The answer to the challenge I posted yesterday is 70%.
Two people responded on my blog with what I consider common sense, totally reasonable answers, both favouring 46% but considering the possibility of 66%. Neither is correct. I don't blame them, I blame the rulebook.
What people think happens, what I thought happens for two years after owning the book, is that you roll the character's Fellowship score (since they're trained in the Command skill), plus or minus any modifiers, and a success determines whether or not the target does what you command them to do.
The actual rules in question are hidden away on page 230 (and their location is not listed in the index to maximise one's ease in finding them). Interaction skills change dispositions. Better or worse dispositions act as modifiers to a base chance of 50% (70% if directly supervised) to obey a character, in steps of 10%. A NPC with the Devoted disposition (+20) has a 70% chance to obey the character without supervision, 90% with. I didn't specify the supervision status - my bad, I only noticed it was relevant while rereading the rules yet again. It's the last sentence in the last paragraph in the last column on the page, the only time it's mentioned in the entirety of the rules. Dispositions are also the only social modifiers listed, despite the game's extensive lists of modifiers for other situations (combat, etc.).
The only rules I know of used less in Dark Heresy are the investigation rules (pg. 186). Until I discovered them and suggested that we use them in a Dark Heresy game in 2010, I had never seen another player, in my games or in online discussion, mention or use them (nor since, and I've been keeping an eye out for it). This is unfortunate, because they actually assist players in succeeding in social interactions, boosting the chances that NPCs will comply with their requests dramatically. This helps low-ranked characters who are unable to leverage the talents and attribute boosts they get at higher ranks to succeed socially, and would incentivise players to attempt social solutions to problems that they currently shoot their way out of. The fact that these rules are poorly presented is especially odd for a game that is about a bunch of investigators trying to dig up corruption, using a system known for complaints about the "whiff factor" on skill use, and which encourages players to solve problems by means other than shooting them (though it does encourage a certain amount of shootiness).
The lesson here is: Don't hide a set of rules that will change how people play the game somewhere where they will never find them.