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Starting at the bottom, though, the p.s.s. : this has been done to death many times before, including in the discussion pages here, and you aren't raising anything that hasn't already been (quite extensively) dfiscussed and debated.
Yes, the mod default setting (easily changed, of course) is quite deliberately Western- centric (derived from US postwar practices as implemented globally), with a culturally-bound foucs on middle-class suburbia (when using US-centric model of race relations, typically white) and is based on real-world statistics. It is specifically to model the post-war car-centric suburbia represented by the game and desired by the vast majority of mod users, and which is seen as the dominant geographic feature of the post-WW2 cities found all around the world as presented by the game and expected (and experienced) by users. This is very much by design and user demand. The mod's default settings are not aspirational or projective, but very much descriptive, reflecting current and historical reality; again, though, the power is in the hands of the user to change that.
It has been demonstrated time and time again that that is what users expect of this mod's default - to reflect the standard practice of the cities that they live in (which is overwhelmingly Western or Western-style cities). There are always exceptions, of course, but exceptions are excatly that - exceptions - and should not dicate the default.
Multi-family dwellings (noting that family here is very much the nuclear family, as the game has no concept of any other family structure nor any capacity for extended family relationships) already feature in the mod and game as high-density buildings; the division between low and high density is simply whether or not there is one family per building. High- density in the game should not be interepreted as e.g. high-rise buildings, but simply buildings where there is more than one family (and therefore some attention in calculations needs to be paid to shared assets, e.g. common areas). A high-density building in the game may thus have two households, or two thousand, and is the natural model for any multi-family building, no matter how small. It would be good if the game offered a more granular and nuanced depiction of residential options (not just the addition of 'medium density', but even just that would be a start) - but it doesn't, and we need to work within the practical limitations of what we have. Nevertheless, the current approach of using the high-density designation to model multi-family households and using differential calculation to represent modal differences is quite adequate in practice.
That being said, the mod is deliberately designed to enable the easy implementaiton of any alternative paradigms, and they can easily be implemented using the mod's inbulilt custom calculation tools. I've also repeatedly said that I'm more than happy to include any such alternative models, as soon as somebody can provide me with real-world statistics and data to model - so far, nobody has, but my offer still stands (and the only data I've found myself just reinforces the current default).
To use an analogy, you're looking at the list of supplies purchased by a bakery, and trying to guess the exact max and amount of ingredients in an individual pastry.
To determine how many households a building contains, you look at the building. Not the city, not the country, not the hemisphere; just the building. The number of households (or whatever) per square kilometre in a particular city is an irrelevant (and distracting) metric; there's far too many varibles and confounding factors to have that meaningfully apply to any individual building. City-level population average population density includes a myriad of factors that have a far greater effect on the measured outcome than buildings. The amount of space dedicated to roads, railways, open space, parkland, utilities, and even just private gardens and courtyards (just to mention a few) will have a far greater impact on the resultant figure than anything to do with the residential buildings themselves. Simply put, the signal to noise ratio of using average population density figures across a city area is so overwhelmingly low as to be effectively meaningless.
You're dealilng with buildings here, not cities. Cities are comprised of buildings, but abstraction is a one-way path; you can extrapolate from buildings to cities only with great difficulty, and the reverse is practically impossible in any meaningful sense. To use the appropriate metaphor, a building with stats derived from such an exercise is just as useful as assuming a spherical cow.
I hope that doesn't come across as too harsh or anything; I'm just trying to explain why the approach you've taken isn't going to produce meaningful inputs for an agent-based simulation.
Next post I'll go into a better approach for determining building capacities, which is that used by the mod.
This is the start of a bottom-up approach to get where you want to go. There are many advantages to doing things this way, including that this is going to be much more useful when it comes to implementing what you're trying to do within the game's agent-based model.
The key to this is to take data that looks at exactly what your looking for, without having to resort to over-abstracted proxies, and with a limited number of confounding factors. Fortunately, the starting point is straightforward - average apartment sizes. Depending upon the target area, publically available data may be patchy, but even media articles can give a good general guide for an area. This gives us a hard starting figure for the actual amount of space needed per household.
I say 'starting figure' here, because there's still more work to be done. This is where a knowledge of building design and planning comes in useful, because (of course) an any multi-household space there's a surprising (to many) amount of space that is not dedicated to any household - everything from the space taken up by exterior and shared interior walls (always a lot more than people think), to circulation and transit spaces, utiltiy provision, etc. Once more, we need average figures for these, which are typically available via building design resources relevant to the target area (my own reasearch indicates that a good starting average across most Western nations is around 15%).
There are several different ways to calculate all this, and the relevant data sources you find may only use one particular method (e.g. NFA vs GFA, percentages, fixed amount, combinations). I've deliberately built the mod to be able to handle the most common methods, so you don't have to perform data manipulations yourself when it comes to setting up calculation packs.
And that's all you need to work out how many apartments per building floor - building gross floor area less non-habitable components, all divided by the area per apartment. This has been tested on a wide variety of real-world designs and has been shown to be quite robust, and is the model the mod is based around.
The same technique works for employment, too. Local-level governments (councils/counties/etc.) typically publish planning guidelines that lay out typical design factors, e.g. average employees per square metre for various types of activity. Again, those are what I've used in the preset calculation packs for the mod, and again, I've made it easy to customise.
Floorspace of a building is then calculated from the actual physical size of the building, or (in the game) the actual size of the building model. Don't approximate to the 8x8m squares; when you do the analysis you'll be surprised by exactly how inaccurate this method is, as even small errors in the conversion snowball quickly. Use actual dimensions instead (at least to within 1m, which is not difficult to do).
Floor heights tend to be fairly standardised in each region, so choose whichever is appropriate. Again, if in doubt, refer to resources on local building standards and/or regulations, but this is usually easy to 'eyball' (and the mod's floor preview makes it trivially easy to visually adjust the parameters against the actual building model). The mod also offers some other options, such as the ability to extrapolate units over multiple floors, but this probably isn't relevant right now.
Anyway, all that gets you an accurate count per building, useful for simulation and what-if analysis, that offers a much more detailed level of granularity than you can ever get from starting at the regional level. Emergent behaviour is very important when looking at livable cities (even moreso than with, shall we say, "non-livable" cities), so it is important to start at an appropriate level of granularity that encourages that emergence on the simulation level, and not homogenize the experience via interpolation from an overly-abstract starting point. That level of granularity is typically at the building level, which is now where we've got to.
The next part is to place these granular building blocks within the broader urban context, i.e. looking at all those factors outside the buildings themselves which are the ultimate arbiter of final population density.
First, thank you so much for the substantive replies. i appreciate all the time you put into fashioning your responses. They were actually more helpful than you may have expected.
I hope this first comment doesn't shade your perception of what I take away from your response. In the human sciences, it isn't "fundamentally flawed" to adopt a basically etic approach in search of correlation across macro samples. For example, there is a distinct divergence in density and household size when comparing "global" cities with the rest (7,511/km2 vs 5,920/km2 and 2.47 vs 2.84 -- respectively). There are obvious reasons for these differences, based in long-standing knowledge regarding development, urbanization and fertility rates in dense populations. I understand your point, however, about the "abstract" nature of approaching planning for building level population density. [I'd be happy to share the data I collected with you. I just don't want to post up a link in a public forum for fear of hackers.]
With your points about the granular nature of residential density, the argument that building structure is the main driver, therefore, I've been digging into your GitHub manuals. The floor and population packs make complete sense. No disagreement from me whatsoever with this. Also, if I understand the mod screens correctly, I could create new population packs of my own dimensions for the build I envision. For example, High Density Eco Lvl 5 buildings utilize the European apartments (modern) population calculation pack to derive households per building. That provides 110 m2 per unit (household). This works out to approximately 1,184 sf apartment for a single family. The United States high rise calculation pack allows 102 m2 per household, or 1,079 sf apartment for a single family. These numbers just seem out of whack with reality. For example, this source from rentcafe.com shows in 2018 the average size of 1 br apartments at 757 sf and 2 br apartments at 1,138 sf (https://tinyurl.com/55s225fy). And according to another source, average one- and two-bedroom apartments in NYC (the kind of cities I'm thinking about) are around 700-850 sf (https://tinyurl.com/3e85dzk6, {LINK REMOVED}https://tinyurl.com/2w5nnedu). Based on this research, a more realistic area per unit figure (in NYC, for example) would be 80 m2.
I'm just wondering from where you derive your area per unit figures. Are these based on prescriptive building codes? How do you arrive at the modifier of 110 m2 per unit or 102 m2 per unit in your European and U.S. High Rise population packs?
Also, and this is not necessarily a question related to the mod, but I'm wondering about clarification regarding what constitutes a "household" in Cities Skylines. According to PDXCO we're talking two workers and, "one or more children," (https://tinyurl.com/cfxa9jpb)--but my understanding has been that high density residential in-game tends to attract smaller families than low density. Does this comport with your understanding? And does this correlate with your calculation models? In other words, if your calculation pack shows 102 m2 per "unit" in high density residential, we're talking essentially, about a family of 3-5 in a single apartment, or two adults and (maybe) one child? It makes a difference because in MOST dense urban centers, average households are much smaller. It makes little sense in the real world that you would see a 1,079 sf apartment for a young couple. I'm just trying to get an understanding of where your modifiers come from so that I can better understand your population calculation packs.
I want to reiterate how much I appreciate your thoughtful previous responses. Also, please don't think I'm being critical. Your replies are helping me derive a set of data that I can use to create residential calculation packs for the build I'm envisioning.
Not even sure I want to dig into production and consumption models for commercial, industrial and offices. Thanks again for the obvious hundreds of hours of work you must have put into this mod!
Of course, I can't (and won't) stop you from doing anything yourself, I'm just offering my opinion in the sprit of academic discourse! But I do believe you'll have a much stronger result by first treating buildings in isolation, and then expanding to the other factors influencing population density - these other factors being especially significant in living cities, and having a greater impact than buildings themselves. Taking the mid-west postwar US as an example, when over 50% of available land space is dedicated to automobile transport, then quite naturally the population density will be much less than in pedestrian-oriented cities, even with the same building composition. This, I fear, will be lost in the use of aggregated statistics, but is absolutely vital for what I think you're trying to achieve.
Regarding the area per unit figures, they are derived from a variety of sources, with some compromise to fit in with game mechanics. For example, the game has no concept of a 'one bedroom unit', so I've used larger apartment sizes as references and discounted the contributions of single-bedroom units - in the game, all households are deemed to be 'family-sized'. The figure you've given above to 1,138sf for a 2br apartment is slightly larger than, but broadly within the same quantum as, the figure of 1,079sf that I've selected for this purpose (and probably accurate within measurement error, given that my figures were an aggregate of various statistics from between 2018 and 2020).
NYC is very much the outlier in the US apartment space, and obviously there is a lot of variation across the US. I'd like to add some specific packs for places like NYC, San Fransisco, Seattle, Chicago etc. at some point, but so far I haven't had time to do the specific research needed, and on initial analyis the use of other existing calculation packs appears to provide a satisfactory alternative (e.g. old EU for NYC, which for level 2 buildings exactly duplicates the 80m2 figure you have there). I'm certainly open to others providing such info, of course.
In Cities: Skylines, a household is defined in technical terms by a residential CitizenUnit, which will contain 1 or 2 adults, and 0-3 children. There is no difference to the game whether this unit is the only one in a 4,000m2 mansion or a 20m2 Ikea demonstation apartment. You're correct that in most dense areas in real-life the family size is smaller, but the game doesn't reflect this; hence why I need to select apartment sizes that take this into account and produce (at least roughly) meaningful and accurate aggregate population sizes. I've found that once you factor out single-bedroom apartments, the statistical mathematics falls into place almost automatically. Modelling 'singleton/DINK' apartment buildings is certainly something I have in mind, as part of a broader socioeconomic overhaul that I'm currently toying with - but that will be some time away, at best. In the meantime, we need to live within the constraints of the simulation model, and that brings us to another 'devil in the detail' of applying aggregated statistics. If you were to take the aggregate density in those cities and apply it to C:S, you'll soon find the in-game population booming far above what your aggregate should suggest, simply because of the limitations of the CitizenUnit model. Hence why I prefer the approach of starting with the smallest components and working up, adjusting as you need to get the desired aggregate starting point - that way you can be sure the model is robust within the limitations of the game's simulation.
Related to your thinking with respect to emergent behavior in agent-based simulations, I totally understand your logic, but I’m not understanding how establishing a basic parameter (in this case, “area per unit”) derived from aggregated parameters from a statistically correlated sample (i.e. dense, global, sustainable cities – see link below) would adversely limit emergent behavior in the simulation. Based on your earlier feedback, my thinking has evolved a bit, and all I’m really contemplating is identifying a different “area per unit” to input into the population calculation pack. Based on the discussion above, if I’m reading everything correctly, the population calculation pack “area per unit” parameters are themselves essentially derived from aggregated statistics. In the mod, for example, you’ve extrapolated “area per unit” for European Apartments (old), European Apartments (modern), and U.S. High Rise apartments. These are parameters that define how many cims populate buildings that grow in accordance with each population calculation pack.
When you look at my sample, I don’t think you would be wrong to point out the ranges of population, population density, households per km2, and household sizes in the top 15 cities in my sample--and how those variances exemplify your main point about starting from the ground up. This is a diverse sampling of urban settings.
I’d respond, however, by pointing out the clear and significant variance between the average densities and household sizes in those top 15 cities when compared to the total sample (which included nearly 70 other cities landing either on a global cities index or a sustainability metric–but not both). Across all of these cities there is discernible correlation between density and household size connected with sustainability and their positions as global nexuses (however each of those two descriptors are characterized). The most obvious argument would be that--given their positions as centers of trade, finance, culture, governance, etc.--and thus their obvious desirability as places to live--property values and cost of living in these cities are higher than others, which drives people to have smaller families. There is also the attraction these cities hold for single young professionals launching careers which arguably drives average family sizes down. Ironically, in this global sample, the four U.S. cities are closer to the mean apartment size than the rest (New York = 73 m2, San Francisco = 70 m2, Chicago = 74 m2, and Los Angeles = 75 m2)--and this leads me to wonder to what extent the claim that New York City is an “outlier” in this respect among U.S. urban centers, given its close correlation with the three other cities mentioned, might be contestable. Although, I'm largely supporting that claim with my contention that cities we regard as "global" manifest different trends from the rest... so NYC, San Francisco, Chicago, Los Angeles are ALL outliers belonging to a different category of city.
In any event, I do think there is validity to establishing a smaller “area per unit” as a parameter in a supposed “global and sustainable” population calculation pack. The trick–especially keeping in mind your point about how population sizes grow in the simulation–is to figure out exactly where "area per unit" should be set.
With that in mind, then, I have a different question related to household size… are household sizes produced by the simulation based on random number generation (or is there a specific algorithm the game uses to generate households)? If so, I would assume that household sizes generated by the simulation fall into a natural bell curve (especially the longer the simulation runs). Secondary to this, I assume the game calculates the numbers of adults and children separately, correct? Theoretically, one can predict what the likely mean household size would be in-game. If I understand things correctly, then each “apartment” in a building (as defined by the floorspace calculation algorithm) will always be occupied by 1-2 adults and 0-3 children, correct? For example, a building set to the U.S. High Rise calculation pack, totaling 10,200 m2, would be allotted 100 households (because in that population pack a unit is allotted 102 m2)--and therefore would total approximately 100-200 adults and 0-300 children?
I set up two random number generators in parallel in Excel, one for 1-2 adults and the other to generate 0-3 children. Over 11k random iterations, household sizes fell on a natural bell curve, with the mean household size being 3, the mode 3, and the median 3.
Therefore, essentially, the data I’m aggregating is potentially problematic because household sizes in-game will never average out to a household size of 2.47 (which is the mean) across 15 global, sustainable, dense cities. I’m basing an “area per unit” aggregate on research of m2 floor space across apartment and condo units in each of the fifteen aforementioned cities. But, given the variance between average household size in-game and real-world across these 15 cities, I would need to adjust my proposed “area per unit” (as you discuss above as you did in the mod) to accommodate.
Once again, thank you so much for all of your thoughtful replies. I really do appreciate it!
This is a png -- not the actual spreadsheet: https://drive.google.com/file/d/1wiPwMdHIptbMPtY1cMv7_He6tK5ELvGC/view?usp=sharing
You're correct that the 'area per unit' figures are derived from aggregated statistics, but from an aggregation that focuses solely on the issue at hand, specifically apartment sizes. Thus the number of counfounding factors is, while not (of course) completely eliminated, at least is significantly reduced. Using data aggregated at higher levels (block/subdivision/suburb/city/etc.) rapidly loses its accuracy the further away from the target level you aggragate, as all manner of complicating factors are introduced at each level of aggregation.
I note that at the city level the vast majority of land surface area is not dedicated to residential accomodation, with other factors being signifcant drivers of relative population density; a problem that doesn't exist (at any material scale) when looking solely at data aggregated from measurements of only the very specific component that concerns us. My major concern with your proposed approach remains the fact that population densities cannot be solely attributed to building density, and when modelling dense and sustainable urban cores this needs to be taken into account appropriately. I still believe that you might find the approach of first determining average dwelling size (and modelling that at the building level) and then examining those other factors in more detail. Once a certain 'base'level of population density is reached, I believe that you'll find those other factors key to any further analysis/modelling of dense urban areas, as well as having a greater impact on both objective and subjective 'livability' measures. The amount of space dedicated to transportation, recreation, and decoration will be (I feel) of significant interest, but this variable is abstracted away if the starting point of data aggregation already includes such effects.
Regarding US apartment size outliers, I'm referring compared to US metropolitan areas generally. The average apartment size in the four cities you've listed (plus Seattle) are significantly below the statistics I've found for other US cities, and noting that there are several hundred of those, those five definitely stand out as exceptions, rather than norms. As you've pointed out, these cities also tend to have different family sizes compared to the US average, and this is reflected in these cities' characteristic of having a greater proportion of smaller apartments, which in turn drives down the average apartment size (noting that New York in particular has additional historical factors also influencing its statistics in this area that don't apply to the other cities at anywhere near the same scale). when I crunched the numbers, though, at first approximation it seemed to roughly even out - substituting larger apartment sizes (2br, 3br) while simultaneously increasing typical family sizes seemed to give roughly equivalent results (at least close enough not to warrant any further investigation on my part). Perhaps this is good enough for your purposes too?
You're correct in your understanding about the adults and children per apartment. The game's household sizes (other than immigrant households) are actually the product of individual behaviour elements - cims find their own residence, and will then try to 'partner up'. Partnered adult (not young adult, but 'full' adult) cims then have a chance to produce a baby (1 in 12 chance per simulation step, where 3.5 simulation steps = 1 year of age; reduced to 1 in 8 chance per simulation step if local childcare is available), stopping only once the containing CItizenUnit is full (three simultaneous children) - which doesn't give a nice bell curve distribution, unfortunately, and will flucutate materially with small sample sizes. But you're right because the in-game household size is quite unlikely to average 2.47.