Applying the concept from this problem to the one at hand, try the following scheme:
Alice picks an arbitrary point A on the pizza.
Bess picks a second point B, and Cath then picks a point C.
Cut the pizza from the centre to those points. Alice then picks the piece either to the left or right of her point A. Everyone else has to take the piece in the same direction of their point.
Under this scheme, if Cath makes a bad choice she will get the smallest piece, and either Alice or Beth gets a bigger piece then the other depending on which way Cath's choice was bad.
If Beth makes a poor choice, assuming Cath makes the best choice, she will always get the smallest piece.
If Beth and Cath conspire against Alice they can force her to have a tiny piece, however one of them will have an even smaller piece. If each instead tries to get the most for herself then it will work out roughly even.
Alice picks an arbitrary point A on the pizza.
Bess picks a second point B, and Cath then picks a point C.
Cut the pizza from the centre to those points. Alice then picks the piece either to the left or right of her point A. Everyone else has to take the piece in the same direction of their point.
Under this scheme, if Cath makes a bad choice she will get the smallest piece, and either Alice or Beth gets a bigger piece then the other depending on which way Cath's choice was bad.
If Beth makes a poor choice, assuming Cath makes the best choice, she will always get the smallest piece.
If Beth and Cath conspire against Alice they can force her to have a tiny piece, however one of them will have an even smaller piece. If each instead tries to get the most for herself then it will work out roughly even.