Biasedness or biasness?

Neither. The correct word is "bias".

Example: He showed huge bias in his choice of actor.

Example: He was biased in his choice of actor.

I agree with Eimai_Anglos. You only need the word "bias".

I would consider "biasness" to be wrong in any situation. You might possibly be able to justify the use "biasedness" for reasons of style (e.g. parallel structure), but as a general rule I would recommend not using either one of those words.

Biased is an adjective. Bias is the noun. Neither biasedness nor biasness -- bias.

AnonymousBias is the noun

Exactly, Anon. And that's what makes adding -ness to the word bias so wrong. The suffix -ness is used to create nouns from adjectives and participles.

Biasness is actually okay.

http://www.morewords.com/word/biasness/
http://www.wordnik.com/words/biasness

I don't know how legitimate these sources are, though.

Biasedness doesn't exist.

Biasness is an obsolete word and is not used any more.

Wrong, biasedness is still very much used today.

AnonymousWrong, biasedness is still very much used today.

Where to you live?
I'm in the US and I have never heard or read the word "biasedness."
It's not in any of the 31 on-line English dictionaries.

I'm British and I have never heard or read the word "biasedness."