Within the ViSE (Voting in Stochastic Environment) model, we study the effectiveness of majority voting in various environments. By the pit of losses paradox, majority decisions in apparently hostile environments systematically reduce the capital of society. In such cases, the basic action of ``rejecting all proposals without voting'' outperforms simple majority. We reveal another pit of losses appearing in favorable environments. Here, the simple action of ``accepting all proposals without voting'' is superior to simple majority, which thus causes a loss compared to total acceptance. We show that the second pit of losses is a mirror image of the pit of losses in hostile environments and explain this phenomenon. Technically, we consider a voting society consisting of individual agents whose strategy is supporting all proposals that increase their capital and a group whose members vote for the increase of the total group capital. According to the main result, the expected capital gain of each agent in the environment whose proposal generator $\xi$ has mean $\mu>0$ exceeds by $\mu$ their expected capital gain with generator $-\xi$. This result extends to the shift-based families of generators with symmetric distributions. The difference by $\mu$ causes symmetry relative to the basic action that rejects/accepts all proposals in unfavorable/favorable environments.

翻译：在ViSE（随机环境中的投票）模型中，我们研究了多数投票在不同环境中的有效性。根据损失陷阱悖论，在明显敌意的环境中，多数决策会系统性地降低社会资本。在这种情况下，“不经过投票直接拒绝所有提案”的基本行为优于简单多数投票。我们揭示了在有利环境中出现的另一种损失陷阱。在这里，“不经过投票直接接受所有提案”的简单行为优于简单多数投票，因此与完全接受相比造成了损失。我们表明第二种损失陷阱是敌意环境中损失陷阱的镜像，并解释了这一现象。从技术上讲，我们考虑一个由个体代理组成的投票社会，其策略是支持所有增加其资本的提案，以及一个其成员投票支持增加总群体资本的群体。根据主要结果，在提案生成器$\xi$均值为$\mu>0$的环境中，每个代理的预期资本收益比生成器为$-\xi$时高出$\mu$。这一结果扩展到具有对称分布的基于平移的生成器族。$\mu$的差异导致了相对于在不利/有利环境中拒绝/接受所有提案的基本行为的对称性。