The origins of the draft are mysterious as it is. Sources talking to the Washington Post corroborated the existence of the draft and that it had been distributed in the White House, but didn't know who wrote it or even where it came from. It didn't, however, stem from the National Economic Council (which would have had to conduct investigations under the order) or the Office of Science and Technology Policy. The draft has reportedly been circulating around companies like Facebook as well as Washington law firms.
The Post has heard that the OSTP only found out about an executive order through an email from Yelp, which has regularly accused Google of unfair practices and pushed for governments to level the playing field. Senior policy VP Luther Lowe reportedly sent the draft order to multiple White House aides earlier in September. Lowe didn't say whether or not he commissioned the order, but he did use an email to the Post to bash Google for "actual bias" in local searches and accused it once again of violating antitrust law.
No matter who wrote it, the order might not go far. Aides said the order wouldn't work regardless. It would have asked most federal agencies to investigate political bias claims and report any instances to the Department of Justice. To put it mildly, that would be a massive undertaking -- and it would raise crucial questions. What would be perceived as bias? And if there were set criteria, what would the Justice Department do when political bias in a private company is legal? The draft order might indicate what the White House has been thinking, but there are numerous obstacles to making it a practical reality.