Extending the procedure of Engelberg et al. (2009) to surveys with varying interval-widths

The approach by Engelberg, Manski, and Williams (2009) to convert probabilistic survey responses into continuous probability distributions implicitly assumes that the question intervals are equally wide. Almost all recently established household surveys have intervals of varying widths. Applying the standard approach to surveys with varying widths gives implausible and potentially misleading results. This note shows how the approach of Engelberg et al. (2009) can be adjusted to account for intervals of unequal width.