While there is some debate as to whether a doll's head or third bite is needed or not, the legitimate debate revolves around the questiuon of whether or not the action has adequate strength without it. The part that is not in question is whether or not the doll's head will stiffen the action.

A well fitted doll's head WITHOUT a third bite (As I've seen on a Jeffery) will tie the breach to the face. Under firing stress the barrels tend to rotate around a different center than when opening the action. Thus, the doll's head grips even without a bite. I have seen some excellent diagrams to illustrate how this works.

Also consider those shotguns that lack what we usually think of as the first two bites and have only what we usually think of as a third bite. Obviously, if a third bite did nothing, they would fly apart on firing.

The caveat for any of the three bites is that they must be well fitted. If not, the load will not be shared among the three and at least one will be doing nothing. (Something I have suspected is the case with some cheap shotguns I've seen with three bites.)

Greener was never afraid to blow his own horn and had a very good demonstration of how his cross bolt type third bite stiffened the action.