Sure.
Under the current system you don't actually get complete information. You know who dropped off. You don't know how the others did. In the U.K., they actually will know how many votes each person got. It's very much like a leadership race under the old-fashioned convention system.
I personally think this is a virtue of the system. It prevents strategic voting. It more or less forces each person to rank the candidates based on their own assessment of the merits of each candidate, whatever those might be. That aspect is a feature rather than a failing of the system I'm proposing.