I probably would not still try to go out with the person who chose another over me even if he were single again. Once I realize a guy isn't interested in me, I move on and don't look back. Maybe this is inflexible and rigid, but it's just what I've always done to help deal with breakups or relationship disappointments. It's a very conscious decision, but it helps soften whatever ego bruising I might feel.
Maybe it's a pride thing or maybe not, but either way, there are so many people out there, I never felt the need to hang on to the thought of any one person.
I also don't think we're all second place prizes. Y was not dating multiple women while he was dating me so how can I feel like his second choice? Maybe he's had heartbreak before me, but I'm pretty sure I am the girl he'd choose over any he's been with before.