No participant is incentivized to alter the cake if they agree that it's value is already equally split in 3.
The person making the trim is also not incentivized to make it 1.5/0.5, because they don't get first choice of those slices.
When dividing cake, if one slice is bigger it may be because there is less frosting on it when frosting is desirable, or it might be because the slicer thought they could trick the others. Then when someone contests this division it's either because their preferences don't match, or they are correctly calling out the trick.
In short, the algorithm is meant to deal with differing preferences and incentivized lying.
The person making the trim is also not incentivized to make it 1.5/0.5, because they don't get first choice of those slices.
When dividing cake, if one slice is bigger it may be because there is less frosting on it when frosting is desirable, or it might be because the slicer thought they could trick the others. Then when someone contests this division it's either because their preferences don't match, or they are correctly calling out the trick.
In short, the algorithm is meant to deal with differing preferences and incentivized lying.