Happiness = Perceived Actual Life / Expected Life --- (1)
where,
Perceived Actual Life = Perception * Actual Life ----- (2)
and in most cases,
Expected Life ∝ Perceived Life of Others ------------- (3)
where,
Perceived Life of Others = Perception * Others' Actual Life -- (4)
and finally,
Actual Life ∝ (1 / Happiness) * Skill * Circumstance - (5)
The most success I had was in breaking equation (3), and then in upward adjusting Perception in (2). But (5) is the kicker -- it implies that your lack of happiness feeds back into other people's lack of happiness, creating a loop. As long as it holds, everyone will try to one-up each other in trying to improve their lives.
Hmm, equation 5 bugs me. I like the model that being less happy can drag down other people, but this directly implies that being more happy drags your own life down, which I feel is antithetical to the definition of happiness.
I think this stuff is really cool though, and I really like where you're going!
Do you have proposed units for the quantities in your equations?
I think it's easier to see the relations once you substitute everything in. I combined the perception terms instead of cancelling since presumably they're different, but here you go:
Happiness = Perception * (1 / Happiness) * Skill * Circumstance / Others' Actual Life
Happiness^2 = Perception * Skill * Circumstance / Others' Actual Life
Happiness = +-sqrt(Perception * Skill * Circumstance / Others' Actual Life)
I'm not certain about the negative root there; maybe that's depression? Otherwise, looking at http://en.wikipedia.org/wiki/File:Square_root_0_25.svg, it seems reasonable; improving one of perception/skill/circumstance if it's near-zero will improve your happiness drastically, but it's a relatively slow-growing function so improving happiness after that has diminishing returns.
Also, as you mention we never defined the terms. I believe all of these are generally measured on self-administered surveys with "rate X" scales, and so are just percentages with no units.
Finally, the terms don't have any obvious correlations with the post, so I just stuck in the things that were mentioned that seemed relevant:
* Happiness - see eqn., you can't affect this directly
* Skill - conscientiousness, self-esteem, optimism, feelings of purpose and fulfillment
* Perception - paying attention to your situation/actions/feelings and in particular adjusting your estimates of success/failure chance to match reality (humans deal very badly with probabilities) - includes "agreeableness" (understanding of others), "memory" (perceptions of self being happy), and "mindfulness" (perceptions of world)
EDIT: corrected error in (1)