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Multi-agent systems are increasingly used for forecasting future events, as deliberation among multiple LLMs is believed to improve reasoning and calibration. Yet existing approaches overlook a critical design choice: what information each agent receives. When all agents are given identical evidence, deliberation collapses into herding rather than genuine belief revision, leaving multi-agent systems little better than a single agent. We identify this as a fundamental gap and propose designed information asymmetry to close it: by partitioning evidence into shared public and disjoint private subsets, each agent holds exclusive knowledge that can only reach others through deliberation. We theoretically show that this decomposition reduces inter-agent error correlation, and instantiate it in InfoDelphi, a framework combining relevance-aware evidence routing, rationale-based iterative deliberation, and confidence-weighted aggregation. On PolyGym, a benchmark of 375 binary forecasting questions derived from real-world prediction markets, InfoDelphi outperforms the strongest single-agent and multi-agent baselines by 12--18% in Brier score and 4--8 percentage points in accuracy. More detailed experiments confirm that removing information asymmetry eliminates most deliberation gains, establishing diversity of input as the key enabler of effective multi-agent reasoning.