Summit Model

Model 4

Explanation:

Intent:

This, we believe, is a much improved model that we hope will more accurately represent the agents within Summit County and be a source for new insights and way forward on our model. It was run twice. The third run is a slightly modified model.

Run Three: I ran a slightly updated version of this model, I do not believe it warrants its own model page, but there were many insights to be drawn from it so I will explain the changes below, and the observations I drew from it. All information relating to the third run will begin with "Run Three."

Agents and Environment:

The agents are in the different quantities this time; Penny = Poor (12); Dime = Middle Class (10); Nickel = Upper Class (6), with 36 vacancies on the board. The numbers were cut to give although more movement by the agents and allow new rules that will be described below to play out. The environment is still a 64 block (8x8) grid ,and the arrangement was forced again, this time into clusters. I continued with a forced model because Summit County is already segregated, and the second model proved that with our rules segregation would appear.

Run Three: The number of agents and all of the rules above apply to the new run. However, I created an even larger environment (16x16) to allow for greater spacing between agents and the possibility of new observations on the behaviors of dimes and pennies (which was taken from our plan of making a 16x16 grid for the computer model).

Rules of Movement:

The rules were changed significantly for this model. Nickels do not move; dimes are limited to moving two blocks and seek nickels, and pennies are limited to moving one block and seek dimes instead of nickels. Also, there is a 50/50 percent chance that dimes and pennies can move. That is, they have a 50% chance of being able to move when they want to, but also a 50% chance of nonmovement.

Run Three: The one rule addition was that nickels can now move and have a 50/50 threshold as before; that is, as long as 50% of their neighbors are nickels they remain, otherwise they move. Nickels were also given a movement cap of 3 blocks as opposed to dimes 2 and pennies 1. Also, nickels had a 50/50 chance of movement. Nickels are permitted to jump over one agent in their three block movement (dimes, the only other agents capable of moving more than one block, cannot jump any agent if it is sitting in the direction they want to move).

Method:

My method of random sampling was discarded for this model, as it was in the last one. Horizontal movement, running from the upper left corner to the bottom right corner row by row was used again. Dimes and Pennies moved according to their rules, and each time their "turn" started, a coin was flipped to determine whether or not they would move, implemented the 50/50 rule for movement we inserted in this model. The model was run twice. Pictures for both runs are below.

Run Three: The method for this run was the same as above, however it was necessary to assess whether or not nickels were inclined to move each iteration. Since both dimes were seeking nickels and pennies seeking dimes, it took a few rounds before any nickel "desired" to move and they were subject to the 50/50 movement/nonmovement rule. In this way nickels movement is fundamentally different from pennies and dimes; nickels only remove in response to dimes or pennies being within their vicinity, it is reactive. Dimes and pennies movement is proactive.

Before and After:

Observations:

Note: On the first run the dimes had an statistically improbable advantage and were able to move 67% of the time and the pennies were only able to move 50% of the time. This resulted in the dimes quickly surrounding the nickels and blocking the pennies out. On the second run, the odds were more even as noted below with dimes able to move 46% of the time and pennies able to move 50% of the time.

With the new rules the interaction between pennies and dimes were more robust. Likewise the interaction between dimes were more robust, instead of moving freely they were affected by the movement of local pennies and dimes, shaping future movements. This appears to be closer to how movement may really occur in the places we are trying to simulate.

Still it is clear that dimes have the advantage in both runs. When the ratios of movement were a little closer, pennies did seem to do a little better, but were still mostly blocked out (run 2).

One question raised by this model is whether or not dimes can jump an agent, since they are capable of moving two blocks, whereas it would be impossible for pennies that can only move one block.

Observations of Modified Model 4

Note: The modified model has not settled; the reason for this is described below in my discussion on observations from the nickels behavior.

The movement ratios for this run were 55/45% for dimes and 55.8/44.2% for pennies, although somewhat skewed into the "move" category, they are very close to each other. I did not calculate the movement ratios for nickels because their movement is reactionary and only happens in later iterations and even there it is not consistent; one or two might try to move, not the whole block.. Also, in expanding the model size I was not trying to mimic our computer model, running it manually takes far too much time compared to a computer simulation. I simply wanted to give the agents more spacing and observe interactions that occurred over their "seeking" period.

This modified version of model 4 has been one of the most insightful manual models I've run. It helped bring together many of the analysis throughout the various models as I discuss in the Summary of Results.

The most important observation, however, is that it is not useful to have nickels move. This would later be used when making the computer, simply giving them rules to cluster but not to move reactively to dimes and pennies encroachment.

The larger model also provided a better long term picture of the dimes and pennies interactions; ultimately however it was mostly the dimes that made it to the nickels. Also, in the bottom right corner an "underclass" of pennies that seem to be consistently disadvantaged.

Other observations largely tie together past observations and lead into the computer model. They are discussed in more detail in the Summary of Results.