Anchoring is a cognitive bias where an individual depends too heavily on an initial piece of information offered (considered to be the “anchor”) to make subsequent judgments during decision making. Once the value of this anchor is set, all future negotiations, arguments, estimates, etc. are discussed in relation to the anchor. Information that aligns with the anchor tends to be assimilated toward it, while information that is more dissonant or less related tends to be displaced. This bias occurs when interpreting future information using this anchor to gauge.
From Wikipedia.