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There is a large range of mathematical and computational techniques to analyse voting patterns and opinion polls, and predict what voters want. Data is often made available and can be analysed by any interested party. 

The following image looks at the Brexit vote in the UK. The middle panel shows the actual election result on a local authority level; red means in favour of Brexit and green means remain. Using a statistical a model to infer what people wanted, i.e. taking non-voters and population statistics into consideration, we obtain an estimate for what "people really wanted", which is based on some model assumptions. The results are shown on the left. The right figure shows the difference between the inferred results and the actual results. 

So: What did people really want?

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