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Increasingly taking place in online spaces, modern political conversations are typically perceived to be unproductively affirming -- siloed in so called ``echo chambers'' of exclusively like-minded discussants. Yet, to date we lack sufficient means to measure viewpoint diversity in conversations. To this end, in this paper, we operationalize two viewpoint metrics proposed for recommender systems and adapt them to the context of social media conversations. This is the first study to apply these two metrics (Representation and Fragmentation) to real world data and to consider the implications for online conversations specifically. We apply these measures to two topics -- daylight savings time (DST), which serves as a control, and the more politically polarized topic of immigration. We find that the diversity scores for both Fragmentation and Representation are lower for immigration than for DST. Further, we find that while pro-immigrant views receive consistent pushback on the platform, anti-immigrant views largely operate within echo chambers. We observe less severe yet similar patterns for DST. Taken together, Representation and Fragmentation paint a meaningful and important new picture of viewpoint diversity.