People throw away a lot of coffee cups. That was the motivation behind the BetaCup Challenge, a competition to create a more "sustainable" alternative to the disposable coffee cup.
If I'd found out about the competition while it was going on, I might have entered my "dig paper cups out of the trash and re-use them" idea, but I guess it's kind of late for that, since they've announced the winner:
The Karma plan: A chalkboard at the coffee shop will chart each person who uses a reusable mug. The tenth person to order a drink with a reusable cup will receive his or her drink free. By turning a freebie program into a communal challenge, Karma Cup would create incentives for everyone to bring reusable mugs. (After all, the more people participate, the more free stuff is given away and the more likely you are to get something free.) That, in turn, would eliminate rather than simply redesign the nefarious disposable cup.
It's pretty clear that the inventors of this idea (as well as the judges) have never worked retail, or they'd know the Hobbesian depths that consumers will sink to in order to get free stuff. The "Karma" plan is a recipe not only for barista-customer arguments, but also for chalkboard-stalking and line-cutting and fistfights. A better name might be the "There Will Be Blood" plan.
More interesting is the claim in the Fast Company article: "After all, the more people participate, the more free stuff is given away and the more likely you are to get something free." It's interesting because it doesn't make any sense. The likelihood of getting something for free depends on two factors: whether you bring a reusable cup, and where the chalkboard count stands.
The first doesn't depend on how many people participate -- the decision to bring a reusable cup is (presumably) yours alone. The curious thing is that (in the absence of fistfights and line-cutting) the second doesn't either. The relevant criterion is the "previous mug count," which runs from 0 up to 9. If it's 0 when you arrive, you move it to 1. If it's 1, you move it to 2. And so on, and then if it's 9 (which makes you the tenth customer), you get your coffee for free and it resets back to 0.
Now, as long as there are no fistfights and line-cutting, there's no reason why the mug count should favor any number over the other. When you go to Burger King and they give you a number on your ticket, you should be just as likely to get a number ending in 0 as a number ending in 5, no matter how many customers are going through the place. So you should get a number ending in 0 about 10% of the time.
If we ignore strategic (i.e. fistfight) considerations, the same should be true of the mug count. It should be 9 about 10% of the time, which means that (if you bring a mug) you should get your coffee free about 10% of the time. This is true whether one customer out of 20 brings a mug or every customer brings a mug. (Obviously, if no one brings a mug the count will be stuck at 0 all day, but even if you're the only customer who brings a mug, you should still get every 10th cup free.)
The big caveat again is that there are no fistfights. Probably, though, what happens is that you get lots of chalkboard-stalkers who hide in the restroom until the count reaches 9 and then cut in line to get a free coffee. In this case it's easy to imagine that, unless you are one of the line-cutters, the chalkboard count will almost never be at 9 when it's your turn to purchase.
However, the basic idea is good -- psychologically a 10% chance of saving \$2 is more exciting than for sure saving 20 cents. Accordingly, a superior implementation (from a fistfight perspective) might involve a random 10% chance of getting your coffee free when you bring your own mug. This would get rid of the incentives to cut in line, hide in the bathroom, and punch people. Plus, that way they could let you make your own mark on the chalkboard, which is better for both baristas (who won't have chalky hands while they're preparing your coffee) and customers (who like writing on the chalkboard because it reminds them of Coach Wickman's geometry class).
It just needs a catchy, Eastern-religious name. I'm thinking "Samsara."