Your first paragraph indicates that you may not fully understand the sorts of weapons systems that are available. I don't have up to date information, and if I did I probably wouldn't be allowed to share it, but there is a class of weapons called "theater ballistic missiles" that includes a sub-category of "Short range ballistic missiles".
Then I suggest you read further. The Wikipedia link I gave specifically referenced 'short range ballistic missiles' as part of the Indian arsenal. SRBM is not ICBM. And even if it were; the targets a Pakistani/Indian war would engage in would still not be long-enough range for it to matter.
This is a serious concern because that's a lot of extra radiation floating around,
Given the kiloton yield of the weapons involved, and the persistence of radiation -- not really. You're looking at well under a million statistical deaths globally.
Unless it's another Franz Ferdinand moment.
One might as well hypothesize that an Indian/Pakistani war cause the aliens on the dark side of the Moon to destroy us out of a fit of pique. It's equally as likely.
Any nuclear interchange between Pakistan and India will almost certainly be isolated to those two nations. There simply aren't any strategic mutual defense treaties that would extend to such an interchange. The history of warfare, furthermore, since the advent of nuclear weapons has been one of de-escalation of the scope of conflicts, not of broadening of them.
Given those positions, my thinking is that it would be Pakistan to initiate the first strike, and even if they did not, they would not present the conflict as a battle between two nation states, but as a religious battle between the West and Islam--at least publicly. This seems to be their (Islam's) standard response to anything that happened after the Reconquista.
I discounted the possibility of this concern from the outset. I can see no rational basis for the assertion that Muslims of sufficient organization as to be in control of a military and nation would willingly engage in behaviors they knew would result in the destruction of their organization. Even al-Qaeda still exists, "ten years after".
A historical footnote: black-market nuclear weapons have been available to whatever degree for almost fifty years now. There is simply no valid count of how many nuclear weapons the Russians ever actually made; and it is known that several of their weapons are 'simply missing'. Furthermore, Russian scientists have actually been convicted of selling weapons-grade radioactive isotopes to criminal elements.
And yet, there has never once been a nuclear terrorist attack; there hasn't even been a radiological one. Given the fact that multiple generations of such opportunity have existed, there has to be a reason why this is so.
I apologize for misinterpreting your first paragraph, however the wiki links you refer to were posted after I responded.
I may be over-worried about the actual fallout from an exchange in the range we're talking here. Most of my understanding comes from military training in the context of a US/USSR exchange in the late 80s, and doctrine that weren't re-written after that stopped being a concern.
However, I do think that political ramifications and third and forth order effects will be MUCH worse than you write about. Yes, in a certain sense nuclear weapons...
Last month I was involved in a conversation thread about what the impact of a hypothetical nuclear war would be on existential risk.
There are many potential nuclear war scenarios which would have varying impacts on existential risk. It's difficult to know where to start to gain an understanding of the long-term of nuclear proliferation.
For concreteness, consider the case of an India-Pakistan nuclear war.
According to Local Nuclear War, Global Suffering by Robock and Toon,
[...]
Note that this would presumably cause some degree of chaos in the developed world.
I have not yet investigated the credibility of the papers' claims. However,
Suppose that an all-out nuclear war between India and Pakistan were to occur and were to result in climate change killing 1 billion people. Then would the probability of a positive singularity increase or decrease and if so why?
This question seems very difficult to answer; maybe altogether too difficult for humans to answer. I welcome responses raising relevant considerations even in absence of a good way to compare the relevant considerations. Please read the linked conversation thread before commentating.