So I've read through the thread and I've been thinking of all the ways that a jerkass genie could spoil some of these changes people are requesting. In order to prevent this, I've come up with some basic rules to maximize your power's efficiency while avoiding all jerkass genie messing up.
1) Always
increase, never decrease.
Increasing compounds the chance, meaning each time you increase something you increase it by more than the previous time, making your power usage more efficient over time. Conversely decreasing things decreases the amount you change them by each time, meaning that your power usage becomes less efficient over time. Decreases should only be used if it's impossible to word it as an increase (eternal youth, for example, does not have a good way of wording it as an increase, though immortality might work as "Increase my time before I die").
2) Work with the largest number possible.
Larger number = bigger increase, math is fun! Note that average vs. total makes no difference, they will both lead to the same overall increase from each usage.
3) Work with the smallest group possible.
This removes the chance of a genie screwing you over in the short run (since you always win in the long). For example if you wished for an increase in total or average wealth worldwide it could be done by taking all the wealth in the world and giving it to 1 person. In fact this leads us to the conclusion that the only way to be safe from our jerkass genie is to only work with groups of 1 at a time! Anything more than that and you risk the genie stealing from Peter to give to Paul. Note that groups of 1 does not necessarily mean 1 person, but rather means 1 of whatever the attribute is tied to. For example things like average life expectancy are tied to the person, wishing for them at the country level violates our 1 group law, whereas things like % of citizens to live beyond the age of 60 is an aspect tied to the country, not to the actual citizens.
4) Work with things that have an absolute maximum whenever possible
This is the only way to get around our group limit of 1 person for our jerkass genie (as outlined in rule 3). If something has a maximum then it lets you drastically speed up the process because you can use it to bolster other groups. By wishing for things that have a maximum (such as our % of citizens to live beyond the age of 60 example from law 3) you could bolster 1 group up to the maximum (in this case 100%) and then add it to another group to create faster increases in the second group. (Note that you would want to wish for totals here, not averages, to prevent aspect stealing right at the start). You would still be addressing the problem 1 group at a time, but the previous maxed-out groups would generate increases that would be forced to go to the non-maxed groups, speeding their increase.
Following these laws we can see that the best thing to do would be to pick a single aspect that is tied to a large group but is still non-zero (such as the overall % of citizens in a country to live to be over 100). After that we would rapidly focus on increasing that aspect until it hit its maximum (100%). After that we would then add one more group at a time, waiting for them to be maximized before adding another (which would take less and less time with each already maximized group you have). This would get maximum utility out of our power while locking down pretty much anything a jerkass genie could pull.
Of course if we have a friendly genie then why not go for the
Human Development Index? That lets you simultaneously hit standards of living, life expectancy, and education.
Kill 1% of all sapient life in the universe? If exactly 1% of the human race doesn't drop dead, you've just proved the existence of aliens. And murdered a bunch of people, but hey, SCIENCE!
Or there is enough other sapients out there that you wipe out the entire human race, yourself included.