Most environments where assignment mechanisms (possibly random) are used are such that participants have outside options. For instance private schools and private housing are options that participants in a public choice or public housing assignment problems may have. We postulate that, in cardinal mechanisms, chances inside the assignment process could favor agents with better outside options. By imposing a robustness to outside options condition, we conclude that, on the universal domain of cardinal preferences, any mechanism must be (interim) ordinal.

中文翻译：

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随机分配和外部选项

在大多数使用分配机制（可能是随机的）的环境中，参与者都有外部选择权。例如，私立学校和私人住房是参加公共选择或公共住房分配问题的参与者的选择。我们推测，在基数机制，很有可能里面的分配过程可能有利于更好的外部选择代理。通过对外部选择条件施加鲁棒性，我们得出结论，在基本偏好的通用域上，任何机制都必须是（临时的）序数。