In such periods people in the ruling class follow the principle "Après nous le déluge" and each thinks only of himself, abandoning the public good to the mercy of blind chance.

What is the meaning of "Après nous le déluge"? Thanks

It's a famous French sentence; allegedly, this was said by Madame De Pompadour (King's Louis XIV's mistress) to her lover to comfort him after France was soundly defeated in a battle.

Its literal meaning is something like "After us, the deluge" (if you need a definition for "deluge" go here or think of Noah's deluge): she meant that everything would get worse after the reign of Louis's, but she wouldn't care about what was going to happen to French people.
Similarly, in your sentence the ruling class doesn't care about the public good.

Well, at least this is the way this sentence is used in Italian. Emotion: smile
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Thanks Tanit a lot.
Some fact checking is in order. The phrase in French attributed to both Louis XV and his wife, Madame de Pompadour, is "Après moi le deluge" and it foreshadowed the future of the Republic after Louis - meaning the chaos of the French Revolution.
Not after me (moi) but the royal plural us (nous).
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