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Abstract. Many mathematical frameworks aim at modeling human preferences, employing a number of methods including utility functions, qualitative preference statements, constraint optimization, and logic for-malisms. The choice of one model over another is usually based on the assumption that it can accurately describe the preferences of humans or other subjects/processes in the considered setting and is computa-tionally tractable. Verification of these preference models often leverages some form of real life or domain specific data; demonstrating the models can predict the series of choices observed in the past. We argue that this is not enough: to evaluate a preference model, humans must be brought into the loop. Human experiments in controlled environments are needed to avoid common pitfalls associated with exclusively using prior data in-cluding introducing bias in the attempt to clean the data, mistaking correlation for causality, or testing data in a context that is different from the one where the data were produced. Human experiments need to be done carefully and we advocate a multi-disciplinary research en-vironment that includes experimental psychologists and AI researchers. We argue that experiments should be used to validate models. We detail the design of an experiment in order to highlight some of the signif-icant computational, conceptual, ethical, mathematical, psychological, and statistical hurdles to testing whether decision makers ’ preferences are consistent with a particular mathematical model of preferences. 1

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We show how to transform any inequality defining a facet of some 0/1-polytope into an inequality defining a facet of the acyclic subgraph polytope. While this facet-recycling procedure can potentially be used to construct ‘nasty’ facets, it can also be used to better understand and extend the polyhedral theory of the acyclic subgraph and linear ordering problems.

We find new facet-defining inequalities for the linear ordering polytope generalizing the well-known Möbius ladder inequalities. Our starting point is to observe that the natural derivation of the Möbius ladder inequalities as {0, 1/2}-cuts produces triangulations of the Möbius band and of the corresponding (closed) surface, the projective plane. In that sense, Möbius ladder inequalities have the same ‘shape’ as the projective plane. Inspired by the classification of surfaces, a classic result in topology, we prove that a surface has facet-defining {0, 1/2}-cuts of the same ‘shape ’ if and only if it is nonorientable.

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unknown Type-I error rates and do not replicate within participant