Most of the time when they slice a pizza, the operation looks something like this:
But this method leaves a big question - If two people are sharing the pizza, how do they know they are both getting a fair and equal amount?
There are several ways to get to fair and equal. One way would be to precision-cut the pizza with a computer-controlled laser, like this (you can fast forward through the first 35 seconds to get to the cutting, and note that the first few seconds contains one off-color word, so please do not click into the video if that will bother you):
The laser technique is prohibitively expensive in most cases. So you can use this inexpensive technique instead:
Tl;dr - As long as one cut goes through the center and the two people get alternating slices, the pizza they get is equal.
There is another way to solve the problem, which is described as "a two-party proportional envy-free allocation protocol". It is described here:
In the method, one person divides a good or resource into what they believe are equal halves, and the other person chooses the "half" they prefer. Thus, the person making the division has an incentive to divide as fairly as possible: for if they do not, they will likely receive an undesirable portion. This rule is a concrete application of the veil of ignorance concept. Unlike those for more people, 2 person fair divisions are also automatically envy-free.
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