In looking at the accordion on the right hand-side of our VeriSign homepage, we find that it performs relatively well. But we felt that "I need to" was more actionable than a more benign "Information for" label and perhaps we should switch the order of the two because the links which were displayed by default would get more clicks. So, we set out to test that theory.
We ran an A/B test and found that usefulness trumped accessibility. Despite the expectation that the panel of links which was exposed by default would get more clicks than links in collapsed panels, that was not the case. When the "Information for" panel was second and its links were therefore hidden by default, users still clicked on the links in that panel more than the exposed "I need to" links. So, despite the position of "Information for" - whether it was first or second - it was clear that users found the information in that panel more useful and were willing to seek it out even if it were hidden.