Democratic theory assumes that citizens can form meaningful preferences over policy alternatives. This paper applies the Adaptive Compression Advantage Theory (ACAT; Murata, 2026) to demonstrate that this assumption encounters a fundamental information-theoretic constraint: policy is too complex to compress into the gist representations that drive voting behavior. Modern policy involves multi-causal systems with delayed feedback, non-linear interactions, and domain-specific expertise requirements that exceed the compression capacity of any individual voter, regardless of intelligence. Voters therefore vote on compressed proxies—party identity, candidate affect, narrative gist, tribal affiliation—rather than on policy content. Politicians, recognizing this constraint, optimize their output for compressibility rather than accuracy: slogans over analysis, stories over statistics, identity over policy. The result is a systematic divergence between what democracy promises (policy responsiveness to citizen preferences) and what it delivers (narrative responsiveness to citizen compression patterns). We formalize the compression gap, derive why populism succeeds (maximum compressibility), why technocracy fails (minimum compressibility), and why social media has destabilized democracy (by lowering the compression depth of political input to near zero). The framework is descriptive, not prescriptive: it explains a structural constraint, not a moral failing. Eight testable predictions are generated. Keywords: democracy, political cognition, voter behavior, populism, compression, policy complexity, political communication, social media, polarization, ACAT, rate-distortion theory, information asymmetry, deliberation