance-based aggregation method for preference-approvals, that is, preference data in which voters express both a (weak) ranking and an approval of the alternatives. The consensus is the preference-approval minimising the average distance to the set of voters, measured through the family of distances of Erdamar, Garcia-Lapresta, Perez-Roman and Sanver (2014) . Methods and applications are described in Albano and Romano (2026) . The package is designed to be extended with further methods for ordinal preference data.

TheOrdinals

TheOrdinals provides aggregation and consensus methods for ordinal preference data. The first release implements DIVA (Divide and Conquer for Preference-Approvals), a distance-based aggregation method introduced in:

Albano, A. and Romano, M. (2026). A distance-based aggregation method for finding consensus in preference-approvals. Advances in Data Analysis and Classification. https://doi.org/10.1007/s11634-025-00663-4

The package is designed to grow: further methods for ordinal preference data can be added in future releases.

Preference-approvals

A preference-approval is a pair (ranking, approval): a (weak) ranking of n alternatives together with the subset of approved alternatives, subject to a consistency condition that links the two components. A set of m preference-approvals is stored as a numeric matrix with 2n columns: the first n columns hold the ranking (positions, ties allowed) and the last n columns hold the approval indicators (1 approved, 0 not approved).

Installation

# install.packages("ConsRank")
# from a local clone of the package directory:
# install.packages("TheOrdinals", repos = NULL, type = "source")

Quick start

library(TheOrdinals)

# four voters over four alternatives
x <- rbind(
  c(1, 2, 3, 4, 1, 1, 0, 0),
  c(2, 1, 3, 4, 1, 0, 0, 0),
  c(1, 2, 4, 3, 1, 1, 0, 0),
  c(1, 3, 2, 4, 1, 1, 1, 0)
)

# DIVA consensus
res <- diva(x, algorithm = "quick")
res
res$d_lambda          # achieved average distance

# sensitivity to the ranking/approval weight
diva_sensitivity(x)$d_lambda

# distance between preference-approvals
pref_dist(x, lambda = 0.5)

Main functions

Datasets

• french_election_2002 — preference-approvals on 15 candidates (2002 French presidential election).
• formula1_1950 — rankings of 81 drivers across 7 Grands Prix, top-5 approved (1950 Formula 1 World Championship).
• pa_small — small synthetic universe (n = 4) for quick examples.

License

GPL-3.