What Do They Want

 Liberals and Conservatives, both, seem to want a "fair" society.

The question then is, how is "fair" defined, what is meant by "fair", what does one see when a situation is "fair".

Generally, it seems that Liberals fairness consists of equal access and equal justice so that wealth or political power are not factors in deciding a dispute.  In other words, there is a structure of government and laws in which disputes operate and is defined by equality and collective justice.  By analogy, Liberal fairness consists of two baseball teams of approximately equal strength, competing within the rules of baseball.

For Conservatives, fairness consists of individuals freely disputing between each other, without the interference of third parties such as the law or government rules or institutions. By analogy, Conservatives would resolve a dispute as a boxing match with no limits and no rules, so that a large strong trained person fighting a small weak untrained person would be considered fair.  If rules are involved, then the fact that those rules favor one contestant over the other is fair, so long as the rules are followed.  For example, both contestants can have lawyers, but one side has experienced well-resourced lawyers and the other party has a poorly trained lawyer fresh out of law school.  Since both parties have lawyers, then the contest is fair.