representative death

Relative to the atonement, The New Bible Dictionary on the representative nature of Christ's death:

It is agreed by most students that Christ’s death was vicarious. If in one sense he died ‘for sin’, in another he died ‘for us’. But ‘vicarious’ is a term which may mean much or little. It is better to be more precise. Most scholars today accept the view that the death of Christ is representative. That is to say, it is not that Christ died and somehow the benefits of that death become available to men (did not even Anselm ask to whom more fittingly than to us could they be assigned?). It is rather that he died specifically for us. He was our representative as he hung on the cross. This is expressed succinctly in 2 Cor. 5:14, ‘one died for all; therefore all have died’. The death of the Representative counts as the death of those he represents. When Christ is spoken of as our ‘advocate with the Father’ (1 Jn. 2:1) there is the plain thought of representation, and as the passage immediately goes on to deal with his death for sin it is relevant to our purpose. The Epistle to the Hebrews has as one of its major themes that of Christ as our great High Priest. The thought is repeated over and over. Now whatever else may be said about a High Priest, he represents men. The thought of representation may thus be said to be very strong in this Epistle.