Protests are flawed indicators of public opinion, as it is uncertain to what extent the wider public shares protesters' interests. Nevertheless, the size of a protest is often interpreted to indicate the level of public support for its demands. This inference assumes that protests face participation costs that deter many supporters from taking part, leading observers to extrapolate broader support from the number of participants. However, this reasoning overlooks that protesters are a self-selected group of politically active citizens and makes the strong assumption that the costs of protesting are known. Using survey experiments with Swedish local politicians and citizens, we assess how citizens and politicians infer public opinion from protests. We vary a protest's size and participation costs in vignettes and introduce novel survey measures of public opinion perceptions. Preliminary evidence shows that flawed inferences are common, even when respondents are informed about selection biases or the varying costs of protests.