Broad Coverage, Focused Resolution: Hypothesis-Discriminative Evidence Acquisition for Long Video Question Answering

Long video question answering requires selecting evidence that determines the answer under a limited visual budget. Uniform sampling can miss brief events, while existing selection methods mainly organize evidence by query relevance and temporal coverage. This paper focuses on selecting a compact and complementary evidence set based on the distinctions among candidate answers. We propose HDEA, a two stage evidence acquisition framework driven by competition among answer candidates. Broad Competition Coverage considers all candidate pairs, selects complementary discriminative evidence, and builds an evidence core through temporally constrained submodular coverage. Focused Competition Resolution uses the core prediction to reweight candidate pairs, selects supplementary evidence while preserving the core, and fuses the predictions from the core and two nested expanded visual contexts. The two stages follow one principle: broad coverage before answering and focused resolution after answering. HDEA requires no additional training, subtitles, or external language models. On VideoMME, LongVideoBench, and MLVU, HDEA reaches 67.44%, 65.22%, and 74.25%, respectively, and achieves competitive performance among representative long video methods. Across four frozen video MLLMs and three benchmarks, HDEA demonstrates strong cross model transferability, outperforming uniform sampling in all 12 model and benchmark combinations. These results support candidate answer competition as a common structure for evidence acquisition and refinement in long video question answering. Code is available at https://anonymous.4open.science/r/HDEA.