We formulate the problem of eliciting agents' preferences with the goal of finding a Kemeny ranking as a Dueling Bandits problem. Here the bandits' arms correspond to alternatives that need to be ranked and the feedback corresponds to a pairwise comparison between alternatives by a randomly sampled agent. We consider both sampling with and without replacement, i.e., the possibility to ask the same agent about some comparison multiple times or not. We find approximation bounds for Kemeny rankings dependant on confidence intervals over estimated winning probabilities of arms. Based on these we state algorithms to find Probably Approximately Correct (PAC) solutions and elaborate on their sample complexity for sampling with or without replacement. Furthermore, if all agents' preferences are strict rankings over the alternatives, we provide means to prune confidence intervals and thereby guide a more efficient elicitation. We formulate several adaptive sampling methods that use look-aheads to estimate how much confidence intervals (and thus approximation guarantees) might be tightened. All described methods are compared on synthetic data.

通过对代理人的偏好进行赋值，我们将找到Kemeny排名作为对抗式武装强盗问题。我们考虑了采样和不采样的情况，并提供了概率近似正确（PAC）解决方案的算法，同时详细说明了其采样复杂度。如果所有代理人的偏好都是对备选项的严格排名，我们提供了剪枝置信区间的方法，以便更有效地赋值，并提出了几种自适应采样方法进行比较。

引发Kemeny排名