This technique is used when parties want the value of an independent opinion based on each side's best arguments but not the risk of getting a bad decision. In negotiation, the disputing parties talk directly to each other to try to reach an agreement. When it is successful, negotiation is usually the most efficient way of resolving a dispute because there is no cost or delay associated with the intervention of a third party. But if parties have trouble dealing with one another, negotiation may not work unless they hire agents, lawyers or other representatives to negotiate for them. The conciliator's aim is not so much to resolve the dispute as to merely reduce tensions and get the parties talking.
Parents often play the role of conciliator when their children are fighting.
I'm sure you two can work this out. Fact-finding is most often used in labor disputes, although the process can easily be adapted to more general types of disputes. For example, if a construction dispute concerns a collapsed roof, the parties might agree to hire a physical engineer to examine the roof and report on what caused the collapse. The parties would then use the report to further their own negotiations. The neutral advisor gives an advisory opinion to the executives, who then meet privately to negotiate a settlement based on what they've heard.