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Although melanoma occurs more rarely than several other skin cancers, patients' long term survival rate is extremely low if the diagnosis is missed. Diagnosis is complicated by a high discordance rate among pathologists when distinguishing between melanoma and benign melanocytic lesions. A tool that provides potential concordance information to healthcare providers could help inform diagnostic, prognostic, and therapeutic decision-making for challenging melanoma cases. We present a melanoma concordance regression deep learning model capable of predicting the concordance rate of invasive melanoma or melanoma in-situ from digitized Whole Slide Images (WSIs). The salient features corresponding to melanoma concordance were learned in a self-supervised manner with the contrastive learning method, SimCLR. We trained a SimCLR feature extractor with 83,356 WSI tiles randomly sampled from 10,895 specimens originating from four distinct pathology labs. We trained a separate melanoma concordance regression model on 990 specimens with available concordance ground truth annotations from three pathology labs and tested the model on 211 specimens. We achieved a Root Mean Squared Error (RMSE) of 0.28 +/- 0.01 on the test set. We also investigated the performance of using the predicted concordance rate as a malignancy classifier, and achieved a precision and recall of 0.85 +/- 0.05 and 0.61 +/- 0.06, respectively, on the test set. These results are an important first step for building an artificial intelligence (AI) system capable of predicting the results of consulting a panel of experts and delivering a score based on the degree to which the experts would agree on a particular diagnosis. Such a system could be used to suggest additional testing or other action such as ordering additional stains or genetic tests.