This paper develops a nonparametric revealed-preference method for recovering voter preferences from aggregate election returns in a multidimensional spatial voting model. I apply it to municipal-level results from Germany’s four Bundestag elections between 2013 and 2025, modelling political competition along left–right and anti-elite dimensions. The results reveal a transformation in the basis of support for the radical-right Alternative for Germany (AfD): what began primarily as anti-elite voting became increasingly aligned with the party’s right-wing positions. By 2025, the left–right dimension accounts for as much as 70\% of AfD support. Counterfactuals reveal an apparent but illusory opportunity for the center-right Christian Democratic Union (CDU). If the AfD’s position is held fixed, a modest shift to the right by the CDU—for example, on immigration—attracts more than one-fifth of AfD voters. When the AfD can respond strategically, however, it moves further right and reverses the CDU’s gains; in equilibrium, the CDU does not move right. These results may explain why establishment parties fail to win back populist voters despite an apparent ideological opening.

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