We pay attention to irrelevant anchors such as digits in a phone number. We often develop estimates by starting initial anchor that is based on whatever information is provided and adjust from the anchor to yield a final answer. Confirmation heuristics leads us to selective accessibility in our minds of a hypothesis-consistent information.
Existence of anchors leads people to think of information that is consistent with that anchor rather than accessing information that is inconsistent with that anchor. This phenomenon occurs even when anchors are presented subliminally.
Kahneman and Tversky (1974) pursued a study asking participants to estimate the number of African nations that were represented in the United Nations. Random number was given as a starting point (obtained by a spin of a roulette). Individuals were asked to state if the number was lower or higher than a given one and then delver their estimates. Arbitrary values had a substantial impact on their estimates. This shows anchors have dramatic effects on our judgements.
Similarly, simply exposing an individual to an extreme price can increase the price that a person is willing to pay, even if the focal product is in a different category that the product with an extreme price. This is present and useful in salary negotiations. Furthermore, consider meeting someone for the first time (initial impression) and raising education expectations showing your ability at an early age.
Processes that lead to anchoring bias
Then anchor is externally set, the anchor leads to a biased search for information compatible with the anchor. Assume you view a house whose list price is above market value. High anchor is likely to lead to see positive features of the house that is consistent with high evaluations.
Furthermore, then someone develops their own anchor, they will start with that anchor and insufficiently adjust away from it.
Bazerman, M.H. and Moore, D.A., 1994. Judgment in managerial decision making (p. 226). New York: Wiley.