Why do some societies, from authoritarian rule to liberal democracy, generate prosperity while others stagnate? This paper identifies electoral integrity as the binding institutional constraint: the threshold condition determining whether political and civil freedoms translate into economic productivity. Free regimes already exhibit four times the GDP per capita of Not-Free counterparts ($23,579 vs. $6,221), with lower inequality (Gini 35.2 vs. 37.9)-directly challenging the conventional trade-off between efficiency and equity. Yet this gap is driven by a precise institutional mechanism. Using a global panel of 85 countries (2006-2019), we employ a three-stage empirical strategy-panel fixed-effects analysis, Explainable AI, and a heterogeneous-agent structural model-to identify a critical non-linear threshold: below an Electoral Integrity score of 0.6-0.7, the economic returns to freedom effectively vanish. The erosion of electoral integrity is not merely a political failure but a quantifiable economic catastrophe.