This paper outlines connections between Monotone Boolean Functions, LP-Type problems and the Maximum Consensus Problem. The latter refers to a particular type of robust fitting characterisation, popular in Computer Vision (MaxCon). Indeed, this is our main motivation but we believe the results of the study of these connections are more widely applicable to LP-type problems (at least 'thresholded versions', as we describe), and perhaps even more widely. We illustrate, with examples from Computer Vision, how the resulting perspectives suggest new algorithms. Indeed, we focus, in the experimental part, on how the Influence (a property of Boolean Functions that takes on a special form if the function is Monotone) can guide a search for the MaxCon solution.
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