Why do individuals interpret the same information differently? We propose that individuals follow Bayes' Rule when forming posteriors with one exception: when assessing the credibility of signal sources, they "double-dip" the data and use already updated beliefs instead of their priors. Individuals who make this mistake either over- or underreact to new information depending on the order in which they received previous signals. Traders engage in excessive speculation associated with price bubbles and crashes. Our model provides a theory of the origins of disagreement: individuals disagree about both unknown states and credibility despite sharing common priors and information.