This is very common, and seen when each negotiator arbitrarily picks a “mid-point.” It is a request for a concession “halfway” to facilitate closing. It should be disfavored as it is arbitrary, and often does not meet the requirements of the negotiators. Despite this, it is so enmeshed into the American negotiation dynamic that many people do it automatically thinking it is logical or a good relationship builder.
Consider this garage sale example: “You want $150, but I want to pay $50. Let’s split the difference and I’ll give you $100."
You may choose to accept only the full price, which is a legitimate counter. If there is room to negotiate, the solution is to focus on value. Who gets to define “halfway” makes all the difference, and halfway may leave you short. If an objective value or walk-away number is not known, splitting the split is an acceptable counter. In the above negotiation, the seller would counter with $125, or better yet for the seller, splitting the split of the split with $137.50. If the buyer wants the item badly, the smaller concessions in price will be effective.