ElectDecomp (version 0.0.1-8)

inequality: Inequality in votes-to-seats conversion

Description

Computes the votes-to-seats conversion ratios for each combination of district and party in order to draw the representational inequality (Lorenz) curve of an election (or multiple elections under one electoral system). The Representational Inequality index proposed by Kedar, Harsgor, and Sheinerman, (2016) is calculated as a system-level index based on the area under the curve. (Use plot on its output to draw the curve.)

Usage

inequality(votes, seats)

Value

A list with four components

• inputs: A list containing all the objects with the values used as arguments by the function.

• conversion.ratios: A data.frame of order Nx7 (where N <= k*p) with conversion ratios of votes-to-seats for each combination of district and party. The first and second columns identify the district and party, respectively. The third column contains the conversion ratios. The last two columns (which are derived from the forth and fifth columns) present the cumulative proportions of seats and votes, from which the representational inequality curve of the election can be drawn.

• RI: The estimated Representational Inequality (RI) Index, which equals two times the area between the 45-degree line of perfect equality in votes conversion and the (Lorenz) representational inequality curve.

• other.statistics: A matrix of order 3x1 with the total election proportions of non-represented, underrepresented and overrepresented votes.

Arguments

votes

A data.frame or matrix of order kxp (where k is the number of constituencies/districts and p the number of parties) with the votes gained by each party/candidacy in each constituency/district. When blank and/or null votes are included as columns in votes, they are treated in the same way as the other parties.

seats

A data.frame or matrix of order kxp (where k is the number of constituencies/districts and p the number of parties), with row and columns in the same order as votes, with the seats gained by each party/candidacy in each constituency/district.

Author

Jose M. Pavia,

Alberto Penades,

References

Kedar, O, Harsgor, L and Sheinerman, RA (2016). Are voters equal under proportional representation? American Journal of Political Science, 60(3), 676-691 tools:::Rd_expr_doi("10.1111/ajps.12225")

Examples

votes.ex <- structure(list(Party1 = c(92019L, 112927L, 117482L, 152498L, 89494L,
                                   103697L, 115390L, 223252L, 55837L, 46820L,
                                   138575L, 177843L, 163536L, 187254L, 140237L,
                                   102719L, 64603L, 102362L, 70550L, 39321L,
                                   101891L, 71650L, 89363L, 137495L, 51568L,
                                   108862L, 50270L, 35324L, 104145L, 60626L,
                                   355857L, 45231L, 45191L, 69014L, 148697L,
                                   115729L, 221996L, 87059L, 99440L, 198231L,
                                   737699L, 75036L, 38338L, 0L, 91262L, 181633L,
                                   56917L, 197100L, 84115L, 334705L, 8808L, 10723L),
                         Party2 = c(50723L, 150896L, 122361L, 111746L, 63172L,
                                  123708L, 185095L, 251336L, 33693L, 16423L,
                                  111293L, 182850L, 73554L, 39616L, 50951L,
                                  67611L, 56332L, 79715L, 28350L, 17133L, 83956L,
                                  14984L, 44388L, 64766L, 25878L, 44168L, 18210L,
                                  10757L, 76308L, 26225L, 721880L, 60747L, 27809L,
                                  59926L, 107797L, 54827L, 78598L, 20808L, 21079L,
                                  54642L, 731380L, 54720L, 34244L, 93010L, 140643L,
                                  155871L, 36186L, 213242L, 69976L, 395211L,
                                  7886L, 5186L),
                          Party3 = c(11926L, 41809L, 59668L, 33879L, 10217L, 29847L,
                                  50990L, 91914L, 7398L, 2442L, 22446L, 60297L,
                                  14046L, 7467L, 10643L, 13971L, 13623L, 15562L,
                                  7927L, 5521L, 21942L, 2406L, 4765L, 12460L, 3744L,
                                  5522L, 2101L, 1196L, 15798L, 2783L, 469361L,
                                  24746L, 22680L, 41345L, 21932L, 6797L, 16777L,
                                  2949L, 2627L, 11835L, 247038L, 6319L, 3906L,
                                  12042L, 29968L, 29840L, 3846L, 50444L, 14029L,
                                  106133L, 0L, 966L),
                           Party4 = c(14886L, 20424L, 33616L, 24573L, 9415L, 26422L,
                                  34838L, 42860L, 7223L, 15180L, 34857L, 77932L,
                                  28472L, 15944L, 27828L, 36598L, 16005L, 31310L,
                                  10277L, 12815L, 44091L, 7123L, 28707L, 33285L,
                                  14638L, 15259L, 7407L, 3792L, 20521L, 30677L,
                                  75097L, 7953L, 10067L, 15216L, 21880L, 19516L,
                                  50256L, 36377L, 21502L, 40104L, 242077L, 0L,
                                  7927L, 27048L, 36934L, 30167L, 19925L, 35755L,
                                  14596L, 60410L, 2915L, 2074L)),
                            class = "data.frame", row.names = c(NA, -52L))

seats.ex <- structure(list(Party1 = c(3L, 2L, 3L, 4L, 3L, 3L, 3L, 5L, 2L, 2L, 3L,
                                   4L, 4L, 5L, 5L, 3L, 2L, 3L, 3L, 2L, 2L, 3L,
                                   3L, 4L, 2L, 3L, 2L, 3L, 3L, 2L, 5L, 1L, 1L,
                                   2L, 4L, 4L, 6L, 4L, 4L, 6L, 11L, 3L, 2L, 0L,
                                   2L, 4L, 2L, 4L, 2L, 5L, 1L, 1L),
                           Party2 = c(2L, 4L, 3L, 3L, 2L, 4L, 4L, 5L, 1L,
                                   1L, 3L, 4L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
                                   2L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 2L, 1L, 11L,
                                   2L, 1L, 1L, 3L, 1L, 2L, 0L, 0L, 1L, 11L, 2L,
                                   1L, 3L, 3L, 4L, 1L, 4L, 2L, 7L, 0L, 0L),
                           Party3 = c(0L, 1L, 1L, 0L, 0L, 0L, 1L, 2L, 0L, 0L, 0L,
                                   1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
                                   0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 7L, 0L, 0L,
                                   1L, 0L, 0L, 0L, 0L, 0L, 0L, 4L, 0L, 0L, 0L,
                                   0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L),
                           Party4 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
                                  1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L,
                                  0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L,
                                  0L, 0L, 0L, 1L, 1L, 1L, 1L, 3L, 0L, 0L, 0L,
                                  1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L)),
                           class = "data.frame", row.names = c(NA, -52L))

example <- inequality(votes.ex, seats.ex)
example$RI