The use of Peer Instruction to enhance lectures in large enrollment introductory college science courses has become widespread. In this technique, learner responses to multiple choice questions posed by the instructor during lecture are recorded and displayed in real time by an electronic classroom response system (CRS). Peer Instruction takes place when learners are given time to discuss ideas with their neighbors before registering individual responses. Although much research has been done to study the impact of Peer Instruction on student learning and engagement, little is known about the dynamics of the peer discussions that occur just before students register responses to questions. The results of this study suggest that the grading incentive instructors adopt for incorrect question responses impacts the nature and quality of the peer discussions that take place. Two large enrollment college astronomy classes employing contrasting assessment strategies for CRS scores were observed. In the high stakes classroom where students received little credit for incorrect CRS responses, it was found that conversation partners with greater knowledge tended to dominate peer discussions and partners with less knowledge were more passive. In the low stakes classroom where students received full credit for incorrect responses, it was found that students engaged in a more even examination of ideas from both partners. Conversation partners in the low stakes classroom were also far more likely to register dissimilar responses, suggesting that question response statistics in low stakes classrooms more accurately reflect current student understanding and therefore act as a better diagnostic tool for instructors.