Misanthrope Housing Problem

1 collaborator

WHAT IS IT?

This model was built to answer the following problem posed on 538:

The misanthropes are coming. Suppose there is a row of some number, N, of houses in a new, initially empty development. Misanthropes are moving into the development one at a time and selecting a house at random from those that have nobody in them and nobody living next door. They keep on coming until no acceptable houses remain. At most, one out of two houses will be occupied; at least one out of three houses will be. But what’s the expected fraction of occupied houses as the development gets larger, that is, as N goes to infinity?

http://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/

HOW IT WORKS

Available houses are colored grey. As each misanthrope chooses an available house, it is colored green, indicading the dwelling is occupied. The neighboring houses are also colored red, indicating the dwellings are no longer available.

HOW TO USE IT

To run the model, select the number of houses in a row using the "HousesInRow" slider bar. If using a single row of houses (the original problem) toggle "Grid" to off. Setting "Grid" on will simulate a grid of houses.

Then press the SETUP button followed by the GO button.

THINGS TO TRY

Try using Parameter Sweep experiments to see how changes in the size of the row impacts the expected occupancy rate.

EXTENDING THE MODEL

Get creative and change the misanthrope rules on what constitues an acceptable house. Perhaps uber-misanthropes need two empty dwellings buffering them?

Comments and Questions

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Click to Run Model

to setup
  clear-all
  set-default-shape turtles "house"
  let i 1
  if Grid = true [set i HousesInRow]
  set-patch-size (700 / HousesInRow) 
  resize-world 0 (HousesInRow - 1) 0 i 
  ;; make green atoms on left
  ask patches with [pycor < i ]
    [ sprout 1 [ set color gray ] ]
  reset-ticks
end 

to go
  ;; asks to fill empty houses
  ;; move into the vacancy
let i true
  while [ i = true ] [ tick
      let Misanthrope one-of turtles with [color = grey]
          ifelse Misanthrope = nobody [set i false ]
          [ask Misanthrope [ set color green 
                            ask patch-here [ask turtles-on neighbors
                                                [set color red]]]]] 
end

There is only one version of this model, created over 9 years ago by Robert Patchin.

Attached files

File	Type	Description	Last updated
Misanthrope Housing Problem.png	preview	Preview for 'Misanthrope Housing Problem'	over 9 years ago, by Robert Patchin	Download

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