Large Language Models (LLMs) not only have solved complex reasoning problems but also exhibit remarkable performance in tasks that require subjective decision making. Existing studies suggest that LLM generations can be subjectively grounded to some extent, yet exploring whether LLMs can account for individual-level subjectivity has not been sufficiently studied. In this paper, we characterize subjectivity of individuals on social media and infer their moral judgments using LLMs. We propose a framework, SOLAR (Subjective Ground with Value Abstraction), that observes value conflicts and trade-offs in the user-generated texts to better represent subjective ground of individuals. Empirical results show that our framework improves overall inference results as well as performance on controversial situations. Additionally, we qualitatively show that SOLAR provides explanations about individuals' value preferences, which can further account for their judgments.