Convert a vector of vote shares into a seats-vote curve object, providing estimates of partisan bias.
seatsVotes(x, desc = NULL, method = "uniformSwing")An object of class seatsVotes, with components
Estimated seat shares over the range of simulated average, district-level vote shares
Simulated average district-level vote shares
observed seat shares, with missing data removed
user-supplied descriptive character string
a list of class call, the call to the function
a vector of vote shares for a specific party (either proportions or percentages)
descriptive text
how to simulate a seats-vote curve; the only supported
method at this stage is uniformSwing.
Simon Jackman simon.jackman@sydney.edu.au
Simulation methods are required to induce a seats-votes curve given a vector of vote shares from one election. The uniform swing method simply slides the empirical distribution function of the vote shares “up” and “down”, computing the proportion of the vote shares that lie above .5 (by construction, the winning percentage in a two-party election) for each new location of the vector of vote shares. That is, as the empirical CDF of the observed vote shares slides up or down, more or less seats cross the .5 threshold. A seats-votes curve is formed by plotting the seat share above .5 as a function of the average district-level vote share (a weakly monotone function, since the empirical CDF constitutes a set of sufficient statistics for this problem). The simulation is run so as to ensure that average district-level vote shares range between 0 and 1.
The extent to which the seats-votes curve departs from symmetry is known as bias. More specifically, the vertical displacement of the seats-votes curve from .5 when average district-level vote share is .5 is conventionally reported as an estimate of the bias of the electoral system.
Different methods produce different estimates of seats-votes curves and summary estimands such as bias. The uniform swing method is completely deterministic and does not produce any uncertainty assessment (e.g., confidence intervals etc).
Tufte, Edward R. 1973. The Relationship Between Seats and Votes in Two-Party Systems. American Political Science Review. 67(2):540-554.
Gelman, Andrew and Gary King. 1990. Estimating the Consequences of Electoral Redistricting. Journal of the American Statistical Association. 85:274-282.
Jackman, Simon. 1994. Measuring Electoral Bias: Australia, 1949-93. British Journal of Political Science. 24(3):319-357.
plot.seatsVotes for plotting methods.
data(ca2006)
x <- ca2006$D/(ca2006$D+ca2006$R)
sv <- seatsVotes(x,
desc="Democratic Vote Shares, California 2006 congressional elections")
Run the code above in your browser using DataLab