Is it possible to nominate someone for a posthumous Nobel Prize?
No, it is not. Previously, a person could be awarded a prize posthumously if he/she had already been nominated (before February 1 of the same year), which was true of Erik Axel Karlfeldt (Nobel Prize in Literature 1931) and Dag Hammarskjöld (Nobel Peace Prize, 1961). Effective from 1974, the prize may only go to a deceased person to whom it was already awarded (usually in October) but who had died before he/she could receive the Prize on December 10 (William Vickrey, 1996 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel). See also par. 4 of the Statutes of the Nobel Foundation.
