Infants must infer others’ preferences to decipher the social world. Past research has suggested that infants use statistical information to infer others’ preferences (Kushnir, Xu & Wellman, 2010), but the nature of children’s understanding of preferences has been somewhat underspecified. The current experiment explores how statistical information helps infants decipher the strength (Experiment 1) and hierarchy of preferences (Experiment 2). In Experiment 1, infants observed an actor choosing object A over either three different toys (A vs. many condition) or just one toy (A vs. one condition). Infants in the A vs. many condition inferred a stronger preference for A than infants in the A vs. one condition. In Experiment 2, infants who observed an actor choosing object A consistently over object C and object B inconsistently over C inferred the actor’s preference for object A over B. Results were compared to predictions made by the mixed multinomial logit model.