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Social influence dialogue changes user behavior by altering internal cognitive states. The central evaluation question is whether the user's beliefs, desires, intentions, and emotions measurably change over the course of conversation, a process-oriented criterion that neither surface-level text metrics (BLEU/ROUGE) nor single-score LLM judgments can capture. We propose the \textbf{Cog}nitive \textbf{W}orld \textbf{M}odel \textbf{(CogWM)}, an LLM-based user model that reframes multi-turn dialogue evaluation from ``what did the user say'' to ``how did the user's internal cognitive state evolves.'' CogWM jointly predicts BDI/E cognitive states and user utterances and serves as both a user simulator and an evaluation platform, using a three-tier evaluation framework that covers turn-level fidelity, trajectory-level state dynamics, and task-level composite scoring. Trained via our \textbf{S}ummarize-\textbf{a}nd-\textbf{A}llocate \textbf{(SaA)} annotation pipeline on 150,454 user-turn samples across four social influence scenarios, CogWM achieves 77.6\% emotion accuracy (2.1$\times$ over GPT-5.5). In 3600 multi-agent discrimination trials, it distinguishes six commercial agents by their cognitive influence, with Llama-4-Scout ranking first (CTS +0.233). CogWM moves social influence dialogue evaluation from terminal judgment to process tracking. We have released our code\footnote{\scriptsize Code: this https URL} and models\footnote{Model: this https URL}.