Visualization showing the folly of reconstructing vote time series from rounded vote share data.

rounding-error-sim.Rmd

---
title: "Rounding Error Sim"
output: html_notebook
---


```{r}
library(tidyverse)
library(ggthemes)
library(gridExtra)
```

Simulating errors that come from "reconstruction" timeseries vote deltas for presidential candidates.

For this simulation we assume that vote count deltas between timepoints are drawn from a uniform distribution.

```{r}
timepoints <- 1000
min_delta <- 0
max_delta <- 1000

time <- seq(from=1, to=timepoints, by=1)

getMonotonicIntegerRandomWalkDeltas <- function() {
  diffs <- round(runif(timepoints, min_delta, max_delta),0)
  return(diffs)
}

getReconstructionDeltaFrame <- function() {
  d_deltas = getMonotonicIntegerRandomWalkDeltas()
  d = cumsum(d_deltas)
  
  r_deltas = getMonotonicIntegerRandomWalkDeltas()
  r = cumsum(r_deltas)
  
  totals <- d+r
  
  reconstruct_deltas <- function(cum_votes, totals, rounding_digit) {
    rounded_pcts <- round(d / totals, rounding_digit)
    reconstruction <- round(rounded_pcts * totals, 0)
    reconstructed_deltas <- c(0, diff(reconstruction))
    return(reconstructed_deltas)
  }
  
  df <- data.frame(
    time=time,
    reconstructed_deltas_5 = reconstruct_deltas(d, totals, 5),
    reconstructed_deltas_4 = reconstruct_deltas(d, totals, 4),
    reconstructed_deltas_3 = reconstruct_deltas(d, totals, 3),
    reconstructed_deltas_2 = reconstruct_deltas(d, totals, 2),
    reconstructed_deltas_1 = reconstruct_deltas(d, totals, 1),
    reconstructed_deltas_0 = reconstruct_deltas(d, totals, 0),
    deltas=d_deltas
  )
}

df <- getReconstructionDeltaFrame()

alpha <- 0.5
g <- ggplot(df)  + 
  geom_point(aes(x=time, y=reconstructed_deltas_1, col='rounding_digit 1'), alpha=alpha) +
  geom_point(aes(x=time, y=reconstructed_deltas_2, col='rounding_digit 2'), alpha=alpha) +
  geom_point(aes(x=time, y=reconstructed_deltas_3, col='rounding_digit 3'), alpha=alpha) +
  geom_point(aes(x=time, y=deltas, col='exact'), alpha=alpha) + 
  theme_light()

ggsave(file="rounding-sim.png", g)
```