I allow a maximum of 3 sets, pick the best set. This usually results in characters with mixed +/- stats. I like characters to have some flaws and bumps rather than being Star Trek TNG perfect. Lol. Point buy to me is like RPG eugenics! :-)
It never occurred to me before why I don't like point buying character builds, but this hits the nail on the head. It's an old school attitude I'm sure, but point buy systems equate to genetic engineering, at least in my opinion. That is to say, it's a personal preference.
I have always used this method: roll 4d6 x 6, drop the lowest, with a maximum of 3 sets, chose the set you like and place scores as desired. Doing this right now produces:
Set 1
6, 2, 1, (1) = 9
6, 4, 3, (2) = 13
4, 3, 1, (1) = 8
5, 5, 4, (3) = 14
4, 2, 2, (1) = 8
6, 6, 2, (1) = 14
Total = 66
Set 2
3, 2, 1, (1) = 7
4, 3, 2, (1) = 9
6, 5, 5, (2) = 16
4, 3, 2, (1) = 9
6, 4, 3, (1) = 13
6, 6, 2, (2) = 14
Total = 68
6, 3, 3, (2) = 12
6, 3, 3, (2) = 12
4, 3, 1, (1) = 8
6, 2, 2, (1) = 10
5, 4, 2, (1) = 11
6, 4, 2, (1) = 12
Total = 65
I usually don't total the rolls unless a player just cannot decide between sets. However, the totals can be instructive too. Set #2 looks really good from a totals perspective, plus it has a sweet 16, but that 7 can be really awful to play. It's clearly a mixed bag which is exactly what I prefer in my games. At this point in the process, I also typically recommend the player consider what race to play before picking a set too, because racial adjustments also come into play. Most D&D-based game systems usually recommend considering a class as well, but I think that's of less importance since class ability scores are not as emphasized as a qualification for a character class in Pathfinder. The racial adjustments for the Pathfinder RPG are:
Dwarf: +2 Constitution, +2 Wisdom, and –2 Charisma
Elf: +2 Dexterity, +2 Intelligence, and –2 Constitution
Gnome: +2 Constitution, +2 Charisma, and –2 Strength
Half-Elf: +2 Any Ability Score.
Half-Orc: +2 Any Ability Score.
Halfling: +2 Dexterity, +2 Charisma, and –2 Strength.
Human: +2 Any Ability Score.
I'd pick Set #3 and let's say I decide to play an elven wizard. Here's what my final stats might look like:
Str 8
Dex 12 + 2 = 14
Con 12 - 2 = 10
Int 12 + 2 = 14
Wis 11
Cha 10
Then, at 4th level I get another +1 to spend and another +1 every four levels, so pumping those into Intelligence lets me work up to being an excellent wizard. Anyway this is a viable and reasonable character, IMHO. Power gamers will disagree, which is fine, but I want characters to be more towards the "real people" end of the scale and less like supermen. Peace.

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I also strongly prefer rolling, and oddly enough, when I GM I use the method (or very close to the method) you described, and for the same reasons.
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