  In this paper, a new randomized response technique aimed at protecting
respondents' privacy is proposed. It is designed for estimating the population
total, or the population mean, of a quantitative characteristic. It provides
a~high degree of protection to the interviewed individuals, hence it may be
favorably perceived by them and increase their willingness to cooperate.
Instead of revealing the true value of the characteristic under investigation,
a respondent only states whether the value is greater (or smaller) than
a~number which is selected by him/her at random, and is unknown to the
interviewer. For each respondent this number, a sort of individual threshold,
is generated as a pseudorandom number from the uniform distribution. Further,
two modifications of the proposed technique are presented. The first
modification assumes that the interviewer also knows the generated random
number. The second modification deals with the issue that, for certain
variables, such as income, it may be embarrassing for the respondents to report
either high or low values. Thus, depending on the value of the pseudorandom
lower bound, the respondent is asked different questions to avoid being
embarrassed. The suggested approach is applied in detail to the simple random
sampling without replacement, but it can also be applied to many currently used
sampling schemes, including cluster sampling, two-stage sampling, etc. Results
of simulations illustrate the behavior of the proposed procedure.
