Another Trotsky thread another thread of myths and legends...
So let's tackle a few points before I take a stab at answering the OP's question.
1) Trotsky has to actually get power. This is close to ASB and the only plausible way for Trotsky to end up supreme leader is if Lenin puts him in charge. Something also needs to have removed Stalin for him, since I can't really see any way for Trotsky to be able to deal with Stalin himself.
2) Trotsky was disliked by most of his peers and showed no sign of the sort of political ruthlessness Stalin would show - in all likelihood, this means no purge of the old Bosheviks and Trotsky isn't a very supreme leader at all - instead he'd be first among equals in a Politburo where everyone had an interest to make sure he didn't grow too strong. Now probably things still get done - but controversial things could well end up stalled by political gridlock.
3) A Trotskyite SU doesn't magically become a utopia. Two big reasons for this - first Trotsky is a ruthless operator who was willing to kill hundreds of thousands of people to achieve his aims, second there were hundreds of thousands (if not millions) of ruthless operators below the top guy. There's no doubt that Stalin was an evil man, but people forget that he was also used as a scapegoat by the Communist Party after Khrushchev's secret speech. If Stalin never gains power then he and thousands of his creatures won't have much power in the Soviet Union, but that still leaves plenty of other people who'd sacrifice millions if they thought it would serve the greater good.
4) People also forget that Trotsky was a pragmatic and capable operator. He was a terrible politician, but there's no doubt that he could effectively run large organizations and fudge his ideological positions to justify pragmatic actions to himself and others. The guy was not some beardy-weirdy campus revolutionary who couldn't deal with the real world. Trotsky was one of the key men in
actually winning a civil war and impose a very, very fringe political ideology on an entire empire. As such, anything that Trotsky wrote about his beliefs should be taken with more grains of salt than people usually do (for one thing, much of what he wrote in OTL was a reaction against what Stalin was doing OTL).
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So would Trotsky's USSR have better relations with the West? Well... It depends on how we get Trotsky in charge and whether an aggressive Germany is starting to loom in Central Europe.
Let's say that we get there through Lenin not getting a bullet from Fanny Kaplan, and not suffering his strokes. Lenin lives longer and has better health. Let's say that Stalin is demoted by Lenin around 1925 in this ATL, forever to languish as a cement plant manager in Kazakhstan or something. Let's also say that Trotsky, through long years being seen as Lenin's right hand man and through success in expanding Party membership among the Soviet workers, secures enough political support to squeak in as Lenin's successor when Lenin dies between 1929-1931.
Whether led by Trotsky or Lenin, this Soviet Union is going to have a rapprochement with the West, just as OTL. When it became clear that the Soviet state wasn't going to collapse on its own and that Western Capitalism was likewise going to be around for a while, the pressures to make realistic accommodations and get trade going again would pick up.
Where things could start to change is that it is unlikely that Trotsky or Lenin will be clamping down on travel in the early 30s. As such, as people start to worry about Germany (which is going to happen whether or not Germany goes Nazi in this scenario), the impetus to further improve relations with the SU will be there, and there will be less suspicion caused by the sudden appearance of Stalinist isolationism. So better relations with the West in the early 30s.
Even if Trotsky is no. 1 by this point, the idea of exporting revolution to the industrial West will have an appeal somewhere close to zero. There may be more support for revolution in China and the colonial world, but probably not a whole lot - the Russian civil war had left the country seriously wrecked and people wanted to rebuild. I just don't see the Soviets acting sufficiently differently to be any threat to Western interests in the 30s and 40s (though greater support for, say, scholarships and training for colonial revolutionaries to come learn in the USSR and less purging of those people could mean a very, very different decolonization in the 50s onwards).
In the mid and late 30s, much depends on what is happening in Germany - if the Germans have gone Nazi, France and Britain are going to start to get more serious about reaching out to the Soviets just as they did in OTL. It's hard to see Trotsky being quite as paranoid as Stalin, so probably Soviet/Anglo-French relations improve more.
At that point, if the Soviets, British and French contain the Germans and we avoid WW2, then we could see colder Soviet/Western relations.
So long story short, with Trotsky in the top job, things will go up and down depending on circumstances.
P.S. This assumes the Soviet Union industrialization speed on par with the OTL. I doubt this though. The industrialization rate of Stalin`s Soviet Union was astonishing, therefore any deviations from OTL are likely to reduce Soviet Union military potential.
IMO a non-Stalin led USSR of any flavor would develop at least as fast if not faster than OTL's Soviet Union.
Saying "what was achieved in OTL was amazing THEREFORE doing things differently is most likely to make things less amazing" is well, some kind of logical fallacy. I am afraid I am not a good enough debater to thing of the fancy Latin name for this sort of thing.
fasquardon