In contingent valuation studies, while dealing with the estimation of average willingness to pay (WTP) the commonly used approach is double bound referendum format. The response here is interval censored and generally logit or probit models are used to estimate the mean WTP. In this paper we compare the performance of model-based and design-based estimators of the mean, when the variable is continuous and interval censored. A second question that is addressed in this paper is the comparison of the bias and mean square error (MSE) of the maximum likelihood (ml) estimators in the single and double bound approaches. We have carried out simulations to compare the single and double bound approaches. The investigation indicates that the design-based estimators perform better in double bound case compared to single bound, while the performance of the model-based estimators in double bound case is dependent on the second bid values and the underlying estimation procedure.