Progressive in Principle, Centrist in Practice: LLM Political Bias Is Instrument-Dependent

Prior work establishes that instruction-tuned LLMs exhibit left-of-center political bias, but measures it exclusively through abstract questionnaires. We show it does not predict how models vote on concrete policies. We introduce a dual-instrument methodology grounded in Swiss direct democracy. First, we administer the Smartvote questionnaire (75 policy questions) to 66 LLMs and compare their answers to those of 184 elected members of the Swiss National Council. Second, we put 48 real federal referenda (Volksabstimmungen) to 9 flagship LLMs in four national languages and three information conditions, and compare their votes to the actual outcomes and to party recommendations (Parolen). The instruments disagree. (1) The left-to-right agreement gradient that dominates Smartvote replicates prior work (mean rho = -0.77). On referenda it shifts to center-peaked: models align most with centrist Die Mitte and FDP rather than leftist SP and Gr"une (Wilcoxon p = 0.008). (2) For some models the language of a question changes the answer: cross-linguistic consistency ranges from 50% (Mistral) to 98% (GPT-5.4). (3) Two models vote Nein on 83-94% of referenda at similar rates on progressive and conservative proposals (binomial p < 0.0001), change-aversion rather than a left-right bias. What prior work measured as "leftward bias" may not extend beyond abstract instruments: confronted with real decisions, LLMs behave less like coalition partners of the left than like cautious civil servants, centrist and inconsistent across languages.