[1][2][3][4][5] Most theories of conversational scorekeeping take one of the scoreboard's elements to be a common ground, which represents the propositional information mutually agreed upon by the interlocutors.
When an interlocutor makes a successful assertion, its content is added to the common ground.
Depending on the particular theory of scorekeeping, additional elements of the scoreboard may include a stack of questions under discussion, a list of discourse referents available for anaphora, among other categories of contextual information.
[4][3][5] The notion of a conversational scoreboard was introduced by David Lewis in his most-cited paper Scorekeeping in a Language Game.
In the paper, Lewis draws an analogy between conversation and baseball, where the scoreboard tracks categories of information such as strikes, outs, and runs, thereby defining the current state of the game and thereby determining which future moves are licit.