Please, stop drinking the Kool-aid
What exactly are these "many" benefits? In fact there are exactly 2 benefits. You get +3 happiness in your largest 5 cities. You get +3 beakers for every specialist. That's it, nothing subtle there. Except, maybe, the awkward way the +3 happiness bonus shifts around when your cities change in size (due to whipping, for instance) but I don't count that as a benefit
Ah a literalist. Yes, in fact that's all representation does on its own but all a hydrocarbon does on its own is create dirty, hot fire but the
consequence of that is the internal combustion engine and everything that was suddenly attainable from that point on is history.
Hyperbole aside you know as well as anyone here that the real value of representation is the unparalleled early research without leaning on the research slider. The subtle consequences therein are that you can over-expand and over-warmonger while still at least maintaining parity technologically if not gaining. I believe that this is both a blessing and a curse as I've noticed in my own progression up the difficulty slider that I've learned a lot of bad habits from this which fail to succeed as the difficulty slider goes up ... which is why I concur with your previous sentiment to avoid rail-roading people into linear thinking (SE is all about representation; You just built 'mids, get libraries, get SoL, and post your screenshot of your easy Diety victory
)
But while I can in principle concur with your sentiment I'm having too much fun with the argument to let it go and still feel that you're committing as many overarching gesticulations as the SE zealots here.
To wit, I'll attempt to paraphrase your salient points in a convenient manner that makes it easy as possible for me to defraud them so I can make myself look smart
. Of course doing this will make it much easier for you to say "I didn't actually say that" or "you're missing my point" ... both of which are very likely true and ultimately all I'll end up doing is making it easier for you to discredit my paper thin argument. Worst case scenario we end up in a bloody typing duel to the forum death of which only 2 people witness ... you and I ... but for the purposes of my pedantic, self righteous argument ... I'll risk it
Here's your points.
#1. HR facilitates size 16 cities while representation allows size 10 cities in the same happiness context.
#2. Given #1, HR allows you to have many size 16 cities which is > than many size 10 cities under representation.
#3. The extra GPP converted into GS bulbing in a size 16 HR city allows it to produce more effective beakers / turn than a size 10 Rep city assuming a GPP conversion of 1GPP = 5 beakers.
OK lets dig in.
#1. HR facilitates cities of whatever size your health cap is. This I will give you. That said there is a cost associated in troops which I will only handwave at a bit but for a single capital style city I don't see it as a huge ordeal ... specially if you plan ahead and build a bunch of warriors knowing you're moving towards an HR strategy. I believe for the premise of this argument we are assuming 6 garrisoned troops which give +6 happiness. What I must have missed is why 6-3 = 6. By that I mean granted HR in the above scenario provides +6 happiness but where did Rep's +3 wander off to? Is it at the bar hitting on ugly chicks, wallowing in its inferiority to the mighty HR? Why are we comparing a size 10 rep to a size 16 HR? Why isn't it size 13 vs size 16 or size 10 vs size 13? Is there something I missed? So that said if the difference in size is only 3 population the HR argument starts to lose some teeth.
#2. "AHA!!" you might say ... "but I can run more than 3 cities with +6 happiness, you poor Representation suckers are stuck with only 3 cities ... muhahahaha ..." This is true fact, yes an HR empire can have any number of cities with nigh infinite happiness in them. My answer is ... <insert hand waving about impracticality of having 24 or more units built explicitly for happiness purposes>. Joking aside but isn't that compelling? I mean it though ... I can see the argument being made for a single capital type city with a ton of troops ... I just don't see that many players filling up all their cities in a similar manner. I may be mistaken but it seems impractical and counter productive because the hammer costs REALLY start to add up at that point and the Rep player would be cranking out critical infrastructure in that time period. Additionally unless you're talking fairly late game don't you require some health buildings as well to hit that 16 sized city fairly early? More hammers invested into that big city that rep doesn't have to bother with.
That said I will say representation is one of the weirdest things in Civ because it doesn't scale in any way with size of the map. Rep on a tiny map is incredibly powerful while using it on a huge map ... well the happiness aspect seems almost non-existent. I really don't know how that's relevant but I felt like pointing it out.
#3. And then here's the meat. I believe you came up with the number that a size 16 city can support 2 more scientists than a size 10 rep city. I believe the stated values were 4 scientists in the rep city, 6 in the HR city. 4 rep scientists = 24 B/T + 8GPP/T while the HR city is 18 B/T + 12GPP/T. Even if those aren't the stated values they sound reasonable. With a 5:1 conversion ratio that leaves representation with 24 + 40 = 64 B/T and HR with 18 + 60 = 78 B/T. That's the point of your argument anyhow that running larger cities allows more specialists which allows more GPP/T.
I have A LOT of issues with the above. I'll label them to make it more convenient to rebut them
.
A. As stated before why does a 6 garrisoned HR city allow 6 more pop than Rep? Yeah if this is your 4th super science city ok I'll concede ... but who runs 4 super science cities early enough for the context of this argument? I don't know about you but by the time I'd be assigning my 4th dedicated science city I usually have more than 50% of the landmass and am wrapping up my game. That said I suppose on a huge map this might not be true but I hardly consider that a talking point in this context. I also recognize that your three largest cities are not necessarily science dedicated but at least for the way I build my capital is nearly always my SSC and my 3rd city is nearly always my Wall street/wannabe SSC. Those are almost always two of my big 3 ... with my 3rd usually being the enemy capital I take over early.
B. The conversion of GPP to beakers goes down FAST over time and long before anyone could have grown a size 16 city (which requires more than just happiness, you will need some health), the GPP/B ratio will have gone down into the break even range (around 3ish B/GPP is break even for the above example of HR vs Rep) if not below. I'd be intellectually curious to see how fast one can get a size 16 HR city on Emperor or above ... but I really doubt its going to happen within the first 4 GPs.
C. The above example requires caste system to even get off the ground ... which is not something I see non-spiritual leaders doing very often. I personally really rely on Spiritual leaders so I tend to have it but still its not fair to consider this a stipulation. Slavery is just too important early game.
D. Representation benefits more from the multiplier buildings (academy, library, university, etc ...) because in the end raw beakers get multiplied, not GPPs turned into beakers. That said Phi leaders, parthenon, Pacifism, and NE all effectively multiply into the GPP conversion rate ... unfortunately aside from Phi the other three come after the first few super conversion rate GPs are spawned (Although I think I do sometimes get Pacifism around GP #3 or 4 ... which is fairly early). That said to be fair you can build most of the multiplier buildings across your cities (which you will be doing anyhow if you aren't running caste system). I think in the end Representation wins out on this one.
E. One of the subtle side effects of representation is that it boosts nationwide research outside of your science dedicated cities. A bad example is my HE city is almost always running a couple engineers and priests who all produce some beakers (its a bad example because my HE city doesn't have a single science multiplier in it.) A good example is what eventually grows into my Wall Street city (usually my third city). It does have all of the multiplier buildings and tends to run a huge mess of merchants and/or scientists who all produce a lot more B/T under rep. Another good example is the espionage city ... tons of spies all cranking out solid B/T getting multiplied into the buildings under Rep but not HR.
F. E leads right into this point, in any city EXCEPT your SSC or your GP farm ... the GPP/B conversion is 0 ... which really hurts the entire HR vs Rep thing. A scientist under Rep in a city that will never produce a great person is still making 6 B/T (before multipliers). That same scientist under HR is only half the scientist.
I guess that's all I've got ... good luck.