What is the most appropriate way to include randomness in the movement - NetLogo - netlogo

Question

First, let me describe what I am doing and why I am asking this question.
I have 74 cities included in the model and I want to simulate movement between them. I have an OD probability matrix where rows are origins and columns are destinations. Matrix looks like this:
0 1 ..... 73
----------------------
0 |0.5 0.1 .... 0.0
...| . . .. . .
73 | 0.1 0.2 .. 0.3
Please note: if we look at the first row, that means that an agent from the city with index 0 has the probability to stay in it 0.5, to move to the city with idx=1 0.1 and so on.. What I want to do is to on the best statistically speaking way distribute agents' destination. For the agents which origin is city 0 I want to stay approximately 50% of agents (not exact 50%), but also I want to give some chance to the cities that have 0% probability, like pair 0-73.
I already coded the randomness according to the answer to this question: Netlogo: How can send agents from "area x" to "area y" using an O/D matrix?
But the answer for me in this question is not logical, concretely this part:
ask turtles with [residency = "nw"]
[ let myrandom random-float 1
ifelse myrandom <= 0.5 [ set destination "nw" ] [
ifelse myrandom <= 0.8 [ set destination "ne" ] [
ifelse myrandom <= 0.0 [ set destination "sw" ] [
set destination "se" ]]]
If I understood well, myrandom would take a value in the range 0-1 and then it would go to check one by one condition whether its' value is smaller or equal than this constant values.
In that sense, myrandom wound never get to the "sw" part (0 would always be smaller than 0.5) and there is more chance to get the "nw" part where probability is 0.5 than the "ne" part where the probability is higher-0.8. And only because it's not listed first. I am no sure that this is the right way to go, and also I am not sure which is (I can't sort my probabilities because their position represents city-id(see below)). Or I understood wrong?
Here is presented the part of my code. I imported the matrix without the headings/cities ID because they are equivalent to NetLogo indexing. The cities with ID are already imported into the model. Also, in each point/city I created the corresponding number of agents that I read for each city from the CSV file. During the creation of the agents, I use the row from the matrix that corresponds to the current city/origin and go through the probabilities as JenB did in his answer above.
breed [city cities]
breed [inhabitant inhabitants]
;; part of the setup
;; open the csv file that contains population per city
file-open path
while [ not file-at-end? ] [
let data csv:from-row file-read-line
let city-id item 0 data
let population item 1 data
to add-inhabitants
create-inhabitants population [
set city-home one-of cities with [id = city-id] ;; set the origin
move-to city-home
set-destination(city-id) ;; for this origin chose the destination
]
]
to set-destination [row] ;; row from the matrix which represent the movement from the current city/origin to other cities
let row-probabilities matrix:get-row od-matrix row ;; use the row that correspondents to the city
let random-value random-float 1
let i 0 ;; index counter
foreach row-probabilities [ ;; for each probability in row
p ->
if random-value <= p ;; this part is coded as in the JenB's answer
[
set destination one-of cities with [id = i] ;; i is column index which is actually index of destination city
stop ;; if you set city -> stop
]
if i = 73 [set destination one-of cities with [id = i]
stop] ;; the last city -> there is no more option/reason to check
set i i + 1
]
end
I know it's a little bit longer, but I wanted to explain clearly. Some guidelines and explanations would be much appreciated!

Answer 1

Your question suggests that you don't understand what the code in that section is doing. This is the corrected code for that bit:
ask turtles with [residency = "nw"]
[ let myrandom random-float 1
ifelse myrandom <= 0.5 [ set destination "nw" ] [
ifelse myrandom <= 0.8 [ set destination "ne" ] [
ifelse myrandom <= 0.9 [ set destination "sw" ] [
set destination "se" ]]]
Yes, the first line in the block draws a random number in the range 0 to 1. Imagine that the draw gave 0.4. Then the first ifelse would be true and the destination would be set to "nw". Now imagine the draw was 0.6, then the first ifelse would be false and the code would go on to test the else part, which is true because 0.6 <= 0.8.
The code works because the initial draw is uniform. That is, 10% of the time (on average) it returns a number in the range 0 to 0.1, and 10% in the range 0.1 to 0.2 and so on. So 50% of the time it returns a number in the range 0 to 0.5, which returns true for the first line. 30% of the time it returns a number in the range 0.5 to 0.8, which is false for the first test and true for the second test. 10% of the time it returns a number in the range 0.8 to 0.9 and 10% of the time it returns a number in the range 0.9 to 1.
So breaking the interval with check points at 0.5, 0.8, 0.9 (and 1 for the remainder) gives you sections that are 0.5, 0.3 (=0.8-0.5), 0.1 (=0.9-0.8) and 0.1 (=1=0.9) in length. And a uniform random number will fall into those sections with probability distribution 50%, 30%, 10% and 10% of the draws.