As I believe everyone who has played ISdK will readily agree, the balance is exceptionally well crafted. Regarding the electors' privileges, I'd argue that their value as such is aproximately the same. However, a player will find certain of these more valuable than others depending on his position and that of others.
Here some odd ramblings regarding those seven:
Erzbistum Trier (pay and take the action of a no longer available action card):
The flexibility of this action is unrivalled and thus has the greatest potential to critically change the balance of power in an electorate or in the electoral college in one's favour.
I believe players will tend to find it more useful the further the game progresses. At the beginning of the game players will be particularly short on cash (at least if buying a city) and thus may not have the cash to make the most of this privilege. I dare say it'll be used at first as a "Medicus". In that case, it's obviously inferior to Köln's privilege, as one has to pay for the services of that physician.
Similarly, the last player in the action round might find it particularly useful as that player may particularly be hurt by an action card type no longer being available.
Erzbistum Cologne (de facto a freebie Medicus card):
This is together with the archdiocese of Trier the most popular elector placement in game setup following the placement of the emperor. I think it should be selected by the player following the emperor, next being Trier and lastly the Palatinate (though the placement of the first Reichsstadt might give rise to second thoughts).
Clearly, that personal physician will be of great use. The trouble is that others might feel much the same and contest Cologne quite a bit, forcing you either to step down from power or investing a considerable share of your resources.
Combining this privilege with that of either the Palatinate or Brandenburg - over a longer time - might be problematic, as if used to keep one's own nobles in good health, a lack of undeployed nobles might occur (particularly if you're also using those "mercenary" physicians as well on a regular basis in the same manner). So, pay extra attention to "generation management" with any of those combinations as otherwise you might face wastage in the mid- to late-game. Seeking to produce female offspring (after the first 1-2 rounds) and focussing more upon ageing others however does also make such combinations more viable. Trouble though is that early in the game it's easier to produce daughters while later sons are easier to produce (just consider city building activity and its decrease over time).
Should you control Cologne in the first turn, you might also be more willing to take on the imperial dynasty in a battle for the control of an electorate. After all, on top of using one Medicus card to keep your own kin in good health, you might wish to bump of that ailing emperor and force the imperial dynasty to decrease its board presence. That might well make your task in that contested electorate easier.
Erzbistum Mainz (extra VP):
The Archbishop of Mainz was the doyen of the electoral college and traditionally the chancellor of the Holy Roman Empire. No wonder his privilege is that coveted extra prestige.
In our games, we frequently see the emperor despatching his kin to Mainz from the outset. After all, any emperor would like to have a member of his own family assume the important position of imperial chancellor, no? (Again, one of those many subtle historical touches to this game). More pragmatically, the emperor will probably have seen his peers take control of Trier and Cologne, leaving him alone Mainz among the clergy's electorates (without having to pick a fight right from the beginning - here assuming nobody has placed a baron onto the bishop's throne of Mainz - which happens not to be so useful given it not having any use prior to Phase V - IMO there are better choices). As the emperor begins each setup round, he really cannot be beaten in building up a solid lead in Mainz (probably scaring off potential rivals). Many a victory has been built upon retaining control of Mainz for a longer period of time. Perhaps I am thus too rash in discounting the possibility of anyone placing a baron right onto the Mainz's throne during setup.
Certainly, Mainz is the electorate where it's most worthwhile to hold on to power. Building a considerable power base there can do the trick - and also maximise the usefullness of the Kirchlicher Einfluß (clerical influence) card, which happens to be the other major reason why it pays for the emperor to go for Mainz. It can be the key stone in retaining the imperial crown (which tends to be not too easy in round 1, particularly if the player 2nd in turn order becomes a pretender to the throne (as the neutral players would improve their turn order by voting for him).
My view is that if you're the emperor at start and you want to stay il supremo, you should either go for a clerical electorate (as reasoned above, that more often than not should be Mainz) or Bohemia - or if you can pull it off both (if you achieve that and obtained the Kirchlicher Einfluß card, the chances there won't even be a challenge to your authority should be pretty good).
Another consideration: That extra VP corresponds to the Ablaß card. In other words, to two talers - in card terms (leaving aside the card scarcity issue). The Palatinate is worth three talers in card equivalence. Bohemia and Cologne equal 1 taler in card value. However, Cologne's value does not lie in that saved taler, but in the scarcity of the medicus action. The Pope tends not to be in too high demand (though picked up frequently later in the action phase). This points to one characteristic of the Bohemian privilege. It's of relatively little use for those who aren't the emperor or pretender to the throne. But for those it could mean a hold on those juicy benefits of being Kaiser. Bohemia's privilege thus varies the most in its usefullness - all depending on player intentions and the balance of power in the electoral college.
Pfalzgraf bey Rhein (an extra baron):
Kudos for the old-fashioned spelling! I wonder whether the Pfalzgrafen were historically paticularly good at producing offspring (there tends to be a rationale behind these various privileges). This is a great privilege to increase your board presence in the early goings and - if your generation management is efficient - will supply you with new nobles throughout the game.
Herzogtum Sachsen (two extra talers):
All those silver mines! No wonder this is Saxony's privilege. Much as the Palatinate, this privilege is most useful early on and tends to be less so later on. After all, money requirements decrease once one has built one's cities and get extra funds from these.
More money buys more actions. Further, the more money you have, the longer you can stick round in the action phase without passing. That can be critical.
I like this one. Who doesn't want to be rich!?!
Markgrafschaft Brandenburg (entitled to pick the Graue Eminenz card).
This card can make all the difference offensively and defensively. It is as much valuable for the threat in being as in its actual use. After all, contesting an electorate against the interests of the Margrave of Brandenburg might prove tricky. Offensively, it's particularly useful in that it lets you add influence where otherwise all spaces are already taken. As this occurs more as the game progresses, I'd argue that the value of the Brandenburgian privilege tends to increase over time. Further, it's of particular use if contesting the clerical electorates. After all, they're "smaller" and hence the spaces are soon all filled - if hotly contested.
However, one needs to watch out that one's got that extra deployable noble. For that reason owning both the Palatinate and Brandenburg might prove problematic and leave you short of deployable nobles.
Königreich Böhmen (one extra electoral vote):
Seems to be the most unpopular privilege. It's the most dependent on player strategy and the electoral counts. If it's the critical difference between being emperor or not, well, then it's certainly a very good privilege (especially in the first three rounds).
There is however one caveat. If you want its votes to make that crucial difference in electing the new emperor, you should closely consider picking up the Ausschluß card. Otherwise your electoral influence might well be cancelled. All for naught then...
In a three player game, the dynamics regading Böhmen change once more, but as the game is best with four players (though I still like the three player version - better than I tought it'd be), I'll leave that aside.
Okay, now I've run out of steam. Certainly, these ramblings are far from exhaustive. I'd sure be interested to hear what you people out there have to say on this matter. Any preferred privilege combinations as well?
I was going to start a thread like this myself and then I noticed yours - great! I can just jump to the things I really want to say without having to give an introduction.
The one thing that struck me as odd about your assessment is how highly you value the free doctor privilege of Koln. This seems to me to be the weakest of all privileges. One thing I like about it is that you pose the threat of killing someone else's 45-yr old aristocrat even after the doctor cards have been exhausted - this is what I would consider the card's strongest function, but it is an ability it shares with the privilege of Trier, which can also perform the doctor action after all the cards have been exhausted. The two differences are: with Koln the action is free, and with Trier the action can be any action that pertains to round IV including but not limited to doctor. To me, the second difference is much more powerful than the first (except maybe the first round for the reasons you mentioned above), and thus Trier is markedly better IMO than Koln. Only if you were truly strapped for cash and using an additional doctor was part of your plan could the Koln privilege really feel like it was a lifesaver.
Therefore, you may not find it surprising that I think Rhein is an obvious choice for the second player to place his 45-yr old aristocrat during game setup. The value of Rhein decreases if you already have many aristocrats on the board and need to focus more on getting those to the right places while they are still alive rather than birth new ones, but during the first two rounds this is rarely ever the case and therefore Rhein remains - all other things equal - the most valuable privilege those first rounds. This is also why I think that placing the first emperor city on Rhein is pretty much an obvious choice as well. The problem with placing it on Mainz instead in an attempt to grab and hold onto power in that region is that later in the game the imperial city will serve someone else!
The only other place I'd consider placing an imperial city would be Saxony, because of the importance of money early in the game, although I still think Rhein is better, and this is why:
Rhein gives you a 15-yr old aristocrat, which costs 3. Saxony only gives you 2, BUT you retain the flexibility to spend those 2 somewhere else. The additional advantage of Rhein, however, is that you get to place an extra guy WITHOUT having to take a permit card, which is pink. Considering it's the second round of the game (which is when you would be in control of the electorate), you will probably also take the ordinance card to build a city. This means two pink cards, which leaves your chances for having a boy in round 3 pretty low, when you would still be wanting boys more than girls.
Of course, my argument relies on premises that given certain situations can be rendered untrue (e.g. it may be more important to do something else with the $2 than get another aristocrat on the board), but I think GENERALLY Rhein is a more desirable electorate to put the first imperial city than Saxony.
So generally speaking, I would always place the first imperial city in Rhein as emperor and as second seat I would always place my elector in Rhein. But what about third seat? As you mentioned above, the Trier privilege isn't as good as Koln the first round, so the choice for me is generally between Koln and Brandenburg (there are no other electorates whose privilege activates in phase 4, and there's virtually no incentive to hold onto the electorate where you place your 45-yr old baron).
Brandenburg has the drawback of bringing a pink card into the mix, which is bad early in the game for reasons mentioned above. However, it can be useful as a threat and discourage other players from competing with you for electorates the first round, and if you are really ambitious you can try to win 3 electorates the first round with its help. But generally, I'd say Koln is better, although I would consider switching it up from time to time.
The fourth seat actually has a dilemma as well (if Rhein and Koln have been taken), since being fourth seat makes the Trier privilege more valuable (since you are later in the turn order and possibly something will get taken you might want, e.g. ordinance). I'm not sure which I would take between Trier and Brandenburg, but my intuition is that I'd tend to go Trier just cause Brandenburg seriously hinders one's chances of having a boy in round two.
Bohemia is perceived as weak because it does not actually give you anything tangible but rather increases your chances of acquiring VPs in phase 6 (whether you are going for emperor seat or not). The problems are of course the excommunication card plus the fact that there may not even be an emperor election. I think it is stronger in the early game when players have less money to invest in taking cards that pertain to round 6 (pope, excommunication, church influence), so having an extra vote really makes a difference.
I agree that Mainz is great for holding onto throughout the game, especially if you can do so with just a baron, a knight, and two cities, which frees up all your other aristocrats. Then if you throw some aristocrats/knights in there you can really exert some electoral power with the Church Influence card. All around a good deal.
As far as my own personal approach to the game, I've come to realize that I must undervalue being emperor, since I seldom ever try to become him - I would say in more than half the games I've played I have not been emperor even once. Being able to break ties is a great privilege to have, and the imperial cities don't hurt either, but I find that the effort to become emperor unless you are perceived to be the person with least VPs (and even then you may need to pick up a phase 6 card or two) is usually not worth the effort, or at least I don't bother with something so uncertain and rather focus on investing my money in winning electorates the old fashioned way. In a recent game I played the first round badly and ended up fairly behind the others, so I experienced the unusual position of being emperor during the midgame. It opened my eyes to how powerful the position is, but I still don't think it is an "imbalancing" position one way or the other.
Got some more games under my belt, and actually starting to develop an increased appreciation for Brandenburg as an option for placing your 45-year-old elector. Despite throwing another pink card into your mix in round 1, the Grey Eminence really gives you the power to snag an additional region or relax about the ones you're already leading in and do something else like take Indulgence. As of right now I will take Rhein as my first choice and Brandenburg as my second.