Inequality in London | Socyberty
11 Mar 2009 ... Immediately, the prince becomes the pauper and people treat him as such, ... Although discrimination seems worse back then, it still affects us today. ... Living conditions between the royalties and the lower classes ...
socyberty.com/history/inequality-in-london/ - Cached

What price loyalty? -- Phillips 4 (12): 845 -- Journal of ...
by J Phillips - 2009
It is difficult to draw parallels between the iPod and Google from which one can ... is always available without discrimination to prince and pauper alike; ...
jiplp.oxfordjournals.org/cgi/content/full/4/12/845

It is better to say this than "prince and pauper", which would ring as a very literary reference. Of course it depends upon the text you are translating, but your quote looks more political than literary. The term I am suggesting makes an allusion to Anatole France: " la majestueuse égalité des lois, qui interdit au riche comme au pauvre de coucher sous les ponts, de mendier dans les rues et de voler du pain."

Usually translated as "the law in its majestic equality forbids the rich and poor alike from sleeping under bridges, begging in the streets, and stealing bread."

There is no exact equivalent idiom in English, unless you wish to acknowledge this as one.

So here is a tentative translation for your phrase

تقوم على مبدأ المواطنة، وعلى المساواة بين المواطنين أمام القانون دون تمييز بين وزير وخفير

based upon the principle of citizenship and the equality before the law of all citizens, rich and poor alike

Indiscriminately, thrown together, not kept apart or divided, arbitrarily, at random, every which way, haphazardly, randomly