Non-probability samples involve some form of arbitrary selection of units into the sample, and, as a matter of fact, inclusion probabilities are unknown. Hence, it is not possible to apply probability randomization theory to make inference about the finite population parameters. In this paper the concept of uncertainty on data generating model, resulting from the lack of knowledge of the sampling design acting in the non-probability sample is discussed. A measure of uncertainty is introduced and its asymptotic proprieties are evaluated.