Hint #8

Spoiler: This will reveal the first three steps of the solution.

Applying the algorithm in Hint #7:

Start by ordering the men. In this example we will use the default order presented in the game, but if you order them closest to what you think the correct order will be, it makes the algorithm go much faster. The closer your guess to the correct solution, the fewer steps you will need.
The default order is:

Blake (Sleazy)
Richard (Married)
Gilbert (Fat)
Broderick (Handsome)
Ralph (Old)
Jaxon (Young)
Caleb (Womanizer)
Albert (Smart)
Joey (Dumb)
Andre (Hung)

Select Andre (Hung): The last available guy on the list, guaranteed to not have sex.
Select Blake (Sleazy): No sex. Not the next guy, so back up one guy.
Select Richard (Married): No sex. Not the next guy, so back up one guy.
Select Gilbert (Fat): No sex. Not the next guy, so back up one guy.
Select Broderick (Handsome): Sex! This is the next guy, so back up two guys.

We now know that Broderick (Handsome) is the first guy in order!
Select Broderick (Handsome)
Now to find the second guy.

Select Andre (Hung): The last available guy on the list, guaranteed to not have sex.
Select Blake (Sleazy): No sex. Not the next guy, so back up one guy.
Select Richard (Married): No sex. Not the next guy, so back up one guy.
Select Gilbert (Fat): No sex. Not the next guy, so back up one guy.
Select Ralph (Old): No sex. Not the next guy, so back up one guy.
Select Jaxon (Young): No sex. Not the next guy, so back up one guy.
Select Caleb (Womanizer): Sex! This is the next guy, so back up two guys.

We now know that Caleb (Womanizer) is the second guy in order!
Select Caleb (Womanizer)
Now to find the third guy.

Select Andre (Hung): The last available guy on the list, guaranteed to not have sex.
Select Blake (Sleazy): No sex. Not the next guy, so back up one guy.
Select Richard (Married): No sex. Not the next guy, so back up one guy.
Select Gilbert (Fat): No sex. Not the next guy, so back up one guy.
Select Ralph (Old): No sex. Not the next guy, so back up one guy.
Select Jaxon (Young): No sex. Not the next guy, so back up one guy.
Select Albert (Smart): No sex. Not the next guy, so back up one guy.
Select Joey (Dumb): No sex. Not the next guy, so back up one guy.

We have finished all the guys with none of them having sex, that means the starting guy, Andre (Hung), was the correct one. We don’t need to do any more backing up as he is already selected.
We now know that Andre (Hung) is the third guy in order!
We have now found the first three guys in the order, Broderick, Caleb, then Andre, and it only get easier from here. If you order the men in the closest you think to the solution instead of this default order, this algorithm will go even faster, probably just one, two, or three tries each!

Keep applying this algorithm until you have found everyone!

This is just one way I thought of to solve this, please send me a message on how you solved it (no spoilers in the comments please), maybe you found a more efficient way than mine!