Majority voting is the standard for aggregating multi-agent responses into a final decision. However, traditional methods typically require all agents to complete their reasoning before aggregation begins, leading to significant computational overhead, as many responses become redundant once a majority consensus is achieved. In this work, we formulate the multi-agent voting as a reliability-aware agent scheduling problem, and propose an Efficient Majority-then-Stopping (EMS) to improve reasoning efficiency. EMS prioritizes agents based on task-aware reliability and terminates the reasoning pipeline the moment a majority is achieved from the following three critical components. Specifically, we introduce Agent Confidence Modeling (ACM) to estimate agent reliability using historical performance and semantic similarity, Adaptive Incremental Voting (AIV) to sequentially select agents with early stopping, and Individual Confidence Updating (ICU) to dynamically update the reliability of each contributing agent. Extensive evaluations across six benchmarks demonstrate that EMS consistently reduces the average number of invoked agents by 32%.