Belief Bias
The tendency to judge the strength of arguments based on the plausibility of their conclusion rather than the validity of the reasoning. People accept arguments with believable conclusions and reject those with unbelievable ones, regardless of logical structure.
Origin
British cognitive psychologist Jonathan Evans, along with Julie Barston and Paul Pollard, formally identified and named the bias in their 1983 paper "On the conflict between logic and belief in syllogistic reasoning" in Memory & Cognition. Using controlled experiments at Plymouth Polytechnic, they showed that people consistently judged logically invalid arguments as valid when the conclusion was believable. Earlier observations of the phenomenon date to M.C. Wilkins in 1928 and Woodworth and Sells's "atmosphere effect" in 1935, but Evans's work controlled for confounds and gave the bias its name.
Everyday Use
When someone presents a logically flawed argument but you nod along because the conclusion sounds right, that's belief bias in action. "Exercise is good for you, therefore everyone should run marathons" — the conclusion feels plausible enough that you might not notice the logic doesn't hold. We all tend to drop our critical thinking guard when a conclusion matches what we already believe.