Classification algorithms are increasingly used in areas such as housing, credit, and law enforcement in order to make decisions affecting peoples' lives. These algorithms can change individual behavior deliberately (a fraud prediction algorithm deterring fraud) or inadvertently (content sorting algorithms spreading misinformation), and they are increasingly facing public scrutiny and regulation. Some of these regulations, like the elimination of cash bail in some states, have focused on \textit{lowering the stakes of certain classifications}. In this paper we characterize how optimal classification by an algorithm designer can affect the distribution of behavior in a population -- sometimes in surprising ways. We then look at the effect of democratizing the rewards and punishments, or stakes, to algorithmic classification to consider how a society can potentially stem (or facilitate!) predatory classification. Our results speak to questions of algorithmic fairness in settings where behavior and algorithms are interdependent, and where typical measures of fairness focusing on statistical accuracy across groups may not be appropriate.
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