At least three quarters of the sample surveyed attempted to date aspirationally, meaning they tried to initiate a relationship with someone who was more desirable, 25% more desirable, to be exact. Bruch recommended sending out more greeting messages, noting that people sometimes managed to upgrade their 'league'. Michael Rosenfeld, a sociologist not involved with the study, told "The Atlantic", "The idea that persistence pays off makes sense to me, as the online-dating world has a wider choice set of potential mates to choose from. The greater choice set pays dividends to people who are willing to be persistent in trying to find a mate." Using optimal stopping theory, one can show that the best way to select the best potential partner is to reject the first 37%, then pick the one who is better than the previous set. The probability of picking the best potential mate this way is 37%. (This is approximately the reciprocal of Euler's number, formula_1. See derivation of the optimal policy.) However, making online contact is only the first step, and indeed, most conversations failed to birth a relationship. As two potential partners interact more and more, the superficial information available from a dating website or smartphone application becomes less important than their characters. Bruch and Newman found that overall, white men and Asian women were the most desired in all the four cities.