The speed-accuracy trade-off (SAT) effect refers to the behavioral trade-off between fast yet error-prone responses and accurate but slow responses. Multiple theories on the cognitive mechanisms behind SAT exist. One theory assumes that SAT is a consequence of strategically adjusting the amount of evidence required for overt behaviors, such as perceptual choices. Another theory hypothesizes that SAT is the consequence of mixing different task strategies. In this paper these theories are disambiguated by assessing whether the fixed-point property of mixture distributions holds, in both simulations and data. I conclude that, at least for perceptual decision making, there is no evidence for mixing different task strategies to trade off accuracy of responding for speed.