Mr. (Harry) Graves Timeline and Summary

Mr. Graves arrives in the town square, following Mr. Summers with the three-legged stool.
He sets down the stool and Mr. Summers places the black box on top of it.
Mr. Graves swears in Mr. Summers.
He waits his turn for the drawing and then goes to the box, prompted by his wife.
He helps Dave Hutchinson draw a paper from the box and then looks at it to determine if Dave's going to be the village's chosen victim. He isn't, of course.
Presumably, he participates in the final stoning.