# Modelling SA1-booth correspondences
Date: 2023-07-01
Elections have geographic aspects: people live *somewhere* and often
your neighbours are similar to you socio-economically. Further, both
boundaries and polling places can differ across the three levels of
government, and they change over time.
So it’s useful to have some sort of universal comparison geography like
the SA1: a block of 200 to 800 people. SA1s are small enough to be
rarely split by electorate boundaries, yet large enough to be a useful
unit of analysis.
The Australian Electoral Commission publishes a correspondence file for
each election mapping polling places to SA1s. This correspondence
permits analyses that project booth-level results onto the SA1s of their
voters - which could then be re-aggregated into different boundaries.
Australian psephologists routinely calculate post-redistribution margins
in this way. More speculatively, I previously used the Senate results
from 2016 to predict the Qld state election in 2017 (as One Nation had
re-emerged).
However, equivalent SA1-booth information is not generally published by
state electoral commissions. As booths and boundaries differ between
elections, we can’t just re-use the federal correspondences either.
But what *is* possible is some sort of probabilistic model. Intuitively,
we’d expect people to be more likely go to a polling place that’s
close(st) to where they live, and for them to be less likely to go to
one that’s far away. However, rank-order on its own seems insufficient:
if the closest and second-closest booths are near-equidistant, we’d
expect a fairly even split.
We also might not want to use pure distance, because that’s tied a
little too much to the specifics of the which polling places exist and
to population density.
So I’ve performed an analysis using distance *ratios* instead: I divide
the distance `D(P, X)` from each SA1 `P` to polling place `X`, by the
distance from the SA1 to its *closest* polling place `C`. So we have
`R(P, X) = D(P, X) / D(P, C)`.
I also clamp the distances to be between 0.1 and 5000 km, so the ratios
are in a reasonable range - and try to exclude special mobile booths,
whose lack of location puts them at [Null
Island.](https://en.wikipedia.org/wiki/Null_Island)
We then can sort every entry by distance ratio, lowest to highest, and
plot by cumulative votes, for a sort of inverted cumulative
distribution. It turns out that all the federal Divisions have
similar-looking curves!
Adelaide
As you can see, I’ve broken out some figures in the title of these
graphs. They correspond to the vote total for `1x`, `<=3x`, `<=10x`
distance ratios, and then the total voters for that Division.
BennelongCooper
Those three are quite inner-city, so let’s look at some large remote
ones too:
KennedyLingiariMaranoa
There’s a pretty consistent trend here: *about* 40% of people (who vote
at a booth) do so at their closest available booth, and then another 50%
vote at a booth that’s less than 10x as far away as their closest booth.
Then about 10% vote much further away. (Or, despite my best efforts,
some pseudo-booths that have missing coordinates — corresponding to 0°N,
0°E — have slipped in.)
We see (on a semi-log plot, at least) that there’s a pretty much
straight line from the 1x maximum to the 3x mark, and often up to the
10x mark, before shooting up for the small percentage of people voting a
long way away from home. So for any sensible set of booths, we can use
the model to estimate where people from each SA1 will vote!
## Downloads
- [Database](https://f.abjago.net/booth-geography/dist_ratios.sqlite)
*32 MB compressed*
- [Analysis script](https://f.abjago.net/booth-geography/distratios.py)
## Table
All values for the 2019 Federal Election. Click on the division name for
its graph, or on a heading to sort by that column.
