In erocoar/vetoboxr: Spatial Voting in R

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(vetoboxr)
library(tidyverse)
library(magrittr)
library(ggridges)

If we were to actually simulate votes over many iterations, chances are that the status quo stabilizes quickly - more so if there are veto players participating in the votes. However, with vetoboxr it is possible to dynamically alter the voters` positions over time via vibration and drift. Vibration refers to random fluctuations in voters' spatial positions, whereas drift refers to systemic changes over time (e.g. radicalization of a party). We will take a look at how to specify both.

First we create voters. For running simulations it is convenient to create the Voters object directly via a position matrix, rather than formulas.

library(vetoboxr)
library(tidyverse)
library(magrittr)
library(ggridges)

set.seed(2111)
players <- Voters(position = rnorm(10, 0, 5), 
                  dimension = 2, 
                  role = c("AS", "Veto", "Normal", "Veto", "Normal"))
sq <- SQ(position = c(0, 0))

The drift can be specified via either a voter_count * dimension vector, i.e. a constant change for each voter position that is applied every iteration, or via a iterations * (voter_count * dimension) matrix specifying the drift for each position, for each iteration. Let us use a simple drift that will continuously shift the fourth voter further away from all others.

drift <- c(rep(0, 8), 0.1, 0.1)

Vibration is specified either via a matrix of said dimensions or via a function that takes as its first argument the number of values to return. Let us define our own vibration function using a Gamma distribution:

vibration <- function(n) rgamma(n, 0.75, 10)

Then, we can vote as usual.

vote_standard  <- Vote(players, sq, iter = 500)
vote_drift_vib <- Vote(players, sq, drift = drift, vibration = vibration, iter = 500)

Lastly, we could also let the status quo drift in space.

sq <- SQ(c(0, 0), drift = c(-0.3, 0.2))
vote_sq_drift <- Vote(players, sq, iter = 500)

For further analysis Vote objects can be converted to data frames via vote_df().

vote_sq_drift %>%
  vote_df() %>%
  glimpse()

Lastly, let us compare the densities of the total distance travelled by the status quo for multiple drift values.

base_vote <- function(sq) Vote(players, sq, iter = 500)$total_distance[, 1]
vote_grid <- expand.grid(seq(0, 6, 3), seq(0, 6, 3))

votes <- vote_grid %>%
  pmap(~ list("sq_dist" = base_vote(SQ(c(0, 0), c(..1, ..2)))))

vote_grid %<>%
  mutate(dist = pmap_dbl(., ~ norm(-c(..1, ..2), "2")))

vote_outcomes <- votes %>% 
  bind_rows() %>%
  mutate(distance = rep(vote_grid$dist, each = 500)) 

vote_outcomes$sq_dist %<>% add(1) 

ggplot(vote_outcomes) +
  geom_density_ridges(aes(x = sq_dist, y = factor(distance))) +
  scale_x_log10(limits = c(1, 2))