The diagram and claim would be convincing if it was true. Snopes found it to be "Mostly False": https://www.snopes.com/fact-check/the-f ... -republic/
Professor Joseph Olson of Hamline University was not the source of any of the statistics or the text attributed to him above. When contacted via e-mail, Professor Olson confirmed that he had no authorship or involvement in this matter, and as Fayette Citizen editor Dave Hamrick wrote in January 2001:
I really enjoyed one recent message that was circulated extremely widely, at least among conservatives. It gave several interesting “facts” supposedly compiled by statisticians and political scientists about the counties across the nation that voted for George Bush and the ones that voted for Al Gore in the recent election.
Supposedly, the people in the counties for Bush had more education, more income, ad infinitum, than the counties for Gore.
I didn’t have time to check them all out, but I was curious about one item in particular… the contention that the murder rate in the Gore counties was about a billion times higher than in the Bush counties.
This was attributed to a Professor Joseph Olson at the Hamline University School of Law. I never heard of such a university, but went online and found it. And Prof. Olson does exist.
“Now I’m getting somewhere,” I thought.
But in response to my e-mail, Olson said the “research” was attributed to him erroneously. He said it came from a Sheriff Jay Printz in Montana. I e-mailed< Sheriff Printz, and guess what? He didn't do the research either, and didn't remember who had e-mailed it to him.
In other words, he got the same legend e-mailed to him and passed it on to Olson without checking it out, and when Olson passed it on, someone thought it sounded better if a law professor had done the research, and so it grew.
Who knows where it originally came from, but it's just not true.
Nor was it necessarily Tytler's idea: https://www.lorencollins.net/tytler.html
I think the idea is a seductive, but confused, idea. If the cycle is going to claim the Greeks and Romans, the former fell due to disunity (hello America), the latter largely due to disease and overreach, nothing to do with their fragile democracies.
Given that actual democracies have only existed for about 400 years, and most societies have never embraced democracy, the claim is based on a tiny sample size.
That "Tytler Cycle" is a good example of post hoc rationalisation designed to serve political polemic, noting only that which accords with assumption, ignoring other factors. It also seems that you are blaming democracy for the problematic cycle of fiat currency, a factor ignored by the misnamed "Tytler Cycle".