What is the Jedi Council's military authority?

Question

During the Clone Wars (events on Episode II/III), I find it difficult to understand the relation between the Chancellor and the Jedi Council in terms of authority over the Clone army.

Technically, the clone army belongs to the Republic, which is ruled by the Chancellor. Since he's been granted emergency powers by the Senate, he should have the ultimate authority over the military decisions.

But the Masters in the Council are considered Generals, and on several ocasions we see them making decisions about military strategies, without consulting anyone else, as if they have this autonomy:

MACE WlNDU: Then the Jedi Council will make finding Grievous our highest priority.
(...)
OBI-WAN: In short, they are going very well. Saleucami has fallen, and Master Vos has moved his troops to Boz Pity.
(...)
YODA: Go, I will. Good relations with the Wookiees, I have.
MACE: It is settled then. Yoda will take a battalion of clones to reinforce the Wookiees on Kashyyyk. May the Force be with us all.

On another ocasion, Obi-Wan even called it Jedi Affairs:

OBI-WAN: The fact of the matter is you're too close to the Chancellor. The Council doesn't like it when he interferes in Jedi affairs.

And they get upset when the Chancellor tries to interfere in the decisions:

MACE: The Council will make up its own mind who is to go, not the Chancellor.

So, what is the military position of the Jedi Council in the Republic? How is it that the Clone Army belongs to the Republic and to the Chancellor, but the Jedi use them anyway they want?

Answer 1

Officially, the Jedi Council has no authority over the Grand Army. The Council's role is to oversee the Jedi, and it has responsibilities (education of padawans, maintaining Jedi records) which do not fall under the authority of the Supreme Chancellor. It wants to protect its independence in these matters, which is why Obi-Wan mentions that the Council dislikes interference by Palpatine.

Unofficially, it happens that the senior Jedi also hold high military rank in the Republic. So it is natural for meetings of the Jedi Council to discuss military affairs. Palpatine is in overall command of the army; but just like a real-world President or Prime Minister, he delegates authority to his generals, and doesn't have to be consulted about every single military decision.

Obi-Wan Kenobi has two titles: Jedi Master and General. If Palpatine decides he no longer wants Obi-Wan's services, he can dismiss him from the army, and he is no longer a general; but he is still a Jedi Master until the Jedi Council decides otherwise. (In fact, this is exactly what happened; Order 66 effectively revoked the military rank of all the Jedi.)

A very rough parallel in the real world would be a fraternal organization like the Freemasons. Many senior police officers belong, and it is natural for them to discuss work when they get together at a masonic meeting. But not all police are Freemasons, not all Freemasons are police, and the organization wouldn't want the city mayor poking into its private business (even though the mayor has authority over the police force).

Answer 2

Its organised how most armies are organised.

The head of the army and ultimately the person with the final say is the head of State. Nominally the Queen here in the UK (but for all intents and purpose the Prime Minister) and the President in the US. They would be consulted on the overall objectives, i.e. what is being attacked, why, when and possibly troop break downs. Then it will be down to the generals to implement that into coherent strategies, that will filter down to the lower officers to deal with the tactical situations.

As with the Jedi, the generals in most armies are separate from the government, i.e. when a new government is formed you do not replace all of the generals (unless you are Stalin). The head of state likewise doesn't tend to get too deeply involved in the day to day running of a war, preferring to leave it to the professionals.

This is the same as your closing line of

How is it that the Clone Army belongs to the Republic and to the Chancellor, but the Jedi use them anyway they want?

i.e. the UK army belongs to the Queen, but the generals of her army will use it as they see fit (within their stated objectives). difficulties would occur if one of the generals decided to attempt a coup as the army should be loyal to the Queen BUT the army may have actual loyalty to a general, this happened a lot in Rome, especially towards the later days. Most armies have checks and balances in place to prevent this happening.