John 19:11 Thou couldest have no power at all against me, except it were given thee from above: therefore he that delivered me unto thee hath the greater sin. (KJV)
In the Greek, this statement reads very differently than the English (see this article explaining the Greek source in detail). Your assumptions arise because some of the key context is hidden in translation. There are three issues:
- The first issue is with “sin”, which is why you assume this verse is about who is guilty. The word translated as "sin" (ἁμαρτίαν, hamartia) is a form of a verb that means "to fail in one's purpose", "to neglect," and "to be deprived of." It has no sense of doing malicious evil. The best English translation is "mistakes" or "failures" rather than what we commonly think of as the guilt of "sin." See this article for more information and context.
- The second issue is with the adverb translated as “from above”. In this verse, it describes the source of Pilate’s very limited authority over Jesus. However, this word (ἄνωθεν, anothen) doesn’t refer to God, at least not directly. This Greek word means "from on high," "from the beginning", "from further back", "higher", and "more universal". One sense here is "from further back" because Jesus's death was foretold by the prophets. Because of that, Pilate’s actions were a reflection of a divine plan (“from on high”) not a personal choice. Sacrificing his life was Jesus’s mission, one he accepted from both on-high and from the Law. Interesting side note: This is the same word translated as “again” in “born again”. So when Jesus said that people must be born “again” he is saying they are born either “further back in time” or “from on high”.
- The only person who made a choice was the one who chose to “betray” Jesus, that is, Judas. The word translated as “he that delivered” (ὁπαραδούς, paradidomi) means “give over” and it is often translated in the NT as “betray”. Here, the form of the word could be “the one giving me over” or “the one betraying me”. So this is the person that made the greater mistake.