What would you call an electoral system that, under most conditions, proceeds in the following sequence:
(1) Take either the party or pre-electoral alliance that wins the most votes and give it an automatic bonus for being the largest;
(2) Then allocate the remaining seats proportionally.
With various country-specific features, that is how the Greek and Italian systems operate.
We lack a good name for it. Moreover, what seems to be the most common name given to such systems, both in the press and also by some political scientists, is “proportional”.
However, this is not an accurate name for a system that guarantees a disproportionally large share of the seats to the electoral entity that comes in first place.
So what should we call it?
It is really a hybrid of majoritarian and proportional, but of a fundamentally different sort than any mixed-member system. It aggregates votes nationwide (Greece, Italian Chamber of Deputies) or in regions (Italian Senate) and allocates a bonus or premium before any proportionality comes in to play. The name should reflect this premium on being the largest, as well as the openness to relatively small parties without regard to geographic concentration.
The orchard floor is open for naming suggestions.