How can bias harm negotiators at the bargaining table?

Negotiations should be done in good faith. Being biased is the worst thing a negotiator can do. A biased negotiator can not be expected to do the full justice either to the procurement / project or the very process of negotiation. Negotiator being biased is like defeating the very purpose of negotiation. 

This is an interesting proposition. Bias is rebuffed in legal terms as a Judge, Adjudicator or anyother legal referree is required to be unbiased in his findings, as a predisposition will prejudice his findings and be unfair. Bias in relation to a person or groups culture, ethnicity or any belief is prejudical and unfair, therefore has no place in negotiations. My view is negotiation should be robust, defending your position and putting your case; but should not be personal.

However, we inadvertantly use bias to influence outcomes. Examples of this are starting with a demand at the extreme end of scale in order to influence our opponents thinking, the selective use of facts or statistics to support our claim and early offers that influence acceptance and outcome. 

Bias has it place in negotiations, but use it with care.

Bias will result in prolonged negotiations without reaching an agreement. or an agreement will be reached but it will not be fair.

Mr. Keith has covered the answer quite well.

I'm sorry not understanding what do you mean by Bias, But Practically Bias (in its Positive Meaning) is present through every Negotiations Processes where it's Constructive if Positively Directed, May be Harmful in Case of Conflict Resolution Negotiation

Legal Meaning )Negative or Destructive Meaning ) of Bias is forbidden for Sure 

Thanks for invitation,

The good negotiator has to be always neutral and considering the "Win to Win' situation, but if he insist for only a "Win to Lose"  situation he will not be able to achieve his objectives form any negotiation.

Thanks

From the basics of negotiation, is a neutrality, and  the purpose of negotiation is to reach the base of Everyone is a winner, and when  negotiator  being biased, so there will be a loss for one of parties, so negotiator should be a neutral negotiator to be all   parties winners.