Other cake protocols notoriously “trim” their pieces, ruining them.
Here is my proposal on how to divide a cake more politely.
One person divides the cake into as many pieces as there are cake-eaters such that divider would be happy with any piece. During the rest of this process the divider can’t make claims, they will get what’s left.
Everyone else claims a piece.
During the claiming process, anyone who hasn’t claimed yet may respond to a claim with “Aww, I really wanted that piece”.
If no-one does, then the person who made the claim can take that piece, it’s theirs now.
If someone does, the person who was making the claim might say either “That’s OK, how about I take this one, then?” and make a new claim, or they might say “How about splitsies?”
To the latter, people who have not yet made claims (except the original divider) can say “I want in on that, with this piece” (pointing to an unclaimed piece) to join the splitsies group or “that’s OK, I’m fine with another piece” to opt out.
So splitsies groups might form. Other people outside the splitsies groups can just take their claims and leave.
Everyone in the splitsies group divides their pieces into as many subpieces as there are people in the group.
Let’s say it’s A and B. A select one of B’s halves, B selects one of A’s halves, done. Fair.
If it’s three or more, circle up. Everyone selects a subpiece from their right-hand neighbor, then one from their neighbor’s neighbor and so on. You can only select from the piece that person divided, not pieces they have selected from others. So standing to the left of the biggest piece would be pretty great, if it weren’t for… the recursive “Aww, I wanted that”! Splitsies within splitsies so you’ll end up with just mush (albeit fairly divided mush)! Luckily you can always opt out of a splitsies group, even a sub-splitsies group, and just change your selection instead.
So the drawback of this protocol is that people might not dare to speak up if someone takes a piece they wanted, for fear of the chorus of eyerolls and sighs. But that’s also a good thing. People who are just happy to take any piece rather than have to deal with shaved cake, trimmings, cake mush, divisions etc—or the social awkwardness of unusual algorithms—can do so.
I get that the math nerd version is a bit of a joke, people don’t really deal with trimmings of trimmings of trimmings. But the proposal I present here is one you can hopefully do for real.
The problem I see is that what we traditonally consider to be ‘cake’ is cut into ‘wedge’ shapes, and typically has some kind of filling sandwiched between the sponge layers.
Oh, yeah, Going splitsies makes the cake completely gross. There is a huge incentive to not go splitsies—it’s just a fallback in case the original divider does an awful job. But I mean compare to the original algorithm’s never-ending trimmings of shavings of slicings. It’s a mess all over!