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The political map mode is of course a must have, but I hope I will use it alot less now with this beautifull new map with such clear boarders. They have also said alot more info will be seen and available on the map now. Perhaps fewer map modes are actually needed.
 
The first map mode that is essential is the political mode, it is my default one that I alwasy use. You don't really know where all the countries are with the game's default terrain map. I mostly use the diplomatic mode to see where my cores are. A trade route map mode will be useful to.
But I never used the manpower mode, because I still don't know the importance of provincial manpower.
Other modes that are needed:
Religion
Culture
Revolt Risk
Colonial mode
 
The trouble with this thread is that it doesn't mean much to say "I want mapmode X". The real question is, what should this mapmode do?

This is one place where I've always felt EUIII retrograde. In EuII, simply putting the mouse over a colonial province would bring up a TT which gave you all you need to know; you could quickly scan a swath of territory to decide where you want to colonize, with no clicking at all. And of course, the Diplo mode was vastly more informative. At a glance you could see where your relations might need improving.

And, once again, there are several mapmodes which, to my eyes, do nothing whatsoever, like shipbuilding.

Somewhat OT, but I think the same is true of the ledger, and the unit interface. EUII's was ledger vastly better implemented. It was easier to change screens (right click) and it sorted in many more valuable ways. (And let's not even think of province decisions). The unit organization system was vastly more flexible; you could work with all the units in a province, without reselecting.