They didn't go for it :-)
Back when my kids were young and we had a neighborhood baby sitting co-op, all the Mom's met once a week. We set up a program where we got 15 different cards, every week we put all the cards in a basket at the beginning of the get together, then everyone took a card when they left (the basket was shaken up to randomize cards). That gave everyone a card to use but only aggregate statistics on the whole group rather than individual statistics.
The name was always Jane Smith.
These days Safeway has "fixed" that practice by tying gas rewards to a particular card number. That forces people to use the same card if they want to get gas rewards. I don't know but I suspect it was in response to activities like ours which mitigated their efforts to collect data.