Function to calculate the allocated seats according to the Hill method in a given electoral district.

This function allocates seats to political parties in a given electoral district using the Hill method (also known as the Equal Proportions method), a highest averages approach for proportional representation. Each party's total number of ballots is divided by the square root of the product of the number of seats already allocated plus one and that number itself (i.e., √n(n+1)), producing a list of quotients. Seats are assigned one at a time to the party with the highest quotient, repeating until all seats are allocated. Only candidacies surpassing a specified threshold (as a proportion of total ballots including blank ballots) are considered for allocation.

Usage

hill_seats(
  candidacies,
  ballots,
  blank_ballots,
  n_seats,
  threshold = 0.03,
  short_version = TRUE
)

Arguments

candidacies

A vector containing one of the following variable: unique codes or abbreviations of the candidacies that participated in the election.

ballots

A vector containing the absolute number of ballots (integer positive values) received by each candidacies

blank_ballots

A numerical value indicating the number of blank ballots (integer positive values).

n_seats

An integer positive value indicating the number of seats that are going to distributed for a given electoral district.

threshold

A numerical value (between 0 and 1) indicating the minimal percentage of ballots needed to obtain representation for a given electoral district. Defaults to 0.03.

short_version

Flag to indicate whether it should be returned a short version of the data (just key variables) or not. Defaults to TRUE.

Value

A tibble or a list of tibbles with rows corresponding to each party including the following variables:

candidacies

abbrev or id of the candidacies

seats

number of seats

ballots

absolute number of ballots, just in long format

porc_seats

percentage of seats respect to the number of seats, just in long format

porc_ballots

percentage of ballots respect to party ballots (including blank ballots), just in long format

quotient_x

intermediate quotients of the allocation process

Details

The purpose of this helper function is to be used in a general function, seats_allocation(), to calculate the seats distribution of every electoral district of a given election according to the Hill method.

Author

Javier Alvarez-Liebana, Irene Bosque-Gala and David Pereiro-Pol

Examples

## Correct examples

## Seats distribution with Hill method for given vectors of candidacies and ballots
## without the remainder quotients

candidacies <- c("PP", "PSOE", "PODEMOS", "VOX")
ballots <- c(200, 350, 100, 200)

seats <- hill_seats(candidacies = candidacies, ballots = ballots,
 blank_ballots = 50, n_seats = 15, threshold = 0.03)

# Same results in a long version (providing quotients)
seats <- hill_seats(candidacies, ballots, blank_ballots = 50,
                      n_seats = 15, short_version = FALSE)

# Hill with threshold 0.05
seats <- hill_seats(candidacies, ballots, blank_ballots = 50,
                      n_seats = 5, threshold = 0.05)

# A very high threshold that only one party meets
seats <- hill_seats(candidacies, ballots, blank_ballots = 50,
                      n_seats = 5, threshold = 0.3)

if (FALSE) { # \dontrun{

# Incorrect examples

# Different length of candidacies and ballots

candidacies <- c("PP", "PSOE", "PODEMOS", "VOX")
ballots <- c(200, 350, 100)

seats <- hill_seats(candidacies = candidacies, ballots = ballots,
                    blank_ballots = 50, threshold = 0.03)

# Ballots with missing values
candidacies <- c("PP", "PSOE", "PODEMOS")
ballots <- c(200, 350, NA)
seats <- hill_seats(candidacies = candidacies, ballots = ballots,
                      n_seats = 5, blank_ballots = 50,
                      threshold = 0.03)

# Ballots with char values
candidacies <- c("PP", "PSOE", "PODEMOS")
ballots <- c("200", "350", "100")
seats <- hill_seats(candidacies = candidacies, ballots = ballots,
                      n_seats = 5, blank_ballots = 50,
                      threshold = 0.03)

# Threshold should be a numerical value between 0 and 1
candidacies <- c("PP", "PSOE", "PODEMOS")
ballots <- c(200, 350, 100)
seats <- hill_seats(candidacies = candidacies, ballots = ballots,
                      n_seats = 5, blank_ballots = 50,
                      threshold = 3)
} # }