Multi-label classification is prevalent in real-world settings, but the behavior of Large Language Models (LLMs) in this setting is understudied. We investigate how autoregressive LLMs perform multi-label classification, focusing on subjective tasks, by analyzing the output distributions of the models at each label generation step. We find that the initial probability distribution for the first label often does not reflect the eventual final output, even in terms of relative order and find LLMs tend to suppress all but one label at each generation step. We further observe that as model scale increases, their token distributions exhibit lower entropy and higher single-label confidence, but the internal relative ranking of the labels improves. Finetuning methods such as supervised finetuning and reinforcement learning amplify this phenomenon. We introduce the task of distribution alignment for multi-label settings: aligning LLM-derived label distributions with empirical distributions estimated from annotator responses in subjective tasks. We propose both zero-shot and supervised methods which improve both alignment and predictive performance over existing approaches. We find one method -- taking the max probability over all label generation distributions instead of just using the initial probability distribution -- improves both distribution alignment and overall F1 classification without adding any additional computation.