The Constitutional Coverage Trilemma in AI Governance

Frontier AI systems function as \emph{constitutional institutions}: each deployed model encodes an implicit ranking among safety, helpfulness, honesty, autonomy, and equity. We ask whether the supply of frontier constitutional types covers human demand. Combining a paraphrase-controlled audit of $23$ frontier LLM archetypes with a pairwise-tradeoff study of $1{,}649$ humans on the same instrument, we report three facts. Demand is broad: it spans all five values, with the largest constituency under one-third. Supply is narrow and drifting: the $23$-archetype hull occupies $0.10\%$ of the demand hull, and across six model families autonomy decreases in $5/6$, equity increases in $5/6$, and safety increases in $4/6$. The importance of this drift is not that the frontier moves but that it moves away from a value that is already undercovered, mechanically worsening the welfare floor for the users least well served by the static menu. The fix is sparse: a $2$-vertex menu $\{e_{\mathrm{HON}}, e_{\mathrm{AUT}}\}$ beats the full $23$-archetype frontier by $47$ percent on mean regret ($95$ percent); three vertex additions cut mean regret by up to $81$ percent and worst-group regret by up to $64$ percent. We formalize these findings as a budgeted-pluralism trilemma and show the binding regime is empirically realized.