I think we already have plenty of ways of distinguishing between stronger and weaker presidents – the Shugart and Carey scores and the Siaroff presidential power scores being foremost among them. For example, we could agree to call presidents who score below a certain threshold heads of state. However, what we really need is a more dynamic set of such scores. Alan’s ((I assume Robert means Alan Siaroff.)) index is really useful here because it tries to capture ‘actual’ and not just constitutional powers. So, what we need is not just a score for France since 1963, but France’s presidential power score from 1981-86, 1986-88, etc. Is Hollande as powerful as Sarkozy using this measure? In other words, we need scores to capture such changes and to be updated regularly. Let’s argue over whether France is a 5 or a 6 under Sarkozy on Alan’s measure rather than whether France is premier-presidential or something else. If we had reliable time series scores that captured changes in actual presidential power, then we could test more systematically to see whether presidential power really made a difference to particular outcomes.
My only comment (for now) is that I largely gave up trying to measure presidential powers some years ago. The Shugart and Carey (1992) index has some methodological issues ((which is not to say it is not useful regardless!)) but at least it was an attempt to base powers on constitutional provisions. It is even more challenging to measure powers dynamically, across presidents or even within terms of individual presidents. My last foray into that was in Mainwaring and Shugart (1997), in which we made the distinction between “constitutional” and “partisan” powers.
Why I still prefer the typology of presidential, president-parliamentary, and premier-presidential is that it creates categories that are definable without observation of behavior, ((And, in principle, readily determined from formal rules, although there are of course cases that defy easy coding.)) as well as mutually exclusive. Then it is a matter of exploring contextual variables that affect how these types operate in practice.
Clearly, however, it is on an open research agenda.