It appears that approaching in dating situations makes an individuals less selective of their potential mate relative to if the potential mate had approached them. The effect worked regardless of gender in the experiment.
"Finkel & Eastwick (2009) set about to answer just that question with an experiment designed to test whether a potential partner’s “choosiness” was due in part to whether they were the ones doing the choosing or not. They corralled 350 college students into 15 speed dating events for their study. Participants went on 4 minute “speed dates” with approximately 12 opposite-sex individuals during each event. After each date, participants rated their romantic desire and romantic chemistry for that partner, as well as how much self-confidence they felt that had on that particular “date.”
The researchers found that the speed daters who approached their partners relative to those who stayed sitting would experience a greater romantic desire and chemistry toward their partners, and were more likely to respond “Yes, I would see this person again” to their partners. In other words, the people who rotated from person to person were less selective than those sitting, regardless of which gender was doing the rotating.
When men rotated, women (the ones sitting) were more selective. But when women did the rotating, men (the ones sitting) were more selective. Nothing else changed in the experiment, so it was the act of doing the approaching (or being approached) that helped determine a person’s selectivity toward their partner."