We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of $n$ voters, $k$ candidates, and $\ell$ positions are all located in a metric space. The goal is to choose a set of candidates and assign them to different positions, so as to minimize the total cost of the voters. The cost of each voter consists of the distances from itself to the chosen candidates (measuring how much the voter likes the chosen candidates, or how similar it is to them), as well as the distances from the candidates to the positions they are assigned to (measuring the fitness of the candidates for their positions). Our mechanisms, however, do not know the exact distances, and instead produce good outcomes while only using a smaller amount of information, resulting in small distortion. We consider several different types of information: ordinal voter preferences, ordinal position preferences, and knowing the exact locations of candidates and positions, but not those of voters. In each of these cases, we provide constant distortion bounds, thus showing that only a small amount of information is enough to form outcomes close to optimum in line-up elections.

翻译：我们针对排序选举问题提出了相应机制并给出了新的度量失真界。在此类选举中，$n$个选民、$k$个候选人和$\ell$个职位均位于同一度量空间。目标是选择一组候选人并将其分配到不同职位，以最小化选民的总成本。每位选民的成本包括其与所选候选人之间的距离（衡量选民对候选人的偏好程度或相似性），以及候选人与所分配职位之间的距离（衡量候选人与职位的适配度）。然而，我们的机制并不知晓精确距离，而是仅通过少量信息即可产生良好结果，由此实现较小失真。我们考虑了多种信息类型：序数选民偏好、序数职位偏好，以及已知候选人与职位的精确位置但不知选民位置的情形。在每种情形下，我们均给出了常数失真界，从而证明仅需少量信息就足以在排序选举中获得接近最优的结果。