The League vs the Star Empire of Manticore: Will the League be prepared to support a major war?
If the war results from the arrogance of Frontier Fleet/Frontier Security, will the rest of the League be prepared to go to war in support? And, if the war results from that cause, what sort of sacrifices will the rest of the League be willing to make if/after Frontier Fleet is reduced to wreckage for minimal Manticoran losses?
This is a very difficult call, and the situation could go in several different directions. If Frontier Fleet is handed a salutary drubbing and sent home again by the Manties, but without wholesale slaughter of Frontier Fleet's units, then the most likely probability is that the central League bureaucracy will grit its teeth, declare "no harm, no foul," severely (and very publicly) discipline the Frontier Security putzes who let this whole situation get so far out of hand, and work for some sort of negotiated end of hostilities and settlement with the Star Empire. Another possibility would be for the bureaucrats to ask for a formal declaration of war in the belief that Battle Fleet would be more successful, although they probably wouldn't even come close to getting the declaration they wanted. Yet another possibility would be for the League, and for the Navy in particular, to take the position that the Solarian League isn't going to war against the Star Empire of Manticore, at all. At worst, this is a police action, and it constitutes purely local acts of self-defense, for which no formal declaration of war is necessary. And, of course, after several months of this and continuing military operations, it would become extraordinarily difficult for any sort of negotiated settlement to emerge from the chaos. Yet another possibility would be for the League bureaucrats (assuming that they recognize the qualitative Manticoran edge in hardware) to offer to negotiate and then to spin things out across the negotiating table as long as possible while the SLN worked frantically to acquire matching or at least semi-equivalent technology of its own. I imagine that by now you can see what I meant when I said this could possibly go off in any one (or combination) of several directions.
Now, assuming that hostilities do break out and (especially) that they spread beyond the original area of confrontation, the League's bureaucracy is going to become increasingly committed to defeating Manticore as severely as possible in order to establish that just because you have a few shiny new technological toys, you shouldn't go around picking on the League, anyway. If the bureaucrats make a concerted effort to pursue a military response (as they see it) to "Manticoran aggression," they could create a situation in which momentum, anger, fear, and already-spilled blood would make it extraordinarily difficult for the League as a whole to pull back. None of which means that the portions of the League well separated from the zone of conflict by a comfortable pad of light-years would feel particularly happy about continuing the war and quite possibly drawing devastation down upon their own heads. By the same token, however, those more distant portions of the League may well remain much more poorly informed about what is actually going on and thus feel even more belligerent (and less worried about the war's final outcome) than the folks closer to the point of combat do.
If the Solarian League, as presently constituted, commits wholeheartedly to fighting Manticore because of "what the Star Empire did to our Frontier Fleet," for example, and if it holds together in the process, then the potential for the League to be willing to sustain very heavy losses and continue to prosecute the war becomes much higher. Once things like the concept of "national honor" get involved, and once somebody begins thumping on a lectern and shouting about how the "fundamental unity of the human race, which has protected us all from the evils of general warfare literally for centuries" is under assault, and how the loss of that fundamental unity will "inevitably lead to an unending procession of war after war between the League's successors," it's entirely possible that the League could find war with Manticore actually pulling it together into an effective interstellar government for the first time since its creation. And if that happens, then the League would be prepared to sustain very heavy absolute losses to continue the war until it attained victory.
I'm really not trying to be deliberately misleading here. I'm simply saying that there are way too many variables to be any more specific, and, quite frankly, within the constraints of where I've decided to take the storyline, I usually don't try to pick and choose which variables are going to come into play. The events as they unfold in the various societies and star nations wind up telling me that as I go along.