Yes, there are methodologies to measure direct communication exchanges within a public sphere. One approach is to conduct content analysis of the messages exchanged in the public sphere, such as on social media platforms or through public forums. This can involve coding the messages according to various categories such as the type of message, the tone of the message, and the topics discussed.
Another approach is to conduct surveys or interviews with members of the public to gather information on their communication exchanges within the public sphere. This can involve asking about the frequency, nature, and outcomes of their communications with others in the public sphere.
In both cases, it's important to carefully define the public sphere being studied and to use reliable and valid methods for data collection and analysis.