Mutual coherence is a measure of similarity between two opinions. Although the notion comes from philosophy, it is essential for a wide range of technologies, e.g., the Wahl-O-Mat system. In Germany, this system helps voters to find candidates that are the closest to their political preferences. The exact computation of mutual coherence is highly time-consuming due to the iteration over all subsets of an opinion. Moreover, for every subset, an instance of the SAT model counting problem has to be solved which is known to be a hard problem in computer science. This work is the first study to accelerate this computation. We model the distribution of the so-called confirmation values as a mixture of three Gaussians and present efficient heuristics to estimate its model parameters. The mutual coherence is then approximated with the expected value of the distribution. Some of the presented algorithms are fully polynomial-time, others only require solving a small number of instances of the SAT model counting problem. The average squared error of our best algorithm lies below 0.0035 which is insignificant if the efficiency is taken into account. Furthermore, the accuracy is precise enough to be used in Wahl-O-Mat-like systems.

翻译：互相干性是衡量两种观点之间相似度的指标。尽管这一概念源于哲学，但它对多种技术至关重要，例如Wahl-O-Mat系统。在德国，该系统帮助选民找到与其政治偏好最接近的候选人。由于需要遍历观点的所有子集，且对每个子集需解决SAT模型计数问题（计算机科学中的已知难题），精确计算互相干性极为耗时。本文首次尝试加速这一计算过程。我们将所谓的确认值分布建模为三个高斯分布的混合，并提出高效启发式算法来估计其模型参数，进而通过分布的期望值近似互相干性。部分提出的算法具有完全多项式时间复杂度，而其他算法仅需解决少量SAT模型计数实例。最优算法的平均平方误差低于0.0035，在兼顾效率的前提下可忽略不计。此外，该精度足以满足类似Wahl-O-Mat系统的实际应用需求。