Happiness is

There's a song by this title written by Clark Gesner. It's from the musical "You're a Good Man, Charlie Brown" (1967). You can see the full lyrics here  and you can hear it on YouTube:
Let's just jump to the key 2 lines that drive home the point of going through all kinds of different things to describe happiness:

For happiness is anyone and anything at all 

That’s loved by you.

 In other words, happiness is not one-size-fits-all but a function of one's own subjectivity --whatever or whomever one loves. For some people that may be parties and rock concerts, while for others it may be reading a book on a beach and listening to a string quartet. Though one's choice of activity  is more social on an objective scale, that does not mean the individual is experiencing a greater feeling of happiness.
That's because happiness can be found in quiet contentment just as much as it is in outward celebration. Herein lies the problem of declaring who is the happiest of them all.  As researchers rush in where angels fear to tread, psychologist Will Fleeson of Wake Forest University headed an often quoted  2010 study that declared extroverted behavior is correlated with happiness.

The abstract puts it as follows:

In Study 1, participants reported their extraversion and positive affect every 3 hr for 2 weeks. Each participant was happier when acting extraverted than when acting introverted. Study 2's diary methodology replicated the relationship for weekly variations in positive affect. Study 3's experimental methodology replicated the relationship when extraversion was manipulated within a fixed situation. Thus, the relationship between extraversion and positive affect, previously demonstrated between persons, also characterizes the internal, ongoing psychological functioning of individuals and is likely to be explained by something capable of rapid intraindividual variation. Furthermore, traits and states are at least somewhat isomorphic, and acting extraverted may increase well-being. 

Sophia Dembling addressed the problem with the definitions of happiness here in her book The Introvert's Way: Living a Quiet Life in a Noisy World. As I suspected from the shortness of the chapters in the book, they are based on previously published blog posts. The one on the happiness study is at http://www.psychologytoday.com/blog/the-introverts-corner/201009/is-our-definition-happiness-extrovert-centric:

For his research, Fleeson drew on a three-component model of happiness, using just one of the three components: Positive affect. That's the happy other people can see and hear, and it is strongly related to extroversion. The second leg of the stool is life satisfaction, which is more cognitive than emotional: Even if you're not feeling great at the moment, you know your life is pretty good all around. (Introverts have a little bit less of that kind of happiness than extroverts. We think too much, right?)
The third component of happiness is absence of negative affect--not having anxiety, fear, anger, frustration. "And the opposite of that is feeling at peace, at ease," Fleeson explained.
At peace, at ease. Those also sound introvert-ish to me.
So one could argue that introvert happiness here is being described as a sort of negative space. Feeling peaceful is not positive affect, it is the lack of negative affect.....

As she points out, though, the peaceful, calm type of happy is the one that introverts normally prefer to what she describes as "one long Mountain Dew commercial." Even though they do sometimes want to socialize as much as the next person, extended extroverted behavior drains them of energy, which would make them not exactly happy -- even if they are keeping up a socially accepted smile..

Oh, and whether introverts pay a price for behaving like extroverts is research for another day. Fleeson didn't explore the energy cost for introverts behaving extroverted, although he personally understands the need to crawl into a dark room after a stretch of interaction.
But he did say that when he had subjects sit at a table and assigned them to act either introverted or extroverted for ten minutes at a time, the subjects who got most exhausted by the task were extroverts who had to behave introverted.

 Maybe extroversion is a force so strong that suppressing it is exhausting. Or maybe introversion generates energy of its own, so intense it wears extroverts out. 

A note on the book, it does make some excellent observations about introverts, though as it is a short paperback, it is much less thorough than Susan Cain's book. I also found the short chapters too much like blog posts, which, as self-contained pieces sometimes overlap a bit with other chapters in the book -- though it's great for people who like to just read a couple of pages at a time.  Dembling  refers in places to Laurie Helgoe's writing, which I reviewed, along with Cain's and another name in the field of inroversion in http://uncommoncontent.blogspot.com/2012/05/perspectives-on-introversion-this-is.html Interesting that all these books are written by women. While the other three all identify their husbands as extroverts, Dembling is not altogether clear about that; it sounds like he is also an introvert, though more extroverted than she is.