The executive branch, or government, is typically not elected directly by the people, but rather formed by another elected body or person such as the parliament or the president. As a result, its members are not directly accountable to the people, individually or as a group. We consider a scenario in which the members of the government are elected directly by the people, and wish to achieve proportionality while doing so. We propose a formal model consisting of $k$ offices, each with its own disjoint set of candidates, and a set of voters who provide approval ballots for all offices. We wish to identify good aggregation rules that assign one candidate to each office. As using a simple majority vote for each office independently might result in disregarding minority preferences altogether, here we consider an adaptation of the greedy variant of Proportional Approval Voting (GreedyPAV) to our setting, and demonstrate -- through computer-based simulations -- how voting for all offices together using this rule overcomes this weakness. We note that the approach is applicable also to a party that employs direct democracy, where party members elect the party's representatives in a coalition government.

中文翻译：

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选举行政部门

行政部门或政府通常不是由人民直接选举产生的，而是由另一个选举产生的机构或个人组成，例如议会或总统。因此，其成员不直接对人民负责，无论是个人还是集体。我们考虑这样一种情况，即政府成员由人民直接选举产生，并希望在这样做的同时实现相称性。我们提出了一个由 $k$ 办公室组成的正式模型，每个办公室都有自己不相交的候选人集，以及一组为所有办公室提供批准选票的选民。我们希望确定为每个办公室分配一名候选人的良好汇总规则。由于对每个办公室单独使用简单多数票可能会导致完全无视少数人的偏好，在这里，我们考虑将比例批准投票 (GreedyPAV) 的贪婪变体适应我们的设置，并演示 - 通过基于计算机的模拟 - 使用此规则对所有办公室进行投票如何克服这一弱点。我们注意到，该方法也适用于采用直接民主的政党，即党员在联合政府中选举该党的代表。