How to score class participation, correcting for natural outspokenness? When my students ask questions and participate in discussion, class is more thoughtful, more fun, and more effective. I encourage their participation by checking in with them regularly, and making sure that they have time to speak and that they get a respectful hearing. Still, perhaps half of them never say a word. It seems like being in our mutual interest to get them to speak in class.

Because of these positive effects, like other teachers I have tried to encourage participation by making it part of the grading rubric. Some measures assess students' class presence within a particular timeframe, but this is hard to distinguish from attendance. More subtle is to give credit for speech, by filtering and counting contributions, whether online or in person. The speech measure is confounded by the fact that some students are happy to talk all the time while some never even want to. Without rewarding loudmouths or penalizing shy international students, what are best practices in scoring class participation?
Is "speaking in class" or "communicating about the topic in groups" part of your learning goals for your students? If yes, then you should first communicate this to your students and then think about how to include participation in the grading rubric based on the learning goals you set.

However, if you only want students to participate in the lecture to make your own teaching experience better, I think it is unreasonable to include their participation in their grade.

Put differently: I think that the grading should reflect how well the students achieved the learning goals of the course and nothing else. (This may be different in school, but for a undergraduate and graduate courses, I think this is reasonable.)