Scoring involves the compression of a number of quantitative attributes into a single meaningful value. We consider the problem of how to generate scores in a setting where they should be weakly monotone (either non-increasing or non-decreasing) in their dimensions. Our approach allows an expert to score an arbitrary set of points to produce meaningful, continuous, monotone scores over the entire domain, while exactly interpolating through those inputs. In contrast, existing monotone interpolating methods only work in two dimensions and typically require exhaustive grid input. Our technique significantly lowers the bar to score creation, allowing domain experts to develop mathematically coherent scores. The method is used in practice to create the LEED Performance scores that gauge building sustainability.

Using a model of agent behavior based around envy-reducing strategies, we describe an iterated combinatorial auction in which the allocation and prices converge to a solution in the core of the agents' true valuations. In each round of the iterative auction mechanism, agents act on envy quotes produced by the mechanism: hints that suggest the prices of the bundles they are interested in. We describe optimal methods of generating envy quotes for various core-selecting mechanisms. Prior work on core-selecting combinatorial auctions has required agents to have perfect information about every agent's valuations to achieve a solution in the core. In contrast, here a core solution is reached even in the private information setting.

The Myerson-Satterthwaite theorem is a foundational impossibility result in mechanism design which states that no mechanism can be Bayes-Nash incentive compatible, individually rational, and not run a deficit. It holds universally for priors that are continuous, gapless, and overlapping.  Using automated mechanism design, we investigate how often the impossibility occurs over discrete valuation domains.  While the impossibility appears to hold generally for settings with large numbers of possible valuations (approaching the continuous case), domains with realistic valuation structure circumvent the impossibility with surprising frequency.  Even if the impossibility applies, the amount of subsidy required to achieve individual rationality and incentive compatibility is relatively small, even over large unstructured domains.