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Vorurteil vs. Voreingenommenheit

While both words relate to a lack of objectivity, Vorurteil typically refers to deep-seated stereotypes or clichés about groups of people, whereas Voreingenommenheit refers to a specific standpoint, partiality, or lack of neutrality in a decision-making process.

Vorurteil

B1
Literally meaning pre-judgment, this word refers to a fixed, unshakeable opinion—usually negative—formed without examination of facts. It is the standard word for social stereotypes regarding race, gender, class, or nationality.
Er hat ein Vorurteil gegen Menschen, die nicht studiert haben.
(He has a prejudice against people who have not studied.)
Reisen ist der beste Weg, um Vorurteile abzubauen.
(Traveling is the best way to break down prejudices.)
Es ist ein weit verbreitetes Vorurteil, dass Deutsche keinen Humor haben.
(It is a widespread stereotype that Germans have no humor.)
Sie fällte ihre Entscheidung aufgrund alter Vorurteile.
(She made her decision based on old prejudices.)

Voreingenommenheit

C1
This word translates closer to bias, partiality, or being prepossessed. It describes a state of mind where someone lacks neutrality or objectivity in a specific situation, often because they have a personal interest or prior inclination.
Der Schiedsrichter wurde wegen Voreingenommenheit kritisiert.
(The referee was criticized for bias.)
Wir sollten das Problem ohne Voreingenommenheit betrachten.
(We should look at the problem without preconceived notions.)
Ihre Voreingenommenheit für den Kandidaten war offensichtlich, da er ihr Bruder ist.
(Her bias for the candidate was obvious, as he is her brother.)
Die Studie litt unter der Voreingenommenheit der Forscher.
(The study suffered from the bias of the researchers.)

Summary

Use Vorurteil involves a fixed status or cliché (like a stereotype about a culture). Use Voreingenommenheit involves a lack of fairness or neutrality in a specific moment (like a biased judge or a subjective reporter).