What’s the English for “democrature”, a dictatorship pretending to be a democracy through fraudulent elections?

The term illiberal democracy, first used in an article by Fareed Zakaria, comes quite close to capturing the meaning of democrature

a governing system in which, although elections take place, citizens are cut off from knowledge about the activities of those who exercise real power because of the lack of civil liberties; thus it is not an open society.

With regards to elections

Elections in an illiberal democracy are often manipulated or rigged, being used to legitimize and consolidate the incumbent rather than to choose the country's leaders and policies.

While an illiberal democracy is not necessarily a dictatorship, it does have many of the same characteristics.

The word illiberal is used here in the meaning of

limiting freedom of expression, thought, behaviour, etc.

which ties into the definition above, of a government holding apparently free and fair elections, but not really, since the populace does not have the necessary information to cast an informed vote.

Naturally, nobody can prove the absence of a word from all dictionaries, if you mean that there has to be a word with the same ending as 'dictatorship' or 'legislature'.

But the answer is that there is no such word.

So the question is what word can be made up to do the same job as democratura in Italian and the cognate démocrature in French.

What is being talked about is a new (or seemingly new) idea: democratic forms retained to disguise what is really a dictatorship. Actually, it is not as new as you might think. But that is another story.

There is nothing wrong with using the equivalent English word, 'democrature'. Not least, many of the arguments about this modern phenomenon concern how it should be defined. So it would be a matter for political science and philosophy rather than for semantics and lexicography.

At the moment, if it is used, its first instance in a book or paper should be in 'scare quotes' to signal a neologism (or at least unfamiliar word), and carefully defined for the purpose of the paper itself, so that readers know what the author has in mind.

The term Potemkin democracy has been used in English for governments that would be called democratures in French.

The English phrase Potemkin democracy means a system of government which is designed to look like a democracy to the outside observer, but which is really not one. It's not anywhere near as common as démocrature is in French. (See Ngrams.)

Etymologically, this comes from the phrase Potemkin village, which Merriam-Webster defines as:

an impressive facade or show designed to hide an undesirable fact or condition,

and is named after Grigory Potemkin, who supposedly built show villages along the routes that Catherine the Great was scheduled to travel on.

Machine Politics (or, in Wikipedia "Political Machine")

This is a common enough term -- in old 1970's Chicago you could say "the machine" and it was understood you meant the system of fixing elections so the boss's choice always won. I found contemporary Stacey Abrams Is Building a New Kind of Political Machine in the Deep South. It describes a non-corrupt machine, which is why it's a new kind -- we know the usual kind of machine is anti-democratic.

But the phrase doesn't fit in terms of a dictatorship establishing a cover. "Machine" only makes sense when you start with a democracy. No one would say Stalin ran a machine -- he just made up the vote totals. A machine is a complex system of subverting an otherwise fair voting process.

Cargo cult democracy

More and more nations are becoming what can be described as “cargo cult” democracies. This is a nation ruled by an authoritarian government, which has come to power via electoral processes.

Such authoritarian governments maintain the forms of democracy, while ignoring the underlying principles, and corrupting the institutions which are supposed to prevent abuse.

This isn't a particularly common thing you will hear but the general idea is that cargo cults are groups where the rituals are more theatre than anything else. In other words the democracy part is a façade covering up more sinister things.

https://www.business-standard.com/article/opinion/cargo-cult-democracies-120080100036_1.html

According to the Swedish Wikipedia article for demokratur the corresponding English term is democratorship (something that is lead by a democrator).

Interestingly, according to the Wikipedia articles in languages I understand (German, Dutch, Swedish, Norwegian, French, Danish), the oldest usage of the word listed is a Swedish newspaper, 1938.

It's not a single word, but I would describe this as a hybrid regime.

Wikipedia describes it as

Hybrid regimes combine autocratic features with democratic ones and can simultaneously hold political repressions and regular elections.

I'm surprised no one has already mentioned the common English idiom banana republic.

Wikipedia says this term originally designated "a servile oligarchy that abets and supports, for kickbacks, the exploitation of large-scale plantation agriculture", however, I think the term in modern usage refers to any republic (or former republic) that is so dominated by corrupt money that its outward forms of democracy are just a facade on a self-serving ruling class. In the modern era, American fruit companies are not the major source of money in politics, but the same concept -- that major corporations dominate their national governments by strategic infusions of graft -- is alive and well.