impartial; equitable: evenhanded justice.

1595–1605; even + handed

evenhandedly, adverb
evenhandedness, noun
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Example sentences
But journalists are apt to be less strident and more evenhanded than many of
  the people they quote.
It's all conveyed with an evenhanded, often affectionate tone.
Her naive, proudly open-minded and evenhanded listener wants to know why the
  vehemence, if not murderous venom.
The author does not claim to offer an evenhanded account.
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