How many times to repeat something before it sinks in with a group of people?

repeat.py

import random
import collections

n = 100
p_attend = 0.5
p_listen = 0.5
n_to_remember = 2

people = list(range(n))
random.shuffle(people)

trial_holder = collections.defaultdict(list)
for trial in range(1000):

    listen_count = collections.Counter()
    
    for meeting_number in range(1, 31):
        attend = []
        listen = []
        for i in people:
            if random.random() < p_attend:
                attend.append(i)
        for j in attend:
            if random.random() < p_listen:
                listen_count[j] += 1

        get_it_count = sum(int(k >= n_to_remember)
                           for k in listen_count.values())
        trial_holder[meeting_number].append(get_it_count)

for i, j in sorted(trial_holder.items()):
    avg = sum(j) / float(len(j))
    print(i, avg)

This is a model of how many times something needs to be announced before it "sinks in", or maybe is "commonly known", with a group. Imagine there's a repeated meeting, where some probability that people attend (p_attend), some probability that they hear it, understand it, or find the announcement relevant given that they attend (p_listen), and that people need to hear something more than once before it "sinks in" (n_to_remember). Here's what the number of announcements vs the fraction of the group for which the announcement has sunk in.

This is way over-simplified, and doesn't have anything about:

• people sharing the content of the announcement outside of the context of the meeting
• allowing for variation among people
• whether the "announcement" seems like something worth paying attention to
• anything else that makes it more realistic

Still kind of interesting to see how it varies...