When re-roofing, remove the roof finish and the sheathing, air seal and fill the cavities with insulation and then install the new roofing materials, including an ice-shield membrane. A well-sealed roof will need little to no ventilation. If you are uncertain about whether or not the sealing can be done effectively, leave a ventilation channel under the sheathing from the soffit to the peak. Sometimes insulation can be added to the ceiling inside, although this approach will not stop the air leakage.
An alternative measure to prevent ice dams is to make the roof impermeable by using a self-sealing membrane under the shingles. Building codes require such membranes on the lower part of the roof in new houses. These membranes do not stop ice dams, but they prevent the water from leaking through the roof sheathing and into the house. Ice damming can still occur and possibly damage shingles and gutters.