I suppose the former Soviet states turned EU member states are generally excluded from this as their standard of living has reached a sufficient level post-Soviet, but as someone with many friends and acquaintances from countries like Russia, Ukraine, Kazakhstan, I have heard this being expressed countless times from people old enough to remember living in the USSR.
For large groups of people, is it accurate to say that their living conditions were in fact objectively better under the USSR? Can we settle this with facts and figures? Or is it merely a case of nostalgia, remembering things being cleaner, more efficient, safer than they actually were? Or was it perhaps that the conditions were as bad, the difference being that the citizens of the USSR felt a greater purpose and belonging, and thus were more content even amid poorer standards of living?
There would be a number of factors, but I would argue that it is part nostalgia, and partly just a contrast to how difficult the 1990s (the decade after the dissolution of the Soviet Union) was for pretty much all former Soviet states.
Armenia, Azerbaijan, Georgia, Moldova, Russia (in Chechnya), and Tajikistan all dealt with conflicts (all internal issues, except for Armenia, who was fighting Azerbaijan on de jure Azerbaijani territory). Conflict was not something the Soviet Union had seen since the Second World War in 1945, and for most of these territories they had not seen conflict since even earlier, during the Russian Revolution (1917-23). So most people alive had not dealt with war and all that entails, especially civil conflicts, which often have a particular brand of brutality. Then there was the rise of criminal enterprise (loosely termed mafias), and the issues that stemmed from that: people being extorted, assaulted, and outright murdered.
There was also the economic issue: people went from living their lives in a command economy to a capitalist one almost overnight, and the shock to the system was immense. Rampant inflation, even more severe shortages of food and other supplies (recall that the Soviet Union of the 1980s was already known for queues to get some foods; the 1990s were worse). Unemployment became an issue, when it previously had never been something to worry about (and was indeed illegal in the USSR). Social services were severely cup off, so pensions and the like were greatly reduced.
Politics was also a big issue. As mentioned, several countries had (largely internal) conflicts, but the political situation was not smooth by any means. In some regions (Kazakhstan, Turkmenistan, Uzbekistan) the Communist First Secretary (the de facto leader of the republic) simply assumed the title of President (for life in the case of the latter two; Kazakhstan's inaugural president resigned in 2019 but is still seen as the de facto leader), while most other states had former Communist officials take over (which is logical, as they were the only "politicians" around). But in a lot of cases nationalism became a major issue for leaders: Georgia's first president was overthrown due to his overt, pro-Georgian nationalism (despite Georgia having about 35% ethnic minorities), for example.
Boris Yeltsin, the president of Russia, famously never got along with the Congress of People's Deputies (the Russian parliament, full of former Communists), and literally had their building (the White House) shelled by tanks in 1994, and went through Prime Ministers more frequently than Italy (many lasted less than a year). He also faced severe health issues (as well as a major drinking problem), and it's been speculated that for large stretches he wasn't even coherent enough to make decisions; instead his daughter and son-in-law took over for him.
Lastly there was probably some nostalgia for sure: while part of the Soviet Union, one was a citizen of one of the two global superpowers, one of nearly 300 million people in a state that stretched across 12 time zones and had tens of thousands of nuclear weapons, controlled Eastern Europe and "advised" states across Africa, Latin America, and Asia. Soviet culture and science were respected, while Soviet athletes dominated at the Olympics and various World Championships. But when those citizens woke up and found themselves citizens of a new country like Kazakhstan, Moldova, or Belarus (none of which had ever really existed before), or even those who were in Russia, it was a big change. You're country was small, poor, and globally insignificant. No one feared the Kazakhstani military, or cared about Moldovan sports teams. Most of these countries could barely control their own borders, let alone project power outside of it, and while Russia took control of the nuclear arsenal, the only fear about that was if the Russian government could properly secure them and ensure rogue actors didn't get any.
So it would have been a lot of factors that led to people saying "things were better during the USSR", and while things did start to improve as these countries developed, it still would leave some disillusioned with how things ended up.
Edit: I striked out the note about new states and a past association with older states; as comments below note, there are some connections that I wasn't initially thinking of, and as my point was not to contest the legitimacy of any post-Soviet state, and it is detracting from the main point I was trying to make, I will ask that it be disregarded here. Thanks for those who brought it up.
I want to thank you for asking this question, as it motivated me to stop being a lurker and write my first answer for /r/AskHistorians! I'm usually quite shy about my English skills, but the fact that your question is directly related to my PhD thesis (WIP) gave me some confidence to write an answer here and to try and meet the high standard of the subreddit.
Certainly a very important reason for the rise of nostalgia for USSR was how brutal economically 90's were for Russia and many other post-Soviet states. However, it is quite well covered in /u/kaiser_matias's excellent answer, so I won't repeat it here. Instead, I'll try to fill in some details they haven't covered - so I'd recommend to read their answer first.
It might come as interesting to you that recently (20th century) a whole new academic field emerged trying to answer questions just like yours. The field's name is memory studies. What differentiates it from history - which focuses on seeking objectivity, and determining facts based historical sources - is its focus on memory. Memory, meaning how people remember the past and how it influences the present. [1] The field is quite interdisciplinary, bordering history, sociology and psychology - in fact, it was French sociologist Maurice Halbwachs who in 1925 coined the term mémoire collective (collective memory) in his book Les Cadres Sociaux de la Memoire - attempting to tackle the problem how individual memories of members of the group create something greater than sum of its parts and how it can shape the group's identity. [2]
As memory, either collective or individual, is inherently subjective, I'd argue that you can't "settle" a question about memory with facts and figures. As you noted, memories are very prone to nostalgia and outside influences. One's efforts are better spent on investigating how particular group memories were shaped and what factors led to their creation.
I find the field of memory studies fascinating because so many political actions and movements today can be explained or understood better by taking into context the collective memory of different social groups. The very same historical events can be viewed differently by different groups - with trauma, nostalgia, pride. Even the events or historical figures most widely regarded as traumatic or villainous can have groups having a nostalgic memory of them.
One of my favorite examples of this is the state-owned Joseph Stalin Museum in Gori, Georgia, Joseph Stalin's hometown. Contrary to most world's museums' exhibitions about Stalin, Gori's museum doesn't mention his role in the brutal political repressions during his rule in USSR, how his method to revolutionize Soviet agriculture via collectivization resulted in a famine and millions starved, nor does it say anything about the Molotov-Ribbentrop pact and his strategical failures in the first half of the Second World War. Quite the opposite - Joseph Stalin is glorified throughout the exhibition, shown as a hero of the people, a splendid, capable leader, almost a mythological being and a reason of pride for Georgians. [3]
The exhibition's contents are almost unchanged in the present day since the museum's reopening in 1955. One could try to argue that the Gori's Stalin's museum-temple's exhibition contents are preserved for their informational value, showing how propaganda warped reality in the Soviet times. However, the fact that as recently as 2012, Gori's municipality restored previously taken down Stalin's monument on the city's central square due to citizens' petition or parades dedicated to Stalin's memory make this interpretation quite doubtful. It is rather obvious that Stalin in Gori is remembered with fondness, not hate or fear.
And it's not only Stalin's tiny hometown showing us that nostalgia and pride of the USSR's "great leader" is still alive. According to Yuri Levada Analytical Center's 2018 published research [4], the development of Russian's public opinion towards Stalin in the 21st century can be separated into three periods: mostly negative associations with Stalin (2001-2006), mostly indifferent (2008-2012) and mostly positive associations with the historical figure of Joseph Stalin after Russian Federation's invasion of Crimea (2014-2018). This coincided with the increase of imperial political narrative in Russian mass media, despite Vladimir Putin never publicly condemning nor approving Stalin's rule directly.
But pride/nostalgia for great leadership and being seen as a powerful country across the world are not the only reasons why the communist times might be viewed as "better" by older people. In fact, nostalgia for the communist times isn't even limited to post-USSR states - you'll find plenty of it even in Eastern Bloc countries, such as Poland and Germany. In a truly German manner, there is even a word for it: Ostalgie, meaning nostalgia for Communist East Germany. In these cases, however, the positive memory tends to center around nostalgia for the everyday life - music, movies, more "predictable" life. [5]
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