For example, here's how people typically perceive others in two psychologically important dimensions - Warmth and Competence*:
As you can see from the diagram, an ideal situations puts one into the upper right corner labeled "Partner", which combines high Warmth with high Competence. But research shows that in real life, people typically judge others in just one dimension and infer the other one through an implicit trade-off:
Theoretically, warmth and competence judgments vary independently, but in practice they are often negatively correlated, so that groups are stereotyped ambivalently as warm but incompetent, or competent but cold — an effect termed social compensation. For example, older people are perceived as warm but incompetent, and regarded with pity, whereas rich people are perceived as competent but cold, and regarded with envy.These ambivalent stereotypes are so ingrained that accentuating only one positive dimension about a person actually implies negativity on the omitted dimension — a secret language of stereotypes perpetuated by communicators and listeners. Indeed, the tendency to focus on the positive dimension of an ambivalent stereotype while implying the negative dimension has increased as social norms against expressing prejudice have developed.**
As we can see, even being perceived in a positive light can lead to negative personal and professional consequences. Therefore instead of succumbing to the trade-off, a psychologically-aware problem-solver would have to use one of the separation techniques to break the trade-off and demonstrate both warmth and competence.
I think I'll turn this real-life problem into a quiz for one of Stanford CSP invention/innovation courses.
* source: The Middleman Economy, by Marina Krakovsky
** source: doi:10.1016/j.jesp.2016.01.004. Promote up, ingratiate down: Status comparisons drive warmth-competence tradeoffs in impression management. Swencionis & Fiske, 2016.