Do electoral incentives make politicians speak more ambiguously? I build a signal model in which a rational voter anchors on prior reputation, so vagueness shields a favourable prior but cannot rescue an unfavourable one. To test it I construct semantic dispersion, an LLM-derived measure of how wide a hedged claim's range of meanings is, validated at 92.3% agreement with human raters. Applied to 62,169 hedged Singapore parliamentary claims, a redistricting shock produces opposing-signed responses that rule out uniform confounders: MPs who lost favourable voters became vaguer by 0.15 standard deviations, and those who gained unfavourable voters became more precise by 0.13. A within-chamber control using Singapore's Nominated MP institution, whose members face zero electoral pressure, corroborates the result.