Areal interpolation and the UK's referendum on EU membershipBy Laura Sudulich on 19 April 2017
By Chris Hanretty. Full JEPOP article here
This month we found out that Parliament will have to vote on whether the UK is to leave the European Union, notwithstanding last year's referendum.
Some argue that MPs should vote in the same way their constituents voted. This creates a problem. The results of the Brexit referendum were collected by local authority area (LAA), and not parliamentary constituencies. The 380 LAAs in Great Britain do not normally overlap with the 632 parliamentary constituencies. How are MPs to know how their constituency voted?
One approach is to assume that constituency results are just a mixture of local authority results. If 100% of people in a constituency live in local authority area X, then our estimate is just the result for X. If 80% of people in a constituency live in local authority area X, and 20% live in local authority area Y, then our estimate is 80% of the result for X, plus 20% of the result for Y.
This approach (called dasymmetric interpolation) assumes incorrectly that opinion within an area is homogeneous. In reality, LAAs can contain areas that, for demographic reasons, are very much more likely to have voted Remain (or Leave).
A second approach is to use regression. With data on demographic characteristics of each LAA, we can regress the Leave vote on these demographic characteristics. We can use the resulting regression model to make projections based on the demographic characteristics of Westminster constituencies.
This approach also has flaws. Most notably, it gives incorrect results for constituencies which overlap perfectly with LAAs. The estimates are close to the known results, but it seems strange to use a method that produces results known to be wrong.
A third approach is to start with a regression model, but to scale the projections of this model to match what we know about local authority results. This is the method I used in my article. Instead of moving straight to regression-based projections for constituencies, I made regression-based projections for group of Census output areas, which are formed from the intersection of local authority areas and Westminster constituencies (see figure).
Figure: The figure shows three local authority areas (A, B and C), which have known results, and one constituency area (which does not). Projections are made for the intersections A1, B1, and C1, together with other areas. The projections are then scaled to ensure A0 + A1 = A, B0 + B1 = B, and so on.
We can then divide or multiply projections in each intersection so that they match exactly when added up to the LAA. We can then add together all the intersections from each parliamentary constituency. These estimates will known match the results from local authority areas (where these overlap perfectly), but will be able to incorporate additional information from areas' demographic characteristics.
These are estimates. They're not perfect. The article provides some tests against known results, and I'm confident these estimates are the best that can be produced with the data available.
We do, though, need to use these estimates carefully. Academics and citizens will want to know how different areas voted, and how that matched or affected what MPs did subsequently. That is entirely reasonable.
It would be wrong, though, to use these estimates to abuse and vilify MPs whose behaviour is seen not to "respect" the "results" in their constituency. The referendum was a national referendum, and not a constituency-by-constituency contest. MPs ought to take the result of the referendum very seriously, but MPs can have good and sincerely held reasons for voting against the wishes of a majority of their electors. It was a sad mark of distinction of the referendum that an MP was killed whilst campaigning; but MPs face abuse and harassment on a regular basis. These estimates are provided in good faith: I hope that good faith extends to our interpretations of MPs' motives in the coming months.