In aeggers/votevizr: Tools For Vizualizing Election Outcomes

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The votevizr package provides tools for diagramming ordinal election outcomes given preference data.

The Overview vignette shows how to make diagrams using the votevizr::qplot_votevizr() convenience function.

This vignette is for "power users" who want more flexibility.

Inputting preference data

We will use the November 2018 Brexit poll result, which we store as a named list:

brexit_result <- list("Remain > Deal > No deal" = .375, 
               "No deal > Deal > Remain" = .228, 
               "Deal > No deal > Remain" = .212, 
               "Remain > No deal > Deal" = .087, 
               "Deal > Remain > No deal" = .059, 
               "No deal > Remain > Deal" = .038)

Extracting vertices of the first-preference win regions

library(votevizr)

The votevizr::first_preference_win_regions() function takes the election/poll result as an argument and returns a dataframe with the vertices of each candidate's first-preference win region in a given voting system.

An example:

brexit_rcv <- first_preference_win_regions(brexit_result, split = " > ", method = "RCV")

knitr::kable(brexit_rcv)

Each row in brexit_rcv provides the coordinates for a vertex on the first-preference win region of a candidate (specified in the candidate column). The candidate names are extracted from the names of the brexit_result list.

At this point you could make a figure using base R.[^baseR]

[^baseR]: This was my initial approach, so I have a lot of spare to code to share -- get in touch if you're interested.

Plotting first-preference win regions with ggplot2

Because the output of votevizr::first_preference_win_regions() is in "tidy" format, we can more easily plot the first-preference win regions in ggplot2.

library(ggplot2)
library(dplyr)

Here is the most basic version:

brexit_rcv %>% 
  ggplot(aes(x = Remain, y = Deal)) +
  geom_polygon(aes(group = candidate, fill = candidate)) + 
  labs(fill = "Winning\ncandidate")

I prefer to plot the results in barycentric or ternary coordinates, because it treats the three alternatives more symmetrically.

The ggtern package is specifically for making ternarty diagrams in R. But ggtern causes conflicts with ggplot2 and has lots of functionality we don't need, and it is surprisingly easy to make a ternary diagram without it. So we'll proceed with ggplot2 alone.

To convert data from the simplex in $(x, y, z)$ coordinates into ternary coordinates $(x', y')$, the transformation is \begin{eqnarray} x' &:=& x + \frac{1}{2}y \ y' &:=& \frac{\sqrt{3}}{2} y. \ \end{eqnarray}

So first do that transformation:

brexit_rcv %>% 
  mutate(Remain = Remain + .5*Deal, Deal = sqrt(3/4)*Deal) ->
  brexit_rcv_ternary

Then plot it, with some added style:

brexit_rcv_ternary %>%
  ggplot(aes(x = Remain, y = Deal)) +
  geom_polygon(aes(group = candidate, fill = candidate), show.legend = F) +
  coord_fixed() + # ensures we get an equilateral triangle
  scale_fill_brewer() + 
  theme_void() + 
  expand_limits(x = c(-.1, 1.1), y = sqrt(3/4)*c(-.1, 1.1)) + 
  annotate(geom = "text", x = c(1,.5,0), y = c(0,sqrt(3/4),0) + .05*c(-1,1,-1), label = c("Remain", "Deal", "No deal")) -> p
p

Convenience functions for plotting

We can also add a dot for the observed result, using the votevizr::first_preference_shares() method to extract the observed first-preference shares:

brexit_fps <- brexit_result %>% 
  first_preference_shares(split = " > ") %>% 
  mutate(Remain = Remain + .5*Deal, Deal = sqrt(3/4)*Deal)

p2 <- p + geom_point(data = brexit_fps, aes(x = Remain, y = Deal), cex = .75)
p2

Now add gridlines using votevizr::geom_ternary_gridlines():

p2 + 
  geom_ternary_gridlines()

Handling Condorcet completion methods

votevizr has two ways of handling Condorcet completion methods, i.e. rules for determining a winner in the event of a Condorcet cycle.

The user specifies the completion method (both for first_preference_win_regions() or qplot_votevizr()) with the if_cycle argument.

• when if_cycle is "empty", "kemeny", or the name of a candidate, then first_preference_win_regions() specifies the complete first-preference win regions and qplot_votevizr() simply plots them.
• when if_cycle is "RCV", "IRV", "plurality", "borda", "anti-plurality", or "positional", then first_preference_win_regions() leaves the cyclic triangle empty; qplot_votevizr() plots the first-preference win regions for the completion method (e.g. RCV when if_cycle = "RCV") first and then overlays the Condorcet first-preference win regions.[^why]

[^why]: There may be a clever way to make first_preference_win_regions() get the first-preference win regions for both Condorcet and the completion method and combine them correctly, but for plotting it was easier to just overlay two plots.

Let's illustrate this second approach for the case where the Brexit winner is to be determined by Condorcet with RCV used in the event of a cycle.

First let's show the diagram with the Condorcet cycle not filled in. Get the first-preference win regions and transform them for the ternary diagram:

brexit_result %>% 
  first_preference_win_regions(split = " > ", 
                               method = "condorcet") %>% 
  mutate(Remain = Remain + .5*Deal, Deal = sqrt(3/4)*Deal) -> brexit_condorcet 

Now, reusing code from above, we make the plot:

brexit_condorcet %>% 
  ggplot(aes(x = Remain, y = Deal)) +
  geom_polygon(aes(group = candidate, fill = candidate), show.legend = F) +
  coord_fixed() +
  scale_fill_brewer() + 
  theme_void() + 
  expand_limits(x = c(-.1, 1.1), y = sqrt(3/4)*c(-.1, 1.1)) + 
  annotate(geom = "text", x = c(1,.5,0), y = c(0,sqrt(3/4),0) + .05*c(-1,1,-1), label = c("Remain", "Deal", "No deal")) 

Note the empty triangle. For first-preference results in this area (holding fixed the pattern of lower preferences), there is a Condorcet cycle: "Remain" beats "Deal", "Deal" beats "No deal", and "No deal" beats remain.

Now suppose the winner is chosen by RCV if there is a cycle. We illustrate this rule by redrawing the RCV plot from above (stored as p) and then overlaying the Condorcet first-preference win regions:

p +   # p was the RCV figure 
  geom_polygon(data = brexit_condorcet, aes(group = candidate, fill = candidate), show.legend = F)  # overlay the Condorcet figure

We can do the same using any positional method (Borda, plurality, antiplurality, or others).

To produce the same figure via qplot_votevizr():

brexit_result %>% 
  qplot_votevizr(split = " > ", method = "condorcet", if_cycle = "RCV")  

Want to know more?

Read my paper Social Choice and Welfare (preprint, published), which explains the figures in more detail and discusses previous attempts to represent election results in ternary diagrams.

See also the Overview vignette for some basic background about the figures and more on the qplot_votevizr() function.

aeggers/votevizr documentation built on June 4, 2021, 9:10 p.m.