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In many societal resource allocation domains, machine learning methods are increasingly used to either score or rank agents in order to decide which ones should receive either resources (e.g., homeless services) or scrutiny (e.g., child welfare investigations) from social services agencies. An agency’s scoring function typically operates on a feature vector that contains a combination of self-reported features and information available to the agency about individuals or households. This can create incentives for agents to misrepresent their self-reported features in order to receive resources or avoid scrutiny, but agencies may be able to selectively audit agents to verify the veracity of their reports. We study the problem of optimal auditing of agents in such settings. When decisions are made using a threshold on an agent’s score, the optimal audit policy has a surprisingly simple structure, uniformly auditing all agents who could benefit from lying. While this policy can, in general be hard to compute because of the difficulty of identifying the set of agents who could benefit from lying given a complete set of reported types, we also present necessary and sufficient conditions under which it is tractable. We show that the scarce resource setting is more difficult, and exhibit an approximately optimal audit policy in this case. In addition, we show that in either setting verifying whether it is possible to incentivize exact truthfulness is hard even to approximate. However, we also exhibit sufficient conditions for solving this problem optimally, and for obtaining good approximations. 

We consider the allocation of scarce societal resources, where a central authority decides which individuals receive which resources under capacity or budget constraints. Several algorithmic fairness criteria have been proposed to guide these procedures, each quantifying a notion of local justice to ensure the allocation is aligned with the principles of the local institution making the allocation. For example, the efficient allocation maximizes overall social welfare, whereas the leximin assignment seeks to help the “neediest first.” Although the “price of fairness” (PoF) of leximin has been studied in prior work, we expand on these results by exploiting the structure inherent in real-world scenarios to provide tighter bounds. We further propose a novel criterion – which we term LoINC (leximin over individually normalized costs) – that maximizes a different but commonly used notion of local justice: prioritizing those benefiting the most from receiving the resources. We derive analogous PoF bounds for LoINC, showing that the price of LoINC is typically much lower than that of leximin. We provide extensive experimental results using both synthetic data and in a real-world setting considering the efficacy of different homelessness interventions. These results show that the empirical PoF tends to be substantially lower than worst-case bounds would imply and allow us to characterize situations where the price of LoINC fairness can be high. 

We study settings where a set of identical, reusable resources must be allocated in an online fashion to arriving agents. Each arriving agent is patient and willing to wait for some period of time to be matched. When matched, each agent occupies a resource for a certain amount of time, and then releases it, gaining some utility from having done so. The goal of the system designer is to maximize overall utility given some prior knowledge of the distribution of arriving agents. We are particularly interested in settings where demand for the resources far outstrips supply, as is typical in the provision of social services, for example homelessness resources. We formulate this problem as online bipartite matching with reusable resources and patient agents. We develop new, efficient nonmyopic algorithms for this class of problems, and compare their performance with that of greedy algorithms in a variety of simulated settings, as well as in a setting calibrated to real-world data on household demand for homelessness services. We find substantial overall welfare benefits to using our nonmyopic algorithms, particularly in more extreme settings – those where agents are unwilling or unable to wait for resources, and where the ratio of resource demand to supply is particularly high.