Unhappiness from Slavery

How does the unhappiness from slavery wear off exactly in these cases:

Lets say I whip 1 pop each turn for three turns. Assuming it will take x turns for the unhappiness to wear off. Will it be:

1. 2 unhappy after x-2 turns, 1 unhappy after x-1 turns, 0 unhappy after x turns
2. 2 unhappy after x turns, 1 unhappy after 2x turns, 0 unhappy after 3x turns

Also, what happens when you whip 3 pop for one item?

I think there's a typo in your second option: "2" unhappy after x turns, 1 after 2x, 0 after 3x.

Also whipping more than 1 pop gives you the same 1 unhappiness as whipping 1 pop and for the same amount of time.

Assuming turn x is the turn in which you have 0 unhappy

Turn 1 - whip, 1 unhappy
Turn 2 - whip, 2 unhappy
Turn 3 - whip, 3 unhappy
Turn 4 - 3 unhappy
...
Turn x-3 - 3 unhappy
Turn x-2 - 2 unhappy
Turn x-1 - 1 unhappy
Turn x - 0 unhappy

Assuming Y is the amount of turns for the penalty of ONE whip to go away
Turn 1 - whip, 1 unhappy
Turn 2 - whip, 2 unhappy
Turn 3 - whip, 3 unhappy
Turn 4 - 3 unhappy

...
Turn Y-1 - 3 unhappy
Turn Y - 2 unhappy
Turn Y+1 - 1 unhappy
Turn Y+2 - 0 unhappy

In this case, Y+2 = X, meaning that (the amount of turns to get 0 unhappy) is always (the amount of turns required for one unhappy to go away) plus (2).

Using a quick domino proof which i won't write here because its self explanatory to those who would understand it -
X = Y + C, where C = (number of whips done in succession) minus (1)

For logic laymen, this means simply subtract 1 from the number of whips, then add to the number of turns for one unhappy to go away, and that's how long until your city has no unhappy from whipping.
--
Carl - Sis pacis instro pro bellum

The answer to your question is here.

Thanks, that's a great guide. So I guess the answer is #2.

Actually your guide was helpful in another way. I asked this question with the idea of using hereditary rule and slavery, which would be awesome if unhappiness wore off according to #1. However, I didn't think of building the globe theater there afterwards (possibly using overflow to do it), or to just build a crappy city that overlaps food resources your "good" cities use.

Yeah, crappy cities used for whipping/drafting together with the Globe Theatre city are quite a force. In one of my last games I have two size 6 cities with something like 60 turns of unhappiness, but they were only build for strategic reasons and aren't that great anyway. They did provide a big army though.