My research initiates the use of large language models (LLMs) to automate the design of effective algorithms for challenging problems in computational social choice, namely participatory budgeting (PB) and facility location mechanism design. To this end, I propose two LLM-based frameworks that respectively generate interpretable PB rules and mechanisms fulfilling competing objectives, i.e., optimality vs. fairness or strategyproofness. Future directions include extending these frameworks to achieve provable guarantees and addressing other relevant areas such as fair division.