Psychologists have made striking discoveries about what makes people happy. Some of these findings clash with common sense. It turns out, for instance, that we are much better than we think we are at rebounding from negative experiences—we are usually blind to the workings of what Daniel Gilbert calls our "psychological immune system". Other discoveries mesh with what our grandmothers could have told us, such as the happiness boost from being with friends and the misery that often comes from solitude. Better to live as Donald Duck than as Scrooge McDuck.
Some leading researchers believe that as this work proceeds, we will converge on a complete scientific solution as to how to maximize our happiness. I think this mistaken. Even assuming a perfectly objective definition of happiness—and putting aside the distinction between a happy life and a good life—the issue of how to construct a maximally happy life falls, at least in part, outside the domain of science.
To see why, consider a related question: How can we determine the happiest society? As Derek Parfit and others have pointed out, even if you can precisely measure the happiness of each individual, this remains a vexingly hard question. Should we choose the society with the highest total happiness? If so, then a trillion people living miserable lives (but not so miserable that they would rather be dead) will be "happier" than a billion immensely happy people.
This seems wrong. Do we calculate averages? If so, then a society with a majority of extremely happy individuals and a small minority who are suffering terrible torment might be "happier" than a society where everyone is merely very happy. This seems wrong too. Or consider the contrast between (a) a society in which people are equally happy versus (b) a society with gross inequality— but which has both a larger total happiness and a larger average happiness than (a)? Which is happier? This is a hard problem, with real-world relevance, and it isn't the sort of problem that will be solved through the methods of science because science provides no empirical recipe for how overall happiness should be calculated.
Importantly, as Parfit notes, the same problems arise with regard to an individual life. How should one balance one's happiness across a lifetime? Which life is happier—one that is somewhat happy throughout or one that is a balance between joy and misery? Again, this isn't the sort of question that can be solved experimentally.
Then there are moral concerns. We are often faced with situations in which we have to choose whether to sacrifice our own happiness for the benefit of others. Most of us make such sacrifices for friends and families; some of us do so for strangers. Framed this way, it's a moral problem, not a hedonic one: a perfect hedonist would help others only to the extent that she believed it would increase her own happiness. But now consider that the same trade-offs apply for a single individual, within a single lifespan. Think of your happiness now and ask yourself how much you will give up, not for another person, but for yourself in the future.
Life is full of such choices. When we indulge in certain immediate pleasures—fatty foods, unsafe sex, living like there's no tomorrow—we are greedily maxing out on our happiness now, at the expense of the happiness of our future selves. When we sacrifice for the future—unpleasant exercise, healthy and tasteless foods, saving for a rainy day—we are altruists, sacrificing now for the happiness of our future selves. Surprisingly, then, even the most selfish hedonist has to wrestle with moral questions, and seeming scientific questions about happiness quickly turn into manifestly non-scientific questions about the right thing to do.