Damn, my browser crashed! Lost a whole post. Let's see if a second draft from memory is any better, hopefully shorter

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The OP does not specify that the surviving Russian union actually be the USSR or in any way retain Communism in any form. Nevertheless I argue that it would pretty much have to. If you take away the ideological Bolshevik legacy of an internationalist socialist regime with a mission to blaze a new trail economically and socially, what alternative reason other than naked Great Russian imperialism would there be for this vast multinational union to exist?
In the previous version of this post, I granted a lot of reasons to admit that both strands of this Leninist ideology--a new and superior socioeconomic order and the universal fraternity of all working people--were honored more in the breach than the observance in the USSR. Still I think they were effective factors holding the Soviet Union together, as much in the hope of someday and gradually making good on these grand promises as in actual progress achieved toward the goal. Toss out the CPSU and you toss out the Soviet Union itself, and then what alternative organizing principle can hold the territory together?
Because Soviet economic progress did slow, and then stagnate and even in some respects reverse in the 1970s and '80s, the regime had to rely on propaganda in several layers. First of all, deny their people contact with Westerners or direct experience of the West that might gainsay claims they were doing well relatively--this became harder and harder as the USSR strived for more of a role in the larger world, meaning more and more Soviet citizens would have knowledge and even contact of realities in the West. Second, put ideological spin on what disturbing knowledge did leak through. I won't attempt to recraft what I wrote on that subject before. Bottom line--there were grains of truth in Communist criticisms of Western society, and it was a fact that Russia had started out from a much lower point and was devastated by two world wars, so when Communists urged fellow citizens (and themselves) to bear that in mind and measure Soviet success by their own rate of progress rather than by direct comparison with the wealth Western Europeans and Americans might seem to enjoy, that had some resonance. But a lot less when, in the later Brezhnev years and after, that rate of progress visibly slowed while lots of chickens--notably environmental crises--came home to roost.
Under those conditions, Gorbachev's decisions favoring
glasnost were very risky; he could dare to undertake to tolerate greater "transparency" only because he could argue that it was necessary to achieve economic and social reform, and by the late 1980s no one in the regime could make a strong credible argument to gainsay him. Unfortunately for him, effective reforms in production, distribution, and social justice were slow in coming (if any progress was being made at all, it wasn't dramatically visible) whereas opening the floodgates of greater freedom of travel, freedom of speech, and as Yakov Smirnov put it (from his status as a refugee immigrant comedian in the USA in the 1980s) "freedom
after you speak", unleashed a lot of harsh criticism and unflattering comparisons with the West that too many Soviet citizens knew were basically accurate. This is what doomed Communism in Russia.
So--given the economic mess the Soviet system was in by say 1985, the regime of the Party was on its last legs. But no Party, no Soviet Union. No
Soviet Union, and the only other way a single regime with its capital in Moscow could retain control of all, or even most, of the former Soviet territory would be by naked imperialism--under what banner, exactly? Great Russian nationalism, quite ruthlessly grinding down Ukrainians, Belarussians, Moldovians, Central Asians of various nationalities, etc? The Orthodox Church? (Again, largely a Great Russian thing, and hardly in a position in 1990 to rule even there--even some kind of ecumenical union of eastern churches could not reach many of the former Soviet citizens.) What?
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This is why my own modest proposal is, the USSR (or any union of that territory) could only survive if the Communists had somehow or other made their system more of an economic success. Most suggestions I have seen toward that end on this site, in just about any thread, run along the lines of moderating or abandoning state-centralized socialism. But if they did that, even if they could, it would again hardly be a Union of Soviet
Socialist Republics, now would it. More to the point, abandoning the ideological commitment to a post-capitalist economy that does deliver the goods on the basis of a fair, egalitarian distribution of the collective product of society to everyone again undermines the commitment to Leninism itself, and thus to the premise on which the Union was united. Mind, I don't deny that if the Central Committee turned into a bunch of capitalist entrepreneurs overnight
and they delivered the goods to the Soviet peoples, creating ample work opportunities with decent pay that allowed them to buy actual goods in actual markets, they could still go on pretending to be more or less Marxist-Leninist and no one would want to argue with them much. Still I think that's at least as ASB, if not more so, than imagining they could make the socialist command economy work well. The reality of reforms in a capitalist direction would surely IMHO be that a few would profit, many would lose, probably the overall economic output and share of that available to the regime would fall, and Soviet society, bereft of a key legitimizing link, would fly apart in some fashion.
So--I propose that in order to preserve this vast state, probably some POD is needed to make a Marxist-Leninist command economy work better for its people, the way Lenin promised it would. I agree with Cook that you have to go back at least to the time of Khrushchev if not before, and turn left instead of right at Albuquerque or some such thing. And this is not easy--the Soviet Communists were not complete idiots after all, and if they did not take this or that path it was probably because there were reasons why it would have been risky or difficult.
In the 1970s, the Brezhnev economy looked sound enough from the Soviet point of view. Progress, in the sense of more goods of somewhat better quality becoming more available to more citizens, was still happening. Progress as the regime chose to measure it, in terms of vast, grandiose, new enterprises being built and starting to operate, also appeared to be going along swimmingly.
But I've seen it argued--by people other than mere dogmatic naysayers of the possibility of any kind of progressive socialism, who of course always chime in in abundance--that actually long before then, the USSR was already on a doomed path. One person whom I take seriously is Stephen Kotkin, whose
Magnetic Mountain was a major text in a course on Soviet society I took about seven years ago. Looking at the list of his publications I don't immediately recognize the one I was reading (extracurricularly) back then; possibly it was
Political Corruption in Transition: A Sceptic's Handbook (Central European University Press, 2002). Anyway he argued that if were not for the use-value and then market-value in the West of the various Soviet oil fields, the regime would have surely hit a fatal crisis by the mid-1960s at the latest. I'm not sure I believe it was that bad, though honestly reading other materials on the on-the-ground nature of Soviet society from the Stalin years right up to 1990 I can't dismiss the argument and coming from Kotkin I take it pretty seriously.
(I really should also get around to reading a number of books he has published since I took that class).
So if people like Kotkin are right, they took their wrong turning--if a right one was ever available to them--long ago indeed, and getting out of the corner they were in would have required fancy footwork if anything could work at all.
As I've indicated, I am partial to alternatives that would take them farther leftward, or at any rate in some untried direction, rather than suggestions that they simply should have given up on socialism and done what people like Trotsky and George Orwell accused them of doing--cynically re-inventing capitalism on a harsher basis. I doubt that if the Bolsheviks had ever made that cynical decision and implemented it successfully, they'd have found much of a welcome on the global capitalist markets, nor would doing it successfully be much easier than trying to make socialism work on its own terms.
But to try and propose a specific POD I'd have to propose a specific socialist reform, one with better prospects of success than any of the dozens various Soviet leaders did try to implement at various times, and do it from my ignorance in this armchair whereas they were fighting for their lives in the real world with vast resources available to them to try and flesh out the nuts and bolts.
Just pulling a POD wildly out of the air--Stalin dies in mid-1945, if you like the same day and same way as FDR. This is hardly a surefire guarantee that things would shake down in the post-Stalinist regime so as to favor new thinking that is both idealistic and focused on success, but it just might. In terms of the Soviet regime's own yardsticks and apparent success as a world power, Stalin did not do so badly over the next (last) 9 years of his life, and to my surprise in a class on Stalin I found that he was not quite the ignoramus on Marxist theory I had been taking him for. He had a seriously distorted and not particularly humane view of what socialism and communism entailed, but on his own terms he was quite a serious Leninist. His successors might well have dropped the ball in a number of ways--when Stalin did die OTL, in 1954, police chief Lavrenti Beria let it be known he thought the whole Communist Party structure was obsolete and irrelevant and should be jettisoned, and the current bosses should simply rule in a state dictatorship based on the Soviet government ministries, with no pretense of being Communists. I believe it was as much for this heresy as because he was a deadly threat that a troika of conspirators (Molotov, Malenkov, and Khruschchev) ousted him and had him killed after a summary show trial. Others, without so openly discarding the premise on which they supposedly ruled, might have muddled along cynically and failed to keep Soviet society together; others may have gone down misguided left-wing paths and led to ruin that way. One could do far worse than OTL, after all!
But if I want a hope they might do
better, this I suspect is possibly the latest POD.
It is not inconceivable to me that Khruschchev might have found some correct bearing in the early Sixties, somehow weathered the crisis of confidence he brought on himself with the Cuban missile crisis, and sobered by that experience grown into a truly first-rate global statesman, steering the Soviet and Warsaw-bloc economies into a more sustainable system while earning respect abroad. Maybe; I like the man enough to wish so. But while he was hardly overshadowed in intellect or vision by any of his Kremlin contemporaries he was hardly infallible either; his faults were legion.
That, I agree with Cook, was the last gasp. Without effective and deep reform of some kind--I say, on a more socialist basis--by the mid-60s, the stagnation and collapse of the Communist party regime, and with it the USSR as a whole and the prospect of holding that territory under any pretext was foredoomed. Perhaps the crises of 1990 might have been averted for a while, but the alternative to it collapsing as ignomiously as it did OTL would have been the scenario Western hardliners always assumed would be the endgame--last-ditch Soviet hardliners would refuse to see the writing on the wall, crack down Stalin-style, and given the limited and failing prospects of the economic side of the regime, which this clampdown could only worsen, the upshot would be the regime falling with a bang rather than a whimper--very likely, the bang of a global nuclear war.
