At the dojo I train at, like most Shodokan dojos, we dont actually choose our training partners. We line up on either side of the dojo, and when its time to change partner (usually after each technique) the line moves around, and our new partner is the next person in line.
It would probably seem strange to someone visiting from an Aikikai dojo, maybe even a bit regimented.
What I like about it, though, is that everyone trains with everyone. It isn't possible for anyone to stick with their favourite partner or to avoid their least favourite.