What would make me accept the existence of a deity?

[Angrboda]

The survey finds that constant movement characterizes the American religious marketplace, as every major religious group is simultaneously gaining and losing adherents. Those that are growing as a result of religious change are simply gaining new members at a faster rate than they are losing members. Conversely, those that are declining in number because of religious change simply are not attracting enough new members to offset the number of adherents who are leaving those particular faiths.

To illustrate this point, one need only look at the biggest gainer in this religious competition - the unaffiliated group. People moving into the unaffiliated category outnumber those moving out of the unaffiliated group by more than a three-to-one margin. At the same time, however, a substantial number of people (nearly 4% of the overall adult population) say that as children they were unaffiliated with any particular religion but have since come to identify with a religious group. This means that more than half of people who were unaffiliated with any particular religion as a child now say that they are associated with a religious group. In short, the Landscape Survey shows that the unaffiliated population has grown despite having one of the lowest retention rates of all "religious" groups.

Statististics On Religion In America Report: Pew Forum On Religion and Public Life

It's not clear how many of these were self-identified atheists or agnostics, as opposed to those with "no particular belief" as both groups are counted in the unaffiliated population. Moreover, in Katherine Stewart's book The Good News Club, she quotes that most religious conversions occur between the ages of 4 and 14. I would want to exclude minors from the group for the obvious reason that volatility in their religious beliefs is likely just an effect of the maturation process.

I wasn't referring to abnormal processes or "flaws" leading to religious conversion, but rather to ordinary, everyday psychological processes. I think you completely misunderstood my point, likely due to gross ignorance of human psychology. It doesn't take an unusual event to convert an atheist to a theist. (Reading briefly the story of atheist blogger turned Catholic, Leah Libresco, it didn't take any extraordinary experience at all; her conversion was motivated by a dissatisfaction with atheist accounts of morality, which is a theme I see debated here at AF. And it doesn't take a god descending on fiery wings to overwhelm the human capacity for reason; conversion "experiences" are almost manufactured to order by religious proselytizers with revivals and the like. And the ways in which attachment to a family member or spouse can change one's thinking are pretty obvious.)