I'm a fan of cyclical theories, but in a different way
(I don't see it as constant direct parallels but more rather much more complex). I think you may be looking for parallels and patterns in the wrong places. Because of our two party system and human nature, American politics tends to swing back and forth between the parties over generations. During rise and fall from dominance, the steps taken to get there are not always the same. For instance, you could say Bill Clinton and Eisenhower are parallels - They both came after troubled presidencies and won in landslides, were both moderate and both "reinforced" the dominant political view
(Eisenhower => New Deal, Clinton => Conservatism).. HOWEVER, this doesn't mean every cycle has the same parallel. It just happened to work out that way. Each party and their ideology go through cycles, which means a rise and a fall, and inevitably you will see similar events taking place in both the rise and fall.
Hoover-Carter: Both of these politically moderate presidents are considered failures, and because of them an era of liberalism/conservatism occurs.
Hoover / Republicans really lucked out with the Great Depression which immediately ended an
long era of Republican dominance, whereas Carter simply presided over an electorate who had already begun shifting towards Republicans many years prior. So you could say Hoover ushered in the New Deal era, but only by virtue of him being the guy in charge when all hell broke loose.
FDR-Reagan: Both of these presidents considered heroes of the left/right. They ushered an era of liberalism/conservatism, and also "defeated" foreign enemies of the far-right (Nazi Germany), and the far-left (Soviet Union).
This is a fair comparison, but I would argue that had Reagan not come along, it probably would have been someone else
(albeit with varying levels of success and lasting strength, obviously)Eisenhower-Clinton: These two politically moderate presidents presided over huge economic prosperity and peace. This comparison works the best IMO. The 50's and the 90's are both very similar decades.
If you ask me, both these presidents jumpstarted each of their respective party's after years of stinging losses at the presidential level (and downballot for Rs in FDR era). Studies have shown for some time now that people who grew up (18 - 25/27-ish) under well-liked and influential presidents leaned towards that president's party for most, if not all of their lives, and people who grew up under extremely disliked presidents leaned towards the opposition party most of their lives. People who grew under FDR leaned Democratic their entire lives, quite a lot of people who grew up under Nixon continue to lean Democratic to this day, and Reaganites lean Republican and their aging (and thus voting more in midterms) is what is powering the Republican dominance in midterm elections right now.
People can hate on Bill all they want, but his success and overall luck at being the one to preside over that great economy gave Democrats a lifeline. Young adults who grew up under Bill have leaned strongly Democratic also to this day
(mostly 13 - 19 points more Democratic than the national average, whose numbers surpass Reagan's generation pretty strongly and in combination with the heavily Democratic effect from Bush/Obama's presidency has serious implications for Republicans in the near future)I do like this one.
Bernie Sanders is the Ronald Reagan in this hypothetical scenario. Reagan started a conservative revolution. Reagan narrowly lost the 1976 primaries to Ford. Bernie has started a liberal revolution. He is about to narrowly lose to Hillary in the 2016 primaries. If this cycle stays consistent, then Bernie should run in 2020 defeating President Donald Trump and ushering an era of liberalism.
I just don't see how Bernie would run again in 2020. He would be, what, 78 years old? I just don't see that happening. He may not even be able to physically and/or mentally by that time.
Before anyone starts complaining about this thread, I know that cyclical theories are pseudoscientific garbage. Cyclical theories are interesting to discuss, but shouldn't be taken seriously.
I think it really depends what you are discussing. Scenarios and parallels between different generations is kind of inaccurate/pointless, but there are underlying trends and reasons for those trends that show rising and falling party dominance, and they do tend to run in sometimes-lopsided cycles, but really only because of the 2 party system.