How does happiness work?

In the tab Small Village in the Kittens Game, there is an option to send hunters (when there is enough catpower available) with a happiness percentage in front of it. How is this happiness calculated or influenced by me, and what effect does it have on anything (probably the resource gathering from the send hunters option?)?

Happiness goes down by 2% for every kitten you have after the fifth kitten (so the sixth kitten will drop it by 2% from 100% to 98%)

Happiness is the efficiency of your kittens. For example, a farmer (without any upgrades) normally will yield exactly 1 catnip per tick, but at 98% happiness they'll only yield 98% of that (0.98 catnip per tick)

Hunters can bring in items from the forest (I've only seen fur and ivory), each will increase the happiness by exactly 10%, cumulative (getting both increases by 20%). The amount of each of them only affects how long the bonus lasts, not how many the happiness bonus is

EDIT: Also, Amphitheaters reduces unhappiness by 4.8% each, which means that it will negate the happiness reduction effect by overpopulation, but can't actually increase happiness (so if you have only ever had 5 kittens, it will not increase the happiness)

EDIT 2: In reality, it looks like that as of v 0.9.6 Amphitheater does not actually reduce unhappiness by 4.8%. I have 18 kittens for a projected happiness level of 74%, unicorn raises it to 84%, yet 7 amphitheaters only brings it to 93%, about 1.8% each. I'll see if I can find more on this

Looks like the formula changed since the previous answer. This is what i figured out so far:

Happiness start at 100% up to 5 kitten. Some modifies apply, like every special resource (fur, ivory, spice) give +10% (so if you have fur and ivory, you get 120%). Unhappiness is also simply added to this %, so 24% unhappiness (17 kitten) + ivory + fur = 96% happiness.

Spice, Karma and some other things also effect happiness by a flat %.

Amphitheaters affect unhappiness. Unhappiness start at 0% for 5 kitten, and goes up by 2 for every kitten beyond 5. (So 2% at 6 kitten, 20% at 15 etc.) Amphitheaters only affect this modifier in the happiness formula. If you have 10 kittens and 10 amphitheaters, you get 10% unhappiness * 0.52 amphitheaters bonus = 5.2% unhappiness. If you have only fur, that would result in 104% (rounded) happiness.

To be clear: The amphitheaters bonuses are added up, so the formula is 1 - (# of theaters * 0.048) and not 0.952^(# of theaters) as some might expect. This hold true for all buildings, both those that decrease and increase production. A mine gives 20% bonus flat, and a tradepost decreases rare resource consumption flat. Unhappiness might reach 0 at 21 amphitheaters and rare resource consumption might reach 0 at 25 tradeposts.I cant tell what happened beyond that because i haven't reached that yet - those buildings will be ridiculously expensive at that point.

After 10 tradepost you get diminishing returns, i suspect this i the same for amphitheaters and other buildings that decrease some need. See this post.

Fur, ivory and spice are consumed on use. Once they run out, the happiness bonus you got from them goes away. Unicorns and karma do not get consumed, so once you have these there happiness bonus is permanent.