If the Yellowstone Caldera erupted I'd probably expect to see a war pitting the US vs So. America / Europe for the southern hemisphere. The US has the largest fleet in the world at this time and would be evacuating as quickly as it could. Yes much of the mountain west would be immediately devastated but thankfully the west coast itself would be spared. The biggest problem would be food. The great plains aren't going to be producing any food in the near future and neither is much of the northern hemisphere...
This is where the wars come in as the great powers scramble to gain control of and put into production arable land in the southern hemisphere... Argentina is toast as it is invaded by the US, same with Brazil. Big fight over Australia and Africa as the Euros move massive amounts of people down there to farm. It all gets even more dystopian when you consider that the people who suffer the most will be the indigenous peoples and China / India will mostly be left to fend for themselves and / or get invaded and crushed by the USSR / Japan.
Industry might or might not move out of its current areas... it will mostly depend on how cold it gets and how bad the fallout is. The atmospheric effects would probably last for at least 4-5 years. I would estimate that 40-60% of humanity dies off with most of the casualties being in Scandanavia (80%+), Northern Europe except the UK (70%+ due to famine, war and cold), Africa (65%+ due to European desperation and displacement), the Middle East (60%+ due to war / famine), China and India (a lot due to war with the USSR / Japan), and maybe So. America due to war with the US / Europe / Itself.
I'd actually expect to see a lot less casualties in the US / Canada because even though they are the ones most directly effected by the eruption the eruption itself wouldn't kill all that many people since the region is sparsely populated and people in more heavily effected areas would quickly evacuate east, west or south. Canada would either get help from the Brits or the US or both in evacuating as things turn colder. I would probably say at most the death toll would 'only' be a couple million. Devastating but not apocalyptic... The much greater losses would be taken in the war that would come in order to avoid the famine, which depending on how it is handled could be devastating or 'merely' severe. Say 10-40 million from the famine and another 10 mill from a war vs So. America (and as nice as the US is this is a fight for survival, they are going to take arable land through any means necessary)... I can't really see the US losing over 50% of its population considering its industry.
The big losers are nations and peoples without industry or who are too far north / landlocked to make the rush to warmer climates. Doubly so for nations that have weak governments. The biggest 'winners' are the UK, Japan and the USSR. The UK loses little and maybe doesn't even go through more than a mild famine due to its island position and large transportation network. Japan wins because it takes out the DEI, the Phillipines and Indochina and also avoids the hardest blows. The USSR just rolls south probably with 'kill them all' orders. The US survives, probably not as a democracy though...