notes on Kent’s algorithmic zoning idea

## how would the community decide on setting priorities

### multi layered topics

decision is multi layered

no. | what to prioritise | option 1 | option 2 | option 3 |

1 | types of landuse | housing | commercial | office |

2 | types of housing | luxury housing | family housing | affordable housing |

-> topic 2 seems to be a subset of topic 1, if we take this fact as granted, topic 1 dominates how much affordable housing
we will get after all. But **topic 2** might be more contensious.

have two meetings vs one meeting altogether => you can do both

https://colab.research.google.com/drive/1E_sEWu7B3n-lBKDttaZ1_FpAtWzBSNXG#scrollTo=yN0vYIDU1yeY

#### elements that are important

- housing
- job
- amenities

## lotka volterra model

https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations

this model was used in namaph (in conjunction with CA) to simulate plant diversity, which I see that we can convert it to land use agents.

**I oppose using this model** for October, since this is overkill to convey the idea.

## pro formas

### data

cost = 1_000_000 deposit = 300_000 # this is how much you pay upfront rent = 4500 years = 15 months = 12 * years

### Yield

#### cash flow

cf = - cost + deposit + rent * months cf

11000f

so we are not broke…

#### Gross rental yield

\(r\): rent \(d\): duration \(p\): value

\[ (r * d / v) * 100 \]

yeild = (rent * months / (cost - deposit)) * 100 yeild

115.71428571428572

#### Net rental yield

substracting the expenses from the raw gain.

\(e\): expenses

\[ {(r * d) - e } / v * 100 \]

### NPV (Net Present Value)

\[ NPV()= \sum^N_{t=0} \frac{B_t}{(1 + i)^t} - \sum^N_{t=0} \frac{C_t}{(1 + i)^t} \]

\(t\) : time period \(i\) : discount rate (interest) \(N\) : total number of periods \(B\) : cash inflow \(C\) : cash outflow

positive NPV means the investment is good.

import pyxirr cf = [-cost + deposit] + [rent * 12] * years result = pyxirr.npv(0, cf) result

110000.0

### IRR (Internal Rate of Return)

\[ \sum_{t=0}^{N} \frac{C_t}{(1+r)^t} = 0 \]

\(C\) : Cash flow, \(C_0\) should be negative \(r\) : interal rate of return

you set a base rate, and if the IRR is higher than that it’s a good investment.

result = pyxirr.irr(cf) * 100.00 result

1.882474875730264

## Dynamic Demand Curve and program markets

memo from last meeting

### two step approval process

- high level: land use prioritization
- different levels: ’residential’ vs ’affordable housing’

- individual projects: developer have the ’FAR slider’

the voting mechianism -> use turnout or similar methods developed by previous efforts

### Cities:Skylines

**How would we simulate the process?**

Using Cities:Skylines as an example. This is what the game aready have.

- objective

The games basic objective is to have more population. Although players have other personal aesthetic goals.

- we have a demand

green | blue | orange |

residential | commercial | industrial/office |

Players change the zoning to meet the demand. Areas that are zoned in high demand landuse will get filled faster.

- statistics

Figure 1: Cities:Skyline statistics

#### difference

- Demand is provided by the simulation. In real life you will need analysis procedures for market trend. Individual projects face nearby citiezens response in the process. In algoritmic zoning, we gauge this by the high level prioritization.
- Once you assign landuse, wheather or not it will get developed is purely in accordance with the demand. Obiously, there is no incentive mechanism for the devlopers to get additional (profitable) floor area. Also, if a buidling (not limited to the buildings defined zoning types) gets built, generally it will affect the nearby ’happieness’ of citizens. There is no way to convert that money or compensation.

-> player is indirectly playing the developers side, since A) this will lead to more citizens (pop increase), B) this inturn will generate more tax revenue to futher develop the cities infrastructure.

## homeostasis

For example we have to two types of amenities, a grocery store and a park.

\[ u = \sqrt{n} \]

If we have two grocery stores the sum of the utility will be 4 + 2 = 6, since the second grocery will be less appriciated. Instead, if we have one each, the sum of the utility will be 8 (4 + 4)

Higher diversity in amenities are better.

### substitutional goods and complementary goods

when looking into the relation of two goods, some are complementary and some are substitutional.

so, depending on how people think a is better than b the utility might have impact.

### IRV vs pair wise comparison

IRV is one method of counting votes, where the caculation is recursive. take the folloing example, when five people are choosing from three amenity options.

alice | bob | charlie | david | eva |

park | book store | police sta. | park | police sta. |

book | park | park | book | book |

police | police | book | police | park |

#### first round

we get the following result

park | book store | police station |

2 | 1 | 2 |

none of them got the majority, we step further into the second round, by eliminating the least favorable option, in this case `book store`

.

#### second round

we get winner since, `bob`

’s first preference was crossed out, and park earns another point.

park | book store | police station |

3 | 0 | 2 |

for this irv, we might naturally conclude that we want a `police station`

after a `park`

.

#### pair wise doesn’t conform

if we compare two goods in isolation, we get the following trend:

park > book | 3 |

park > police | 3 |

book > police | 3 |

the top two lines does not contradict with irv’s result. yet this shows that a book store is actually perferable than a police station. you can see the irv shows different results if you eliminate `park`

and do the recusive calculation over again.

## quadratic voting

the initial intent of quadratic voting (qv) is to be able to show different levels of opinion. some migh argue that 1p1v is not fair when someone have stronger opinions that another. which deincentivises to be a professional. in our case we can convert the `stronger opinion`

to for example, distance. if alice lives close than bob to the prospective landfill site, she should have a stronger say about the topic. The question is how strong should it be? It might be qudratic, but this needs mathemtical proofing and revisit the reasoning behind taking the square root.