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Social influence has been shown to create a Matthew effect in online markets, increasing inequalities and leading to “winner-take-all” phenomena. Matthew effects have been observed for numerous market policies, including when the products are presented to consumers by popularity or quality. This paper studies how to reduce Matthew effects, while keeping markets efficient and predictable when social influence is used. It presents a market strategy based on randomization and segmentation, that ensures that the best products, if they are close in quality, will have reasonably close market shares. The benefits of this market strategy is justified both theoretically and empirically and the loss in market efficiency is shown to be acceptable.