Zone design: you help draw the boundaries

The four eight-zone starts are each drawn by a rule somebody could state before knowing what it would do: same number of households in each, compact lumps, whole census tracts grouped together, the city’s own neighbourhoods grouped together. Each is named for its rule and for nothing else, and its R² and its slope print beside the maps once you choose it.

They are not the extremes. Forty zonings were drawn from stated rules, ten for each of four things a preset is here to show, and the one kept from each ten is the best of its own ten rather than the best of the forty. There is room to beat all four. What the four are for is the plain fact that they disagree.

Dissemination areas and census tracts are real, published by Statistics Canada, and cannot be painted over. Somebody drew each of them, for a purpose, and none of the purposes was this question. A dissemination area is built to hold 400 to 700 people and to be compact; a tract is built from whole dissemination areas.

Painting changes eight zones, not a thousand. Eight is what two people can redraw in five minutes, and holding the count still is what makes the comparison about where the lines are.

Choose a zone colour, then click or drag across areas on either map to move them into it. The two maps are one zoning drawn twice, so a stroke on either moves the same areas and every number on the page updates as you go.

With a keyboard: put focus on either map, move between areas with the arrow keys, and press 1 to 8 to move the area under the cursor into that zone.

A zone can end up in two pieces. The widget lets it, and says so under the map, because whether a zone has to be in one piece is a rule somebody chose rather than something the data knows. Census units are built connected; electoral districts are supposed to be; the searched zonings here were kept connected on purpose so that they could not win by cheating in a way the real thing cannot.

Greenness has no choice to make. It is a value per square metre, so a zone's greenness is the average over its pixels, and it comes out the same however the pixels are grouped. Nothing is lost.

Income does have a choice, and there is no right answer to it. What Statistics Canada publishes for an area is a median: the middle household. Medians do not add up. The middle household of two areas put together is not the average of the two middles, and it cannot be worked out from them at all.

So a zone's income here is one of three averages of the areas' medians: a plain one, one weighted by households, or one weighted by people. They disagree, the line moves when you switch, and none of the three is the figure Statistics Canada would publish for the merged zone.

That is worth more than it looks. A number can move because you redrew the boundaries and it can move because you changed how you added it up, and on this page you can see both happen to the same map. On the reversed zoning it is not a small move. On one of the four rules the line is flat when income is weighted by households and clearly tilted on a plain average of the very same eight zones, with not one boundary moved. The size of a finding, and sometimes its direction, is decided by a choice nobody usually writes down.