Count the yeses without exposing anyone

Question

Twelve colleagues want to learn how many of them would answer "yes" to an embarrassing question (say, "have you ever fallen asleep in a meeting?"). Everyone is happy to know the total, but nobody is willing to reveal their own answer, and there is no trusted computer or outsider to collect the votes. Design a passing-a-notebook scheme that reveals only the total count and keeps each person's answer hidden.

Accepted Answer

The idea is to bury each person's contribution inside a big secret offset that scrambles the running total until the very end. The protocol. Sit in a circle and pass a small notebook around. 1. Person 1 secretly picks a large random number R, say a random 6-digit number that only they know, and writes it on the notebook, then passes it face-down to person 2. 2. Each next person privately reads the current number, adds 1 if their own answer is "yes," adds 0 if "no," writes the new total, erases the old, and passes on. 3. The notebook travels all the way around and comes back to person 1, who s…

Count the yeses without exposing anyone

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