Most voting models in the literature neglect abstention, but is such a simplification justified? I investigate this question in a model with outside pressure on voters. For sequential voting (e.g., roll call votes), with and without an abstention option, there is a unique subgame perfect equilibrium, which implies that true majorities always succeed. Abstention can be an equilibrium strategy for some voters, in particular under complex decision rules (e.g., weighted voting, double majorities). Simultaneous voting often has a unique pure strategy equilibrium but also a plethora of mixed and pure/mixed strategy equilibria. Therefore, only with equilibrium selection, can we evaluate the consequences of neglecting abstention. For equal weight voting, equilibria selected by the procedure of Harsanyi and Selten change completely with an abstention option, even if abstention itself is not or rarely used. With small enough outside pressure, however, the selected equilibrium honors true majorities in both cases.

中文翻译：

---

弃权表决

文献中的大多数投票模型都忽略了弃权，但这种简化是否合理？我在一个对选民施加外部压力的模型中调查了这个问题。对于顺序投票（例如唱名投票），无论有无弃权选项，都有一个独特的子博弈完美均衡，这意味着真正的多数总是成功。弃权对于某些选民来说可能是一种平衡策略，尤其是在复杂的决策规则下（例如，加权投票、双重多数）。同时投票通常具有独特的纯策略均衡，但也有过多的混合和纯/混合策略均衡. 因此，只有通过均衡选择，我们才能评估忽略弃权的后果。对于同等权重投票，由 Harsanyi 和 Selten 程序选择的均衡在弃权选项下完全改变，即使弃权本身没有或很少使用。然而，在外部压力足够小的情况下，所选择的平衡在两种情况下都符合真正的多数。