The impact of federal policies often depends on fixed regional differences (economic, historical, geographical). Certain regions can therefore be seen as permanently benefiting from the federation and others as losing. We show that this distorts voting behaviour in two ways. First, voters strategically elect federal representatives that are extremely protective of regional interests. Second, they suboptimally invest in locally funded goods. This distortion is U-shaped in expected federal benefits. Lastly, we do not observe the usual race to be included in the federal coalition, which would reduce the distortion. We test these predictions on national and European Parliamentary elections since 1990, and find that extreme voting is indeed U-shaped: winning and losing states distort more than those in the middle. We conclude that federal political structures foment political polarisation, especially when federal decisions require large consensus. Loosening the ties between representatives and their constituency may mitigate this problem.