Recent research has shown that explanations serve as an important means to increase transparency in group recommendations while also increasing users' privacy concerns. However, it is currently unclear what personal and contextual factors affect users' privacy concerns about various types of personal information. This paper studies the effect of users' personality traits and preference scenarios ---having a majority or minority preference--- on their privacy concerns regarding location and emotion information. To create natural scenarios of group decision-making where users can control the amount of information disclosed, we develop TouryBot, a chat-bot agent that generates natural language explanations to help group members explain their arguments for suggestions to the group in the tourism domain. We conducted a user study in which we instructed 541 participants to convince the group to either visit or skip a recommended place. Our results show that users generally have a larger concern regarding the disclosure of emotion compared to location information. However, we found no evidence that personality traits or preference scenarios affect privacy concerns in our task. Further analyses revealed that task design (i.e., the pressure on users to convince the group) had an effect on participants' emotion-related privacy concerns. Our study also highlights the utility of providing users with the option of partial disclosure of personal information, which appeared to be popular among the participants.