  Incorporating information from a prior survey is generally supposed to
decrease the estimation risk of the present survey. This paper aims to show how
the risk changes by incorporating the information of a prior survey through
watching the first and the second-order terms of the asymptotic expansion of
the risk. We recognize that the prior information is of some help for risk
reduction when we can acquire samples of a sufficient size for both surveys.
Interestingly, when the sample size of the present survey is small, the use of
the prior survey can increase the risk. In other words, blending information
from both surveys can have a negative effect on the risk. Based on these
observations, we give some suggestions on whether or not to use the results of
the prior survey and the sample size to use in the surveys for a reliable
estimation.
