At the risk of getting downvoted by the pedants, I'm going to explain a game called Who Gets This. Our family first learned about this technique while reading about Capt Bligh's survival voyage after he and his crew were put at sea on an overcrowded lifeboat in the wake of the Bounty mutiny. It's how they divided bird meat in the lifeboat during their 4,000-mile trek, and we adopted the same technique in our family with four children.
Here's how it works: one person divides the food into N roughly even portions. Then, one-by-one, someone takes one of the items, and says, "Who gets this?"
Then another member of the party – one who is not allowed to see the portions being chosen – calls out a name (either their own name, or the the name of someone else in the group). This happens N times (in your case, N = 3).
For example, if Leah, Mia, and Liam all had to share three pieces of a brownie, it might go something like this. First Liam cuts the brownie into three pieces. Then Mia turns her back. Liam picks one of the three pieces, and says, "Who gets this?"
Mia: Liam does.
Liam (picking up a second piece): Who gets this?
Mia: I do.
Because there is only one person left, Leah gets the remaining piece.
Advantages of this methodology:
- It can be used with any number of people.
- The process simple to conduct and easy to understand.
- It can be used even when there is no cutting involved (for example, when the teller at the bank hands you four different-colored lollipops to distribute to your four kids).
- Because the person cutting or dividing has no idea when his or her name will be called, there is incentive to cut the pieces equally.
- It's fun. After the very first time we tried this, it immediately became a well-liked and oft-used family tradition.
I mentioned the downvote at the beginning because this method doesn't necessarily guarantee that everyone "will feel like their portion is the same size as the others." Still, there is incentive to divide roughly equally, and at least the apportionment process is fair. Moreover, this technique kept over a dozen men alive under the most perilous conditions, so how bad can it be?