And I wanted to point out the following:
1. The cake-cutting example does not illustrate the veil of ignorance! Of course the person cuts equal pieces, but that is not because the person doesn't know which piece will be left at the end, but rather because the person is certain that the smallest piece will be left at the end, i.e. the person isn't working (cutting cake) in a condition of ignorance, but rather in a condition of perfect knowledge
2. For the above reason, the cake-cutting example and the veil of ignorance cannot really be criticized simultaneously. Anything you say will be criticism of one and support for the other, because they are exact opposites. It's cute :)
3. It's true (and it's clear) that the cake-cutting example will necessary result in equal pieces. But is having equal pieces even a good idea to begin with? Please take a look at this (here's the same story in another place)
And here's Colour Record No. 137, Side B:
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