12:00 Jan 12 

Fine, you’re right in general, but the shorter and more abstract word “objectivity” seems to be fitting better among other –ty, - ness, - y-words , such as “isonomy, “adversariality” (OMG!), due process, etc.

11:43 Jan 12 

observados os princípios da isonomia, da impessoalidade, da publicidade, da probidade, da vinculação ao instrumento convocatório, da ampla competição e do julgamento objetivo.

observed the principles of equality, impersonality, publicity, honesty, entailment to the call notice, full competition and objective judgment.
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aspiram a empregos de alto nível, se você não pode tomar a enormes responsabilidades e, especialmente, se você não pode ter um direito e julgamento objetivo.

In consequence, it's best not to aspire at high level jobs if you cannot take the enormous responsibilities and, especially, if you cannot have a right and objective judgement.
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Re: redundant
214,000 results in Google for this expression seems to me that it's quite a common term in the EN speaking world and not just a literal translation

11:13 Jan 12 

"Judgment" seems to be redundant in EN (and unnecessarily alluding to “judgmental”, to boot, which is quite the opposite of what we want to convey here), and "objectivity" fits in better next to the other abstract nouns ending with -ity / or -ness
PS. I wonder what the Asker is going to do with “competitividade?” I’d consider running with “adversarial” (nature/principle/system) rather than “competitiveness,” nao e'?