A seats-votes curve (with various annotations) is produced
with option type="seatsVotes".
A density plot of the vote shares is
produced with type="density". A bimodal density corresponds to
an electoral system with a proliferation of safe seats for both
parties, and a seats-votes curve that is relatively flat (or
“unresponsive”) in the neighborhood of average district-level
vote shares of 50 percent. The density is fitted using the defaults
in the density function, but with the density constrained
to fall to zero at the extremes of the data, via the from and
to options to density. A rug is added to the
density plot.
If transform=TRUE, the vote shares are transformed prior to
plotting, so as to reduce the extent to which extreme vote shares
close to zero or 1 determine the shape of the density (i.e., this
option is available only for plots of type="density"). The
transformation is a sinusoidal function, a scaled
“log-odds/inverse-log-odds” function mapping from (0,1) to
(0,1): i.e., \(f(x) = g(k\cdot h(x))\) where
\(h(x)\) is the log-odds transformation \(h(x) =
\log(x/(1-x))\), \(k\) is a scaling parameter
set to \(\sqrt{3}\), and \(g(x)\) is the inverse-log-odds
transformation \(g(x) = \exp(x)/(1+\exp(x))\). Note that this transformation is cosmetic, with
the effect of assigning more of the graphing region to be devoted to
marginal seats.