Pooling choices across heterogeneous individuals leads to a fundamental identification problem: the pooled choice curve identifies the distribution of shock-contaminated valuations instead of the distribution of underlying willingness to pay (WTP). Consequently, the price at which the pooled choice probability equals one-half can be arbitrarily far from median WTP, even if the pooled choice curve is known perfectly. When choice probabilities are observed only at finitely many prices, we derive bounds for the mean and quantiles of the WTP distribution under economically interpretable restrictions on choice shocks and the tails of valuations. In an application to experimental estimates of the value of non-work time, the bounds are tight enough to exclude several estimates from pooled logit and finite-mixture logit specifications. We then illustrate how pooled logit models can produce misleading estimates, including estimates outside the range of individual WTPs. These distortions occur even for a population with homogeneous valuations or homogeneous choice errors, and they can worsen as preferences become more homogeneous or the share of noisy types decreases. Changes in the experimental design alone can lead to arbitrary changes in pooled-logit-implied WTP estimates.