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A Guide to Understanding the Hierarchy of Big 4 Leadership

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Forgive the n00b question, but what's the pecking order for the Big 4 poobahs? Is Tax Leader more powerful than Managing Partner? Who can destroy who faster? This is important. I'm making a board (bored?) game out of it.
No question is too n00b, especially if there is frivolous recreation at stake!
Now, then. I'll be speaking from a purely speculative point of view since I have yet to be invited to any Big 4 partner meetings to witness the politics in action, but here goes anyway.
Generally speaking the Big 4 leadership structures are very similar. There are advisory, assurance, and tax leaders in each office. Some smaller offices won't have advisory leaders simply because they don't provide advisory services. On the surface, the three heads appear to be equal in stature, however there is always a certain amount of dick measuring between them. Assurance leaders probably have it the worst due to the myriad of administrative work, regulatory compliance, and ethical issues that exist in the space. They have to come down hard on their partners to dig up new business and it's usually for not very much money, so they are largely despised by their troops. This puts them in far weaker position than advisory or tax leaders.
Tax leaders, on the other hand, have it easier in the sense that the work is predictable and it's easy for them to encourage partners to up their rates because the message to clients is, "Jesus. I mean, the IRS, Congress, like, you know?" and clients usually say, "Yep, I guess you're right." Because of this, I envision tax leaders being envied by their assurance counterparts. However, since most auditors would rather chew glass than work in tax, they see this as a fair trade. Tax leaders are generally viewed favorably by the people in their group because tax people, for the most part, are pretty nice.
Advisory leaders, of course, are the shiny ones. They wear fancy clothes, talk a big game, and are far, far more physically attractive. They get their partners to charge big fees for providing clandestine services and by the grace of God, they get clients to thank them for it and come back begging for more. It's inexplicable. Thus, advisory leaders are the envy of both their assurance and tax equivalents. The downside for the advisory chiefs is that they are more subject to criticism when business is bad, as layoffs are common. Their approval amongst the partners and employees goes with the wind. The most powerful ones are skilled at rolling with the punches.
Of course you have to take other variables – personality, spouse's attractiveness, overall likability – into account, but I'd say that in a three-way battle, the assurance leaders are at a clear disadvantage. They are subject to dangers outside the firm that make them vulnerable to a finishing move by either tax or advisory. From there, it's a toss-up: tax and advisory leaders both have strengths that could give them a clear advantage (Tax: baffling intellect; Advisory: slick moves) but weaknesses (Tax: nose caught in book; Advisory: distracted by their own reflection) could expose them fatally.
These three lucky ducks report to their office managing partner (OMP) who, as supreme overlord of a given office, can destroy any of the leaders at any point in time. The only exception to this is when the OMP comes from position of weakness (age, general incompetence, universally disliked).
After that, the pecking order rises into area/regional leaders for advisory, assurance, and tax where the guidelines outlined above are fairly consistent. These men and women strike me to largely as Moses-types who get to climb a mountain, talk to a burning bush, and come back with orders that are not to be questioned.
After that, you have the national leaders for each group. They have those Darth Vader choking powers. You do not fail them.  
Every office has its own dynamics, so apply the above guidelines in a broad sense. If there are other variables that need included, feel free to elaborate below.