According to the Dual Dodel of Social Hierarchy, one pathway for attaining social status is through dominance (coercion and intimidation). High dominance stimuli are known to more readily attract eye gaze and social attention. However, when there is a competition for non-spatial attentional resources, low dominance stimuli show an advantage. This low dominance bias was hypothesised to occur due to either counter-stereotypicality or attention competition. Here, these two hypotheses were examined across two experiments using modified versions of the attentional blink paradigm, used to measure non-spatial attention, and manipulations of facial dominance in both males and females. The results support the attention competition theory, suggesting that low dominance stimuli have a consistently strong ability to compete for attentional resources. Unexpectedly, high dominance stimuli fluctuate between having a strong and weak ability to compete for the same resources. The results challenge the current understanding of how humans interact with status.