Originally posted by DaviddesJ
Building a granary which will make up as much or more population than you lost
There might be cases when rushing a granary would be useful, I'd have to see the numbers that makes you think this is a generally useful approach. It simply doesn't work out in my mind. In most cases when building a granary and you delay (cut back on growth) to keep the bin full after completion you end up losing overall, rushing is a more extreme case of cutting back on growth so goes doubly.
building a temple or library that will expand your borders and let you work better tiles that will make up the cost
In this case, you'd seriously have to evaluate the cost of the lost pop and using a less-than-optimum tile. I can't really picture a situation where you would not have a workable tile before the border expansion, but yet for whatever reason you've settled there anyway. I'm sure there are examples, but are they odd or extreme cases or is this a general occurance in your games?
or shrinking a city that's grown beyond your development and is working unproductive tiles that actually slow its growth.
Ok, say you have a city with 3 grass tiles, 2 of which are shieldlands, you work the shieldlands first and then the 3rd citizen gets the unimproved grass. In this case in 10 turns he makes 20f, so instead of getting the 20f you rush him and get 20s instead, in one turn.
However, in about ten turns a worker could road two of those tiles yielding 10g, and in another 2 turns you will earn 30g every ten thereafter. For example: 0-000 1-111 2-222, this is move-roadx3. The number is the yield, after 12 turns you are finished 3 roads, and have earned 12g, every 10 turns there after you earn 30g. In total the turn after you finished those 3 roads you have made back your investment.
I have found that if I am working unimproved tiles that this is a very large clue that I don't have enough workers, not as you apparently say a reason to sacrifice some citizens.
In closing something like rushing a temple to get early culture, and an earlier double cannot be obtained in any other way quickly, so it can be reasoned that any cost is worth it. I think some of the cases you mentioned are special cases, or odd cases and do not constitute a sound general strategy. Of course I couldn't compare the results of your QSC since I couldn't find it, did you submit?