ElectDecomp (version 0.0.1-8)

distortion: Decomposition of Votes-to-Seats Distortion

Description

Decomposes the seats-to-votes deviation for each party by means of the geographical distribution of electoral support. The deviation from proportionality is divided into two fractions: one attributable to the electoral system —further separating the mean effect and geographical variance effect— and another due to population distribution, which includes malapportionment and turnout differential effects. Additionally, the function aggregates individual party deviations into an election-wide index of deviation from proportionality (the Loosemore-Hanby index). This index is also decomposed into components attributed to the major causes of deviation from proportionality, along with interactions among them.

Usage

distortion(votes, seats, census)

Value

A list with three components

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

• district2party.contributions: A matrix of order kxp with the district contributions to the total seat-to-vote deviation of each party. The sums across columns of this matrix yields the vector of total seat-to-vote deviations.

• party.distortions: A matrix of order 7xp with the estimates of the distortions at the party level.

• aggregate.distortions: A matrix of order 7x1 with the Loosemore-Handy index and its decomposition due to parties with and without representation as well as its cumulative decomposition step-by-step into mean effects, variance effects, malapportionment effects and turnout (and interaction) effects.

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.

census

A vector (matrix or data.frame) of length k (the number of constituencies/districts), with components in the same order as the rows in votes, with the census (overall population entitled to vote) in each constituency/district.

Author

Alberto Penades,

Jose M. Pavia,

References

Penades, A and Pavia, JM. The decomposition of seats-to-votes distortion in elections: mean, variance, malapportionment and participation.

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))
 census.ex <- c(239935L, 559590L, 451021L, 456952L, 255557L, 403142L, 569535L,
                842042L, 153109L, 112376L, 547396L, 783206L, 407899L, 365063L,
                397732L, 327008L, 211249L, 310547L, 151099L, 95061L, 309595L,
                130998L, 238885L, 364127L, 125385L, 241301L, 99408L, 73992L,
                295410L, 164706L, 3004988L, 304448L, 242148L, 331744L, 413193L,
                279372L, 731499L, 302293L, 315033L, 548711L, 2744152L, 319222L,
                153080L, 437592L, 749572L, 551021L, 167030L, 677156L, 283161L,
                1287981L, 31672L, 25368L)

example <- distortion(votes.ex, seats.ex, census.ex)
example$party.distortions