More mapping "not quite how-to" - Voronoi regions

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What this post is about

In the previous post we showed how to set up a simple interactive map using Python and its folium package. As the example, we used a Federal electorate situated within the city of Melbourne, Australia, and the various voting places, or polling places (also known as polling "booths") associated with it.

This post takes the map a little further, and we show how to use Python's geovoronoi package to create Voronoi regions around each booth. This (we hope) will give a map of where voting for a particular party might be strongest. (We make the assumption that every voter will vote at the booth closest to their home.)

Because some voting booths are outside the electorate - this includes early voting centres - we first need to reduce the booths to only those withing the boundary of the electorate. In this case, as the boundary is a simply-connect region, this is straightforward. The we can create the Voronoi regions and map them.

Message about the underlying software

NOTE: much of the material and discussion here uses the Python package "folium", which is a front end to the Javascript package "leaflet.js". The lead developer of leaflet.js is Volodymyr Agafonkin, a Ukrainian up until recently living and working in Kyiv.

Leaflet version 1.80 was released on April 18, "in the middle of war", with "air raid sirens sounding outside". See the full statement here.

Stand With Ukraine

(This banner is included here with the kind permission of Mr Agafonkin.) Please consider the Ukrainian people who are suffering under an unjust aggressor, and help them.

Obtaining interior points and Voronoi regions

We start by simplifying a few of the variable names:

1hbooths = higgins_booths.copy()

We will also need the boundary of the electorate:

2higgins_poly = higgins_crs["geometry"].iat[0]

Now finding the interior points is easy(ish) using GeoPandas:

1higgins_gpd = gpd.GeoDataFrame(
2    hbooths, geometry=gpd.points_from_xy(hbooths.Longitude, hbooths.Latitude))
3higgins_crs = higgins_gpd.set_crs(epsg=4326)
5interior = higgins_crs[higgins_crs.geometry.within(higgins_poly)].reset_index(drop=True)

We should also check if any of the interior points double up. This might be if one location is used say, for both an early voting centre, and a voting booth on election day. The geovoronoi package will throw an error if a location is repeated.

1ig = interior.groupby(["Latitude","Longitude"]).size()
4Latitude    Longitude
5-37.846104  144.998383    2
6dtype: int64

The geographical coordinates can be obtained with, say

1double = ig.loc[ig.values>1].index[0]

This means we can find the offending booths in the interior:

1interior.loc[(interior["Latitude"]==double[0]) & (interior["Longitude"]==double[1])]
PollingPlaceNm Latitude Longitude geometry
28 South Yarra HIGGINS PPVC -37.846104 144.998383 POINT (144.99838 -37.84610)
29 South Yarra South -37.846104 144.998383 POINT (144.99838 -37.84610)

We'll remove the pre-polling voting centre at row 28:

1interior = interior.drop(28)

Now we're in a position to create the Voronoi regions. We have the external polygon (he boundary of the electorate), and all the internal points we need, with no duplications.

1from geovoronoi import voronoi_regions_from_coords, points_to_region
3interior_coords = np.array(interior[["Longitude","Latitude"]])
4polys, pts = voronoi_regions_from_coords(interior_coords, higgins_poly))

Each of the variables polys and pts are given as dictionaries. We want to associate each interior voting booth with a given region. This can be done by creating an index between the points and regions, and then adding the regions to the interior dataframe:

1index = points_to_region(pts)
3N = len(polys)
4geometries = [polys[index[k]] for k in range(N)]

What this has done is replace the original geometry data (which were just the coordinates of each voting booth, given as "POINT" datatypes), to regions given as "POLYGON" datatypes.

Adding some voting data

We could simply map the Voronoi regions now:

1from geovoronoi.plotting import subplot_for_map, plot_voronoi_polys_with_points_in_area
3fig, ax = subplot_for_map(figsize=(10,10))
4plot_voronoi_polys_with_points_in_area(ax, higgins_poly, polys, interior_coords, pts)

But what we want is a little more control. But first, we'll add some more information to the DataFrame. The simplest information is the "two candidate preferred" data: these are the number of votes allocated to the two final candidates after the preferential counting. The files are available on the AEC website; they can be downloaded and used:

1tcp = pd.read_csv('HouseTcpByCandidateByPollingPlaceDownload-27966_2.csv')
2higgins_tcp = tcp.loc[tcp["DivisionNm"]=="Higgins"]

Each candidate gets their own row, which means we have to copy the cotes from each candidate into the interior DataFrame. In the case of the 2022 election, the Higgins final candidates represented the Australian Labor Party (ALP), and the Liberal Party (LP). The party is given in the column "PartyAb" in the higgins_tcp data frame. Adding them to the interior data frame is only a tiny bit fiddly:

1lp_votes = []
2alp_votes = []
3for index,row in interior.iterrows():
4    place = row["PollingPlaceNm"]
5    alp_votes += [higgins_tcp.loc[(higgins_tcp["PollingPlace"]==place) & (higgins_tcp["PartyAb"]=="ALP"),"OrdinaryVotes"].iat[0]]
6    lp_votes += [higgins_tcp.loc[(higgins_tcp["PollingPlace"]==place) & (higgins_tcp["PartyAb"]=="LP"),"OrdinaryVotes"].iat[0]]
7interior["ALP Votes"] = alp_votes
8interior["LP Votes"] = lp_votes

Creating the map

The base map is the same as before:

1hmap2 = folium.Map(location=centre,# crs='EPSG4283', tiles='OpenStreetMap',
2		 min_lat=b1-extent, max_lat=b3+extent,
3		 min_long=b0-extent, max_long=b2+extent,
4	       width=800,height=800,zoom_start=13,scrollWheelZoom=False)

We don't need to draw the boundary or interior as the Voronoi regions will cover it. What we'll do instead is draw each Voronoi region, colouring it red (for a Labor majority) or blue (for a Liberal majority). Like this:

 1for index,row in interior.iterrows():
 2    rloc = [row["Latitude"],row["Longitude"]]
 3    row_json = gpd.GeoSeries([row["geometry"]]).to_json()
 4    tooltip = ("<b>{s1}</b>").format(s1 = row["PollingPlaceNm"])
 5    if row["ALP Votes"] > row["LP Votes"]:
 6	folium.GeoJson(data=row_json,style_function=lambda x: {'fillColor': 'red'}).add_to(hmap2)
 7	folium.CircleMarker(radius=5,color="black",fill=True,location=rloc,tooltip=tooltip).add_to(hmap2)
 8    else:
 9	folium.GeoJson(data=row_json,style_function=lambda x: {'fillColor': 'blue'}).add_to(hmap2)
10	folium.CircleMarker(radius=5,color="black",fill=True,location=rloc,tooltip=tooltip).add_to(hmap2)

And to view the map: