We provide mechanisms and new metric distortion bounds for line-up elections. In such elections, a set of $n$ voters, $m$ 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：我们为队列选举提供了机制与新的度量失真界限。在此类选举中，$n$ 位投票者、$m$ 位候选人与 $\ell$ 个职位均位于一个度量空间中。目标在于选择一组候选人并将其分配至不同职位，以最小化投票者的总成本。每位投票者的成本包括其自身与所选候选人之间的距离（衡量该投票者对所选候选人的喜好程度或与候选人的相似性），以及候选人与所分配职位之间的距离（衡量候选人对其职位的适配度）。然而，我们的机制并不知晓确切距离，而是仅利用较少信息量来产生良好结果，从而实现较低的失真度。我们考虑了多种不同类型的信息：序数式投票者偏好、序数式职位偏好，以及知晓候选人与职位的精确位置但不知投票者位置。在每种情形下，我们均给出了常数级别的失真界限，从而证明仅需少量信息即可在队列选举中形成接近最优的结果。