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While Large Language Models (LLMs) are increasingly used as primary sources of information, their potential for political bias may impact their objectivity. Existing benchmarks of LLM social bias primarily evaluate gender and racial stereotypes. When political bias is included, it is typically measured at a coarse level, neglecting the specific values that shape sociopolitical leanings. This study investigates political bias in eight prominent LLMs (Claude, Deepseek, Gemini, GPT, Grok, Llama, Qwen Base, Qwen Instruction-Tuned) using PoliticsBench: a novel multi-turn roleplay framework adapted from the EQ-Bench-v3 psychometric benchmark. We test whether commercially developed LLMs display a systematic left-leaning bias that becomes more pronounced in later stages of multi-stage roleplay. Through twenty evolving scenarios, each model reported its stance and determined its course of action. Scoring these responses on a scale of ten political values, we explored the values underlying chatbots' deviations from unbiased standards. Seven of our eight models leaned left, while Grok leaned right. Each left-leaning LLM strongly exhibited liberal traits and moderately exhibited conservative ones. We discovered slight variations in alignment scores across stages of roleplay, with no particular pattern. Though most models used consequence-based reasoning, Grok frequently argued with facts and statistics. Our study presents the first psychometric evaluation of political values in LLMs through multi-stage, free-text interactions.