An ideal observer will give equivalent weight to sources of information that are equally reliable. However, when averaging visual information, human observers tend to downweight or discount features that are relatively outlying or deviant (robust averaging). Why humans adopt an integration policy that discards important decision information remains unknown. Here, observers were asked to judge the average tilt in a circular array of high-contrast gratings, relative to an orientation boundary defined by a central reference grating. Observers showed robust averaging of orientation, but the extent to which they did so was a positive predictor of their overall performance. Using computational simulations, we show that although robust averaging is suboptimal for a perfect integrator, it paradoxically enhances performance in the presence of late noise, i.e. which corrupts decisions during integration. In other words, robust decision strategies increase the brains resilience to noise arising in neural computations during decision-making.