This document discusses using ranking fairness metrics to assess viewpoint diversity in search results. It presents existing binomial and multinomial fairness metrics that can quantify the level of viewpoint diversity represented in search rankings. Through simulation studies with synthetic datasets, it evaluates how the metrics perform under different levels of ranking bias and proportions of viewpoints. The results show the metrics are effective in measuring viewpoint diversity, but their appropriate usage depends on factors like the ranking bias strength and direction. The document concludes the metrics can help assess real search results and align metric and user behavior outcomes.