I read this story in an anthology I think in the 1970s or 1980s - in it, the government has (and is known to have) the ability to use time travel to "undo" disasters. The protagonist is a police officer investigating apparently random murders (I think one of a spree of stabbings in a stadium), during a period after an assassination is being investigated so that it can be undone (once enough is learned about who did it, etc. - rather like the later TV series "Seven Days"). The police officer eventually realizes that the murders are occurring because people realize that because an "edit" is impending (to prevent the assassination), nothing they do in this timeline matters. This isn't Niven's All the Myriad Ways, but the point of the story is pretty similar.