The short answer to this is “YOU CAN’T”
The idea of objectivity is one of those theoretical positions that we aspire to but in reality rarely achieve. We picture ourselves as the Minerva holding the scales of justice and blindly adminsitering some objective standard but in reality “WE LEAK”. Social psychologists will tell you that we cannot but reveal the motives, emotions, biases that we carry.
Damage is done when managers convince themselves that they are objective and they end up using this as a mechanism to hide form their own biases. We cant help it we are human. So dont look for complete objectivity, start by understanding and accepting your biases. THis self awareness and self knowledge will help you as you attempt to mediate conflicts oin your organisation. You can begin with our Online Conflict Profile.