We define randomized responses as follows:
In a question that can be responded with a "Yes" or "No", a respondent is asked to flip a fair coin, in secret, and answer the truth if it comes up tails. Otherwise he/she flips another coin in secret, and answers "Yes" if comes up tails, "No" otherwise.
According to the introduction this paper , the $\epsilon$-differential privacy of surveys relying on randomized responses is: $$ \ln(0.75/(1-0.75)) = \ln(3) $$ I am wondering how was this calculated. Note that the proofs contained in paper are related to the RAPPOR protocol.
Úlfar Erlingsson, Vasyl Pihur, Aleksandra Korolova,"RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response" https://research.google.com/pubs/archive/42852.pdf