Can You Date Two People At The Same Time Without Causing A Conflict?

Finding that special person you want to spend your life with is a process which requires spending time with a person, getting to know them and their habits, getting to know their friends and family and ultimately deciding yay or nay, this is the one or this isn't. The process of choosing a mate doesn't have to be painful or even lengthy, but it can be complicated when people choose to "try out" more than one person at a time. It creates a senario of competition, which may lead to two women or even two men , perceiving each other as enemies. Should a person who is striving to build a serious relationship be dating more than one person at a time? Can this be done openly and honestly without causing a conflict between the parties involved?  Can one person be ultimately chosen as "the one" without the other peson feeling as if they "lost the competition?"