Earlier quoted context omitted.
Anchoring is a different effect than you might have thought. In breakthrough research, it was shown that when people were asked to write down completely random numbers (such as the last four digits of their social security number), before taking a guess at the value of a home (say; might have been something else), it had an absurdly strong effect on the value of their guesses. (People with coincidentally high last-fo…
FWIW the phrasing I use with clients is "fixed-price for successful completion of the following objectives" so it's a bit of a moot point. I do think you're overstating the research though. Many studies of unconscious priming haven't been replicated, and psychology as a whole is very subject to publication bias. [1] Anchoring is a real effect, and I'm a fan of Kahneman (especially prospect theory), but the evidence a…
The phrasing you say you actually use isn't an anchor. But you can still try different ways of phrasing it!
Extremely subtle differences in phrasing can have huge effects on people's reactions. If people are not reacting reasonably, try a slightly different phrasing, as well as different offers :)