Package 'prefio'

Compute the Adjacency Matrix for a vector of preferences

Description

Convert a set of preferences to an adjacency matrix summarising wins and losses between pairs of items.

Usage

adjacency(x, preferences_col = NULL, frequency_col = NULL, ...)

Arguments

x	A preferences object or a tibble with a preferences-typed column.
preferences_col	<tidy-select> When x is a tibble, the column containing the preferences.
frequency_col	<tidy-select> When x is a tibble, the column containing the frequency of the preferences. If not provided, each row is considered to be observed a single time.
...	Currently unused.

Details

For a preferences object with $N$ items, the adjacency matrix is an $N$ by $N$ matrix, with element $(i, j)$ being the number of times item $i$ wins over item $j$. For example, in the preferences {1} > {3, 4} > {2}, item 1 wins over items 2, 3, and 4, while items 3 and 4 win over item 2.

If weights is specified, the values in the adjacency matrix are the weighted counts.

Value

An $N$ by $N$ matrix, where $N$ is the number of items.

Examples

x <- tibble::tribble(
  ~voter_id, ~species, ~food, ~ranking,
  1, "Rabbit", "Apple", 1,
  1, "Rabbit", "Banana", 2,
  1, "Rabbit", "Carrot", 3,
  2, "Monkey", "Banana", 1,
  2, "Monkey", "Apple", 2,
  2, "Monkey", "Carrot", 3
) |>
  long_preferences(
    food_preference,
    id_cols = voter_id,
    item_col = food,
    rank_col = ranking
  ) |>
  dplyr::pull(food_preference) |>
  adjacency()

---

Complete preferences by adding unselected items as last place occurrances.

Description

Complete preferences by adding unselected items as last place occurrances.

Usage

pref_add_unranked(x)

Arguments

x	A vector of preferences.

Value

A new vector of preferences, with each selection starting with the corresponding selections made in x, but with all unranked items placed last.

Examples

# Complete partial rankings by adding unranked items last
pref_add_unranked(preferences(c("a > b", "c > a", "b")))

---

Check if a preference is blank.

Description

Check if a preference is blank.

Usage

pref_blank(x)

Arguments

x	A vector of preferences.

Value

A logical vector indicating which preferences are blank, i.e., ⁠[]⁠.

Examples

pref_blank(preferences(c("a > b > c", "", "b > c")))

---

Covariance matrix for preferences, calculated using the rankings matrix.

Description

Covariance matrix for preferences, calculated using the rankings matrix.

Usage

pref_cov(x, preferences_col = NULL, frequency_col = NULL, ...)

Arguments

x	A vector of preferences, or a tibble with a column of preferences.
preferences_col	<tidy-select> When x is a tibble, the column containing the preferences.
frequency_col	<tidy-select> When x is a tibble, the column containing the frequency of the preferences. If not provided, each row is considered to be observed a single time.
...	Extra arguments to be passed to stats::cov.wt.

Value

A covariance matrix containing covariances for the ranks assigned to item pairs.

Examples

# Simple covariance on a vector of preferences
prefs <- preferences(c("a > b > c", "b > c > a", "c > a > b"))
pref_cov(prefs)

# Weighted covariance by frequency
df <- tibble::tibble(
  prefs = preferences(c("a > b > c", "b > c > a")),
  freq = c(3, 2)
)
pref_cov(df, preferences_col = prefs, frequency_col = freq)

---

Get the name of the item(s) assigned a specific rank, e.g., first.

Description

Get the name of the item(s) assigned a specific rank, e.g., first.

Usage

pref_get_items(x, rank, drop = FALSE)

Arguments

x	A vector of preferences.
rank	A single integer, the rank which you would like to inspect.
drop	When FALSE (default), blank preferences will remain. When TRUE, blank preferences will be omitted.

Value

A list containing the name(s) of the item(s) ranked rank in each of the preferences in x.

Examples

# Get items ranked first
pref_get_items(preferences(c("a > b > c", "b = c > a")), rank = 1)
# Get items ranked second
pref_get_items(preferences(c("a > b > c", "b = c > a")), rank = 2)
# Get items ranked first, dropping blank preferences
pref_get_items(preferences(c("a > b > c", "", "b = c > a")), rank = 1, drop = TRUE)

---

Get the rank assigned to a specific item in a set of preferences.

Description

Get the rank assigned to a specific item in a set of preferences.

Usage

pref_get_rank(x, item_name)

Arguments

x	A vector of preferences.
item_name	The name of the item to extract the rank for.

Value

The rank of item_name for each of the preferences in x.

Examples

pref_get_rank(preferences(c("a > b > c", "b > c = a", "")), "a")

---

Compute the instant-runoff voting winner for a set of preferences.

Description

A very rudimentary implementation of the IRV counting algorithm. It does not handle ties elegantly, and should only be used for demonstration purposes. This implementation eliminates all candidates with the fewest first-choice votes in each round until one candidate has a majority or fewer than two candidates remain.

Usage

pref_irv(x, preferences_col = NULL, frequency_col = NULL)

Arguments

x	A vector of preferences, or a tibble with a column of preferences.
preferences_col	<tidy-select> When x is a tibble, the column containing the preferences.
frequency_col	<tidy-select> When x is a tibble, the column containing the frequency of the preferences. If not provided, each row is considered to be observed a single time.

Value

A list containing:

winner

The winning candidate(s) after IRV counting

rounds

A list of tibbles, each containing vote tallies for each round

eliminated

Character vector of eliminated candidates in order

Examples

# Multi-round election with four candidates
prefs <- preferences(c(
  "alice > bob > charlie > david",
  "alice > bob > charlie > david",
  "alice > charlie > bob > david",
  "bob > alice > charlie > david",
  "bob > charlie > alice > david",
  "bob > charlie > alice > david",
  "charlie > david > alice > bob",
  "charlie > david > bob > alice",
  "david > charlie > bob > alice",
  "david > charlie > bob > alice"
))
result <- pref_irv(prefs)
result$winner # Final winner after elimination rounds
result$rounds # Vote tallies for each round

# Using aggregated data frame
df <- tibble::tibble(
  prefs = preferences(c(
    "alice > bob > charlie > david",
    "alice > charlie > bob > david",
    "bob > alice > charlie > david",
    "bob > charlie > alice > david",
    "charlie > david > alice > bob",
    "charlie > david > bob > alice",
    "david > charlie > bob > alice"
  )),
  freq = c(2, 1, 1, 2, 1, 1, 2)
)
pref_irv(df, prefs, freq)

---

Keep only specified items from preferences.

Description

Keep only specified items from preferences.

Usage

pref_keep(x, items)

Arguments

x	A vector of preferences.
items	The names of the items which should be kept for preferences in x.

Value

A new vector of preferences, but only containing items from each selection.

Examples

# Keep only 'a' and 'c'
pref_keep(preferences(c("a > b > c", "b > c > a")), c("a", "c"))

---

Check the length (number of rankings) of a preference.

Description

Check the length (number of rankings) of a preference.

Usage

pref_length(x)

Arguments

x	A vector of preferences.

Value

The number of items listed on each of the preferences.

Examples

pref_length(preferences(c("a > b > c", "", "b > c")))

---

Remove specified items from preferences.

Description

Remove specified items from preferences.

Usage

pref_omit(x, items)

Arguments

x	A vector of preferences.
items	The names of the items which should be removed from the preferences in x.

Value

A new vector of preferences, but with items removed from each selection.

Examples

# Remove 'b'
pref_omit(preferences(c("a > b > c", "b > c > a")), "b")
# Remove 'b' and 'd'
pref_omit(preferences(c("a > b > c > d", "b > c > a > d")), c("b", "d"))

---

Eliminate lowest (or highest) ranked items from preferences.

Description

Eliminate lowest (or highest) ranked items from preferences.

Usage

pref_pop(x, n = 1L, lowest = TRUE, drop = FALSE)

Arguments

x	A vector of preferences.
n	The number of times to remove the bottom rank.
lowest	If TRUE, eliminates the lowest ranked item(s) for each selection.
drop	If TRUE, drops blank preferences from the output.

Value

A new vector of preferences which is equal to x but with the least preferred selection dropped for each selection.

Examples

# Remove the lowest ranked item from each preference
pref_pop(preferences(c("a > b > c", "b > c > a")))

# Remove the 2 lowest ranked items
pref_pop(preferences(c("a > b > c > d", "b > c > a > d")), n = 2)

# Remove the highest ranked item instead
pref_pop(preferences(c("a > b > c", "b > c > a")), lowest = FALSE)

# Remove blank preferences that result from popping
pref_pop(preferences(c("a > b", "c", "")), drop = TRUE)

---

Reverse preference rankings

Description

Reverse preference rankings

Usage

pref_rev(x, ...)

Arguments

x	A vector of preferences.
...	Not used.

Value

A vector of preferences with rankings reversed (first becomes last, etc.)

Examples

pref_rev(preferences(c("a > b > c", "b > c > a")))

---

Truncate preferences to a maximum number of ranks.

Description

Truncate preferences to a maximum number of ranks.

Usage

pref_trunc(x, n = 1L, bottom = FALSE)

Arguments

x	A vector of preferences.
n	The maximum number of ranks to include (positive) or number of ranks to drop (negative). Must be an integer.
bottom	If FALSE (default), operates on top ranks. If TRUE, operates on bottom ranks.

Value

A vector of preferences with each selection truncated according to the parameters.

Examples

# Keep only the top 2 ranks
pref_trunc(preferences(c("a > b > c > d", "b > c > a")), n = 2)
# Keep only the bottom 2 ranks
pref_trunc(preferences(c("a > b > c > d", "b > c > a")), n = 2, bottom = TRUE)
# Drop the bottom 2 ranks (keep top ranks)
pref_trunc(preferences(c("a > b > c > d", "b > c > a")), n = -2)
# Drop the top 2 ranks (keep bottom ranks)
pref_trunc(preferences(c("a > b > c > d", "b > c > a")), n = -2, bottom = TRUE)

---

pref_type

Description

Ordinal preferences can order every item, or they can order a subset. Some ordinal preference datasets will contain ties between items at a given rank. Hence, there are four distinct types of preferential data:

soc

Strict Orders - Complete List

soi

Strict Orders - Incomplete List

toc

Orders with Ties - Complete List

toi

Orders with Ties - Incomplete List

Usage

pref_type(x, n_items = NULL)

Arguments

x	A preferences object (or vector data representing preferences)
n_items	The number of items, needed to assess whether a selection is complete or not. Defaults to nlevels(x) if x has class preferences, otherwise defaults to the length of the longest preference.

Value

One of c("soc", "soi", "toc", "toi"), indicating the type of preferences in x (with or without ties / complete or incomplete rankings).

---

Preferences Objects

Description

A tidy interface for working with ordinal preferences.

Usage

long_preferences(
  data,
  col,
  id_cols = NULL,
  rank_col = NULL,
  item_col = NULL,
  item_names = NULL,
  verbose = TRUE,
  unused_fn = NULL,
  na_action = c("drop_rows", "drop_preferences"),
  ...
)

wide_preferences(
  data,
  col = NULL,
  ranking_cols = NULL,
  verbose = TRUE,
  na_action = c("keep_as_partial", "drop_preferences"),
  ...
)

as_preferences(strings, sep = ">", equality = "=", descending = TRUE)

preferences(
  strings = character(0L),
  sep = ">",
  equality = "=",
  descending = TRUE
)

## S3 method for class 'preferences'
format(x, ...)

## S3 method for class 'preferences'
levels(x, ...)

Arguments

data	A data.frame or tibble to extract preferences from
col	The name of the new column, as a string or symbol.
id_cols	<tidy-select> The columns by which to group the dataset to extract a single preference selection.
rank_col	<tidy-select> For data in long-format: the column representing the rank for the associated item.
item_col	<tidy-select> For data in long-format: the column representing the items by name or by index, in which case the item_names parameter should also be passed.
item_names	The names of the full set of items. This is necessary when the dataset specifies items by index rather than by name, or when there are items which do not appear in any preference selection.
verbose	If TRUE, diagnostic messages will be sent to stdout.
unused_fn	When format="long", summarise the values of unused columns (those which are not specified by id_cols, item_col, or rank_col). The default action is to drop all unused columns. This can be a named list (e.g. ⁠list(column = function)⁠) if you want to apply different summaries for different columns or keep only specific unused columns, or it can be a single function to be applied across all unused columns.
na_action	Specifies how to handle NA values. long_preferences "drop_rows" Removes individual rows containing NA values before processing "drop_preferences" Removes the entire preference selection that contains any NA wide_preferences "keep" Interprets rows containing NAs as partial orderings "drop" Removes preferences with any NA ranks
...	Unused.
ranking_cols	<tidy-select> The columns from which to extract wide-format preferences.
strings	A character vector of preference strings
sep	Character separating the items in the string (default: ">")
equality	Character representing equality between items (default: "=")
descending	If TRUE, parse as descending order preferences.
x	A vector of preferences.
format	The format of the data: one of "ordering", "ranking", or "long" (see above). By default, data is assumed to be in "long" format.

Value

A preferences object, or a modified tibble with a column of preferences when data is a data.frame or tibble.

Examples

# Votes cast by two animals ranking a variety of fruits and vegetables.
# This is not real data, I made this up.
x <- tibble::tribble(
  ~voter_id, ~species, ~food, ~ranking,
  1, "Rabbit", "Apple", 1,
  1, "Rabbit", "Carrot", 2,
  1, "Rabbit", "Banana", 3,
  2, "Monkey", "Banana", 1,
  2, "Monkey", "Apple", 2,
  2, "Monkey", "Carrot", 3
)
# Process preferencial data into a single column.
x |>
  long_preferences(
    food_preference,
    id_cols = voter_id,
    item_col = food,
    rank_col = ranking
  )
# The same, but keep the species data.
x |>
  long_preferences(
    food_preference,
    id_cols = voter_id,
    item_col = food,
    rank_col = ranking,
    unused_fn = list(species = dplyr::first)
  )

---

Compute the Rankings Matrix for a vector of preferences

Description

Convert a set of preferences to a rankings matrix, where each preference defines a single row in the output. The columns in the rankings matrix give the vector or ranks assigned to the corresponding candidate.

Usage

ranking_matrix(x, preferences_col = NULL, frequency_col = NULL, ...)

Arguments

x	A preferences object or a tibble with a preferences-typed column.
preferences_col	<tidy-select> When x is a tibble, the column containing the preferences.
frequency_col	<tidy-select> When x is a tibble, the column containing the frequency of the preferences. If not provided, each row is considered to be observed a single time.
...	Currently unused.

Details

For a preferences vector of length $N$ with $M$ items, the rankings matrix is an $N$ by $M$ matrix, with element $(i, j)$ being the rank assigned to candidate $j$ in the $i$th selection.

Value

An $N$ by $M$ matrix, where $N$ is the number of preferences, and $M$ is the number of items.

Examples

x <- tibble::tribble(
  ~voter_id, ~species, ~food, ~ranking,
  1, "Rabbit", "Apple", 1,
  1, "Rabbit", "Banana", 2,
  1, "Rabbit", "Carrot", 3,
  2, "Monkey", "Banana", 1,
  2, "Monkey", "Apple", 2,
  2, "Monkey", "Carrot", 3
) |>
  long_preferences(
    food_preference,
    id_cols = voter_id,
    item_col = food,
    rank_col = ranking
  ) |>
  dplyr::pull(food_preference) |>
  ranking_matrix()

---

Read Ordinal Preference Data From PrefLib

Description

Read orderings from .soc, .soi, .toc or .toi files storing ordinal preference data format as defined by {PrefLib}: A Library for Preferences into a preferences object.

Usage

read_preflib(
  file,
  from_preflib = FALSE,
  preflib_url = "https://raw.githubusercontent.com/PrefLib/PrefLib-Data/main/datasets/"
)

Arguments

file	A preferential data file, conventionally with extension .soc, .soi, .toc or .toi according to data type.
from_preflib	A logical which, when TRUE will attempt to source the file from PrefLib by adding the database HTTP prefix.
preflib_url	The URL which will be preprended to file, if from_preflib is TRUE.

Details

Note that PrefLib refers to the items being ordered by "alternatives".

The file types supported are

.soc

Strict Orders - Complete List

.soi

Strict Orders - Incomplete List

.toc

Orders with Ties - Complete List

.toi

Orders with Ties - Incomplete List

The numerically coded orderings and their frequencies are read into a tibble, storing all original metadata in a "preflib" attribute.

A PrefLib file may be corrupt, in the sense that the ordered alternatives do not match their names. In this case, the file will still be read, but with a warning.

Value

A tibble with two columns: preferences and frequency. The preferences column contains all the preferential orderings in the file, and the frequency column the relative frequency of this selection.

Note

The Netflix and cities datasets used in the examples are from Caragiannis et al (2017) and Bennet and Lanning (2007) respectively. These data sets require a citation for re-use.

References

Mattei, N. and Walsh, T. (2013) PrefLib: A Library of Preference Data. Proceedings of Third International Conference on Algorithmic Decision Theory (ADT 2013). Lecture Notes in Artificial Intelligence, Springer.

Bennett, J. and Lanning, S. (2007) The Netflix Prize. Proceedings of The KDD Cup and Workshops.

Examples

# Can take a little while depending on speed of internet connection


# strict complete orderings of four films on Netflix
netflix <- read_preflib("00004 - netflix/00004-00000138.soc", from_preflib = TRUE)
head(netflix)
levels(netflix$preferences)

# strict incomplete orderings of 6 random cities from 36 in total
cities <- read_preflib("00034 - cities/00034-00000001.soi", from_preflib = TRUE)

---

Write Ordinal Preference Data to PrefLib Formats

Description

Write preferences to .soc, .soi, .toc or .toi file types, as defined by the PrefLib specification: {PrefLib}: A Library for Preferences.

Usage

write_preflib(
  x,
  file = "",
  preferences_col = NULL,
  frequency_col = NULL,
  title = NULL,
  publication_date = NULL,
  modification_type = NULL,
  modification_date = NULL,
  description = NULL,
  relates_to = NULL,
  related_files = NULL
)

Arguments

x	A preferences object or a tibble with a preferences-typed column to write to file.
file	Either a character string naming the a file or a writeable, open connection. The empty string "" will write to stdout.
preferences_col	<tidy-select> When x is a tibble, the column containing the preferences to be written to file. If not provided and x is a tibble, then
frequency_col	<tidy-select> When x is a tibble, the column containing the frequency of the preferences. If not provided, each row is considered to be observed a single time.
title	The title of the data file, for instance the name of the election represented in the data file. If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for TITLE.
publication_date	The date at which the data file was published for the first time. If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for ⁠PUBLICATION DATE⁠.
modification_type	The modification type of the data: one of original, induced, imbued or synthetic (see Details). If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for ⁠MODIFICATION TYPE⁠.
modification_date	The last time the data was modified. If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for ⁠MODIFICATION DATE⁠.
description	A description of the data file, providing additional information about it. If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for DESCRIPTION.
relates_to	The name of the data file that the current file relates to, typically the source file in case the current file has been derived from another one. If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for ⁠RELATES TO⁠.
related_files	The list of all the data files related to this one, comma separated. If not provided, we check for the presence of attr(x, "preflib"), and if it exists we check for ⁠RELATED FILES⁠.

Details

The file types supported are

.soc

Strict Orders - Complete List

.soi

Strict Orders - Incomplete List

.toc

Orders with Ties - Complete List

.toi

Orders with Ties - Incomplete List

The PrefLib format specification requires some additional metadata. Note that the additional metadata required for the PrefLib specification is not necessarily required for the write_preflib method; any missing fields required by the PrefLib format will simply show "NA".

TITLE (required)

The title of the data file, for instance the year of the election represented in the data file.

DESCRIPTION (optional)

A description of the data file, providing additional information about it.

RELATES TO (optional)

The name of the data file that the current file relates to, typically the source file in case the current file has been derived from another one.

RELATED FILES (optional)

The list of all the data files related to this one, comma separated.

PUBLICATION DATE (required)

The date at which the data file was published for the first time.

MODIFICATION TYPE (required)

The modification type of the data. One of:

original

Data that has only been converted into a PrefLib format.

induced

Data that has been induced from another context. For example, computing a pairwise relation from a set of strict total orders. No assumptions have been made to create these files, just a change in the expression language.

imbued

Data that has been imbued with extra information. For example, extending an incomplete partial order by placing all unranked candidates tied at the end.

synthetic

Data that has been generated artificially.

MODIFICATION DATE (optional)

The last time the data was modified.

In addition to these fields, some required PrefLib fields will be generated automatically depending on arguments to write_preflib() and the attributes of the aggregated_preferences object being written to file:

FILE NAME

The name of the output file.

DATA TYPE

The data type (one of soc, soi, toc or toi).

NUMBER ALTERNATIVES

The number of items.

ALTERNATIVE NAME X

The name of each item, where X ranges from 0 to length(items).

NUMBER VOTERS

The total number of orderings.

NUMBER UNIQUE ORDERS

The number of distinct orderings.

Note that PrefLib refers to the items as "alternatives". The "alternatives" in the output file will be the same as the "items" in the aggregated_preferences object.

Value

No return value. Output will be written to file or stdout.

---