Social media are massive marketplaces where ideas and news compete for our attention. Previous studies have shown that quality is not a necessary condition for online virality and that knowledge about peer choices can distort the relationship between quality and popularity. However, these results do not explain the viral spread of low-quality information, such as the digital misinformation that threatens our democracy. We investigate quality discrimination in a stylized model of online social network, where individual agents prefer quality information, but have behavioral limitations in managing a heavy flow of information. We measure the relationship between the quality of an idea and its likelihood to become prevalent at the system level. We find that both information overload and limited attention contribute to a degradation in the market's discriminative power. A good tradeoff between discriminative power and diversity of information is possible according to the model. However, calibration with empirical data characterizing information load and finite attention in real social media reveals a weak correlation between quality and popularity of information. In these realistic conditions, the model predicts that high-quality information has little advantage over low-quality information.