Fair resource division algorithms, like those implemented in Spliddit platform, have traditionally been considered difficult for the end users to manipulate due to its complexities. This paper demonstrates how Large Language Models (LLMs) can dismantle these protective barriers by democratizing access to strategic expertise. Through empirical analysis of rent division scenarios on Spliddit algorithms, we show that users can obtain actionable manipulation strategies via simple conversational queries to AI assistants. We present four distinct manipulation scenarios: exclusionary collusion where majorities exploit minorities, defensive counterstrategies that backfire, benevolent subsidization of specific participants, and cost minimization coalitions. Our experiments reveal that LLMs can explain algorithmic mechanics, identify profitable deviations, and generate specific numerical inputs for coordinated preference misreporting--capabilities previously requiring deep technical knowledge. These findings extend algorithmic collective action theory from classification contexts to resource allocation scenarios, where coordinated preference manipulation replaces feature manipulation. The implications reach beyond rent division to any domain using algorithmic fairness mechanisms for resource division. While AI-enabled manipulation poses risks to system integrity, it also creates opportunities for preferential treatment of equity deserving groups. We argue that effective responses must combine algorithmic robustness, participatory design, and equitable access to AI capabilities, acknowledging that strategic sophistication is no longer a scarce resource.

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