So what do you think the ideal empire size is?

4-5 controled cities and lots of puppets

Yep, and trade post the puppets to limit them from building meaningless buildings.

In my current game, this what I did. I won a space race at 1964AD (might have been sooner) and my research was at 1200+ beakers per turn. I had more gold than I knew what to do with it.
 
That's not even a remotely "ideal" strategy for any victory type other than pre-modern conquest. Once the tech costs, policy costs and building costs skyrocket your 16 beakers-per-turn cities won't be a match to a 100 beakers-per-turn "normal city" for that era (reseach lab), you can also forget communism and all the other stuff that comes with culture, and your cities will struggle with 15 hammers per turn (even with railroad) trying to build a 600-hammer stock exchange. Not saying that having a lot of small cities and several large ones is bad per se.

ICS with endless fields of trade posts will allow you to buy any building you wish in your core cities. Once you get Liberty, you can turn many of your smaller cities into specialist cities to curb their growth and increase your overall happiness.

Even decently sized specialist cities (6-10 pop) will be contributing more happiness to your empire than they consume.
 
The way I figure it, its not the number of cities in your empire but their size. Colosseum+Theater+Stadium= 12 :), so 10-12 is the ideal size depending on whether you plan to take Planned Economy/Forbidden Palace. Civs with UB that boost :) can increase this number as can specialist cities. Once you can get you cities to break even end even have a few 'recreational' cities (i.e size 1 cities with rush buy :) buildings you don't need to worry as long as your expansion is at a reasonable pace.
 
There are two limiters to expansion through plopping down cities: policy cost, and happiness.

If you don't care about policy cost, then happiness is your only issue.

You can research Construction and Horseback Riding fairly quickly. This brings you Colosseums + Circus. Together, they are +6 happiness. If there is a luxury nearby +5 more. This means that wherever a city can work either Horses or any unique luxury, it's a good idea to plop a city there, even early in the game. If it can work both, it can supply lots of empire happiness.

Acoustics for Theatre boosts potential empire happiness +4 per city.

The more I play this game, the more I find that in the latter stages, I don't have to choose between more cities or big cities. I can just have both.
 
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