Anchoring is a classic cognitive bias which has been discussed on Less Wrong before. Anchoring seems very difficult to avoid. Experiments have found that warning subjects about anchoring, or giving them cash incentives, doesn't solve the problem.

Here's an algorithm to fight anchoring that I would like to see a researcher test, based on binary search:

- Tell subjects to think of a number which is clearly too high for the quantity they want to estimate (an upper bound).
- Tell subjects to think of a number which is clearly too low (a lower bound).
- Tell subjects to find the midpoint of the upper bound and the lower bound and figure out whether it's too high or too low.
- The midpoint has now been judged as an upper/lower bound. Combined with the original lower/upper bound, we have a new, narrower range to explore. If this range is narrow enough, report its midpoint; otherwise go to step 3.

You could have two experimental conditions: one condition where subjects think of a number which is clearly too high first (the steps are in the order above), and another condition where subjects think of a number which is clearly too low first (steps 1 & 2 are swapped). If estimates from the two conditions are similar, the technique is successful.