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As various post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to develop a deeper understanding of whether and when the explanations output by these methods disagree with each other, and how such disagreements are resolved in practice. However, there is little to no research that provides answers to these critical questions. In this work, we formalize and study the disagreement problem in explainable machine learning. More specifically, we define the notion of disagreement between explanations, analyze how often such disagreements occur in practice, and how practitioners resolve these disagreements. We first conduct interviews with data scientists to understand what constitutes disagreement between explanations generated by different methods for the same model prediction, and introduce a novel quantitative framework to formalize this understanding. We then leverage this framework to carry out a rigorous empirical analysis with four real-world datasets, six state-of-the-art post hoc explanation methods, and six different predictive models, to measure the extent of disagreement between the explanations generated by various popular explanation methods. In addition, we carry out an online user study with data scientists to understand how they resolve the aforementioned disagreements. Our results indicate that (1) state-of-the-art explanation methods often disagree in terms of the explanations they output, and (2) machine learning practitioners often employ ad hoc heuristics when resolving such disagreements. These findings suggest that practitioners may be relying on misleading explanations when making consequential decisions. They also underscore the importance of developing principled frameworks for effectively evaluating and comparing explanations output by various explanation techniques.