A key challenge in transportation planning is that the collective preferences of heterogeneous travelers often diverge from the policies produced by model-driven decision tools. This misalignment frequently results in implementation delays or failures. Here, we investigate whether large language models (LLMs), noted for their capabilities in reasoning and simulating human decision-making, can help inform and address this alignment problem. We develop a multi-agent simulation in which LLMs, acting as agents representing residents from different communities in a city, participate in a referendum on a set of transit policy proposals. Using chain-of-thought reasoning, LLM agents provide ranked-choice or approval-based preferences, which are aggregated using instant-runoff voting (IRV) to model democratic consensus. We implement this simulation framework with both GPT-4o and Claude-3.5, and apply it for Chicago and Houston. Our findings suggest that LLM agents are capable of approximating plausible collective preferences and responding to local context, while also displaying model-specific behavioral biases and modest divergences from optimization-based benchmarks. These capabilities underscore both the promise and limitations of LLMs as tools for solving the alignment problem in transportation decision-making.