I read this story back in the 1950's or 1960's in an old science fiction magazine. I can't remember its title. You read what the main character is thinking as he begins another normal day in his life. He hears the morning lottery announcement that the person selected in the daily lottery is in North America.
A later announcement is that the selected person is in "I think" New York. The character is shopping and doing other things. The next announcement is that the selected person is in New York City. A bit later the announcement is that the selected person is a Man. The lottery announcements continue on until the selected person is narrowed down to either our main character of the man standing next to him.
Announcement reminds citizen of the severe penalty for plunging their Official Lottery Knife into the wrong person. The story ends when the other mans name is announced and he is killed instead of the Main Character. An interesting insight as to a possible direction our society might take.