Exploratory Analysis

The exploratory analysis for the Stanford Prison Experiment was intended to examine two issues. First, an examination of the diffusion dynamics was conducted. As noted in Section7.2.5, it is valuable to know the rate that different memes diffuse through the population. A second analysis was conducted to determine the transmission dynamics, in particular which agents tended to learn about a meme from which other agents. This section will focus on the Hypothesis condition, as it demonstrated most diffusion of memes.

Diffusion Dynamics

The diffusion dynamics memes can be looked at from two standpoints: learning and expression. Within the simulation, different memes have different diffusion rates and different amounts of delay before they are expressed by other agents. Figures 7.5 and 7.6 show the number of agents aware of the Resist and ThrowInHole memes over time respectively, for the Hypothesis condition. The thick central line of these figures indicates the mean value, while the dashed lines show the progression from individual runs. It should be noted that these figures show learning by all agents, not just the ones able to express the memes.

Figure 7.5: ThrowInHole Learning Diffusion

Figure 7.6: Resistance Learning Diffusion

Both curves can be approximated using s-curve form, as expected. Additionally, the individual runs tended to be similar to the average run with only a few deviant outliers. This was typical for diffusion results using this cognitive architecture in general. Looking at the learning-diffusion charts, it is

evident that ThrowInHole had a slower diffusion rate. Logistic curves were fit to the mean-value curve in each of these graphs, which confirm this interpretation. SciPy, a scientific package for Python, was used to fit generalized logistic curves to each mean-value curve. The learning rate for ThrowInHole was 1.37, while the learning rate for Resist was 3.45. This is approximately double. A major factor in this is that Resist occurred more often than ThrowInHole. This happened for two reasons. Firstly, ThrowInHole was an action that placed a prisoner in the Hole until they were released. With the problem prisoner removed, there was less need to express the meme. Secondly, Resist occurred more often than expected by the ground-truth for reasons as previously explained in Section7.4.1.

Figure 7.7: ThrowInHole Learning Diffusion (Guards)

Figure 7.8: Resist Learning Diffusion (Prisoners)

This difference in learning rate is greatly increased if one looks only at the agents who can express each meme. Since guards worked in shifts, there are distinct periods where information is exchanged. By comparison, the prisoners were in a common environment for the entire simulation. Figure 7.7 shows the number of guards who are aware of ThrowInHole over time in the Hypothesis condition, while 7.8 shows the number of prisoners aware of the Resist action over time. The learning rates for guards in this case are 1.45, while the prisoner learning rate is 10.8. Moreover, the graphs show that the learning was qualitatively different. The individual runs for guard learning show that learning tended to happen mainly at shift transitions, but also at sporadic points during shifts. Conversely, prisoner learning tended to occur in sharp bursts. Once three or more prisoners became aware of the Resist meme, the rest of the prisoners became aware of it within hours during the simulation.

Having looked at the learning rates, it is logical to examine how these relate to the number of agents who have expressed the meme at least once. Figure 7.10 shows the counts of first expressions over time for prisoners taking the Resist action. Interestingly, while prisoner learning diffuses quickly, this does not necessarily correlate to all prisoners resisting. While at least five prisoners tend to

Figure 7.9: ThrowInHole First Expression Diffusion

Figure 7.10: Resist First Expression Diffusion

express resistance fairly quickly after learning it, not all prisoners use resistance and the times at which they first decide to resist are variable. Figure7.9 shows the counts of first expressions over time for guards taking the ThrowInHole action for the Hypothesis condition. Guard first expression times correlate strongly with shift changes, as was seen with learning. This indicates that learning related to the ThrowInHole action could have been an influence for when particular guards started throwing prisoners in the Hole.

Figure 7.11: ThrowInHole Learning vs First Expressions

Figure 7.12: Resist Learning and First Expressions

Figures 7.11 and 7.12 compare the mean values for learning and first expression counts for ThrowInHole and Resist, respectively. From these, it is clear that the first expression times for agents correlate with the learning times. However, these graphs do not establish how much each one causes the other. Learning the meme is a causal factor for expressing it. However, an agent expressing a meme for a first time may help it reach agents who previously were not paying attention to it. In this way, an agent’s first expression can be a causal

factor for learning.

To test for this, Granger causality tests were applied to the time-series of learning and first expression sequences for each run. The tests were run in both directions, to examine which sequence showed better causality for the other. Since Granger causality tests are sensitive to the lag parameter, each test was iterated over a sweep of lag values between 1 and 6 (one hour of simulation time) to find the optimal lag for each test. Table 7.33 shows the results of this analysis for the Hypothesis condition. The percent of runs where the causality test was significant (p<0.001) is indicated for each meme, as well as the average lag time which was optimal in those significant cases.

Table 7.33: Causality: First Learning vs First Expression

Learning First Expression

Meme % p-value<0.001 Avg(Lag) % p-value<0.001 Avg(Lag)

ThrowInHole 97% 3.96 (39.6 min) 21% 3.5 (35 min)

Resist 100% 3.66 (36.6 min) 86% 3.32 (33.2 min)

This analysis indicates that in both cases, first learning appears causal to first expression. This is as expected, since learning is necessary for first expression. The lag indicates that typically agents tend to use the action within 40 minutes after learning it. However, when using a more full sweep with lags up to 1/3 the length of the simulation, optimal lags as long as a full day were found. These might indicate cases where agents tended to learn the ThrowInHole action, but did not take it until their next guard shift.

First expressions are also causal for first learning for Resist, but seldom for ThrowInHole. This may indicate that ThrowInHole was transmitted mainly by a subset of agents, whose expression was a key causal factor for learning. Resistance did not show this trend. This indicates that the first expression of resistance for an agent was a more strongly causal factor for learning. This could mean that first expression is more likely to reach new agents for learning, but it may also result from first expression correlating with the number of expressions in general. To examine this, it is important to look at how agents learned memes, which is the focus of the next section.

Meme Transmission Dynamics

This section explores the who and why of meme transmission. This is an interesting feature of the model, since it allows detailed analysis of who was spreading memes and when they were most effective. The question of who was expressing memes will be examined by breaking down the agents into classes

based on their tendencies to learn and express the meme. Using these classes, the question of why is examined by looking at the differences in personality factors between agents in different classes.

Figure 7.13: Typical Adoption Curve Positions

Rogers(1962) separates adopters into 6 categories: innovators, early adopters, early majority, late majority, and laggards. These indicate the different phases of adoption on the s-curve, as shown in Figure 7.13. Due to the low number of agents, early adopters and early majority will be lumped together. The first analysis performed was a quartile ranking of agents’ relationship to the meme that they could express (Resist or ThrowInHole). Quartiles were calculated for the following metrics: the average time an agent first learned the meme, the average time they first expressed it, the average number of exposures they took to learn it, and the average fractions of their actions that expressed the meme once it was known. Note that for the number of exposures to learn a meme, multiple agents act simultaneously so multiple exposures can occur in the same step. As such, all exposures in the step where they learn are counted, including the ones they learn the meme from. The full tables of these quartiles are contained in AppendixJ.3. These helped provide the insight for the following analysis.

The first learning and first expression times were used to examine which agents could be considered the early adopters versus the laggards. Table 7.34 shows this information for the Resist action under the Hypothesis condition. For

Resist, prisoners all tended to learn quite quickly- on average less than an hour apart. They were effectively all early learners. However, expression was phased out much differently. Certain agents such as S 01 and S 04 were much quicker to resist once it was demonstrated to them. Conversely, agent S 02 did not tend to resist until much later, if at all. This is notable, since S 02 was the agent whose strategy was to vigorously go along with the guards.

Table 7.34: Resist Adopter Categories Learning

Expression Innovators Early Late Laggard

Innovators S 05

Early S 01, S 04, S 06, S 08

Late S 03, S 09

Laggard S 00 S 02

Table 7.35: ThrowInHole Adopter Categories

Learning

Expression Innovators Early Late Laggard

Innovators S 13 (E)

Early S 15 (E), S 20 (E) S 17 (D), S 21 (D)

Late S 11 (N), S 12 (N)

Laggard S 16 (D), S 19 (D) S 18 (N)

The ThrowInHole meme worked very differently, as seen in Table 7.35. Due to the shift boundaries and attention issues, the meme rolled out in a much more staged fashion. To show the effect of shifts, each guard is followed by their shift: Day (D), Evening (E), or Night (N). S 13, the innovator, was part of the evening shift. S 16, S 17, S 19, and S 20 appear to learn during their first cross-over period, where they are leaving their shift and S 13 is starting. One interesting aspect of this is that the more pacifist agents, S 16 and S 19, learned the meme before the ones who expressed the action earlier, S 17 and S 20. To a lesser effect, this was also seen with S 18 versus the other evening shift guards. Guards who were less likely to use the ThrowInHole action were quicker to attend to it. This is an interesting and counter-intuitive effect.

A second question of interest is the matter of who are resistant to the meme and who are more likely to express the meme once they know it. These two factors are interesting to look at together because they show who will tend to be the expressive early adopters, passive carriers, resistant but later expressive, or holdouts. By knowing these factors and the network topology, it would be

possible to get a good estimate of the diffusion rate: resistance shows the number of exposures needed to acquire the meme, while the expression rate gives the output of exposures. The number of exposures required to learn the meme was considered to be a resistance factor- more exposures indicates the agent was less susceptible to the meme in this condition. The intermediate processing of this is contained in AppendixJ.3 also.

Table 7.36: ThrowInHole Meme Resistance vs Expressiveness Expression

Resistance Highest Higher Lower Lowest

Lowest S 11 S 13

Lower S 12 S 15 S 19

Higher S 20 S 18

Highest S 21 S 17 S 16

Table 7.36 shows each guard agent’s resistance (# exposures to learn) and its expressiveness (fraction of actions producing the meme) for the ThrowInHole meme. This analysis reproduces much of what had been expected. S 15 and S 19 (“nice” guards) learn the meme readily, but don’t express it very often. On the converse, guards such as S 21 take some additional exposures before learning the meme but regularly throw prisoners in the Hole once they learn it.

The same analysis was applied to the Resist action and the prisoners, with the results as shown in Table7.37. Unfortunately, while the ThrowInHole results were quite reasonable- the Resist results show some of the issues that were present in the internal validity checks: the expression of the Resist action happens a bit too often, but does not occur quite often among the innovators. S 05 and S 00, while expressing the meme at a reasonable rate, do not express it quite as high as some other agents. This may indicate that the simulation did not capture a factor beyond their basic personality traits led to increased Resist actions from these agents. Both agents had an ideological background, with S 00 believing in meditation and S 05 supporting Marxist-type ideology. In other respects, the classifications seem reasonable. S 02 is shown to be the holdout, both for learning the meme and expressing it. Agents that were known to use Resist with some frequency, such S 04 show up as more expressive than other agents.

At first glance, it seems as if the early adopters take more exposures to learn the meme, on average. To look into this further, a metric was devised to look at the fraction of exposures that lead to learning as a function of the number of agents aware of the meme. This metric only counts new learning, and any exposures on agents with the meme are ignored. This gives an estimate of the exposure efficiency, its ability to cause new learning. Figure 7.14 plots the exposure efficiency of ThrowInHole on guards as a function of the number of

Table 7.37: Resist Meme Resistance vs Expressiveness Expression

Resistance Highest Higher Lower Lowest

Lowest S 00 S 05

Lower S 03, S 06

Higher S 04, S 08 S 01

Highest S 09 S 02

agents knowing the meme. Figure 7.15 shows exposure efficiency for the Resist action on prisoners. In these charts the solid line represents the mean of the points, while the dashed line shows a fitted 2nd-order polynomial. This analysis indicates that the first learners are not disadvantaged with respect to salience. This is supported by looking at the median resistance levels, where the early adopters show lower resistance rather than higher resistance. The reason why they take more exposures to learn, on average, is due to having longer tail distributions. While later adopters may get multiple simultaneous exposures, helping to smooth the distribution, the early adopters generally only see one exposure at a time.

Figure 7.14: Exposure Efficiency for ThrowInHole

Figure 7.15: Exposure Efficiency for Resist

The efficiency curves are interesting in their own right. Both figures show a slight U-curve, where efficiency is lower between the early adopters and the early majority. This is an interesting effect, since it implies that diffusion occurs slightly differently than a traditional diffusion curve. This may indicate that in a social environment memes may tend to have an initial growth spurt, followed by a lull. This makes some intuitive sense- the most interested parties will pay attention early. Despite this, the overall diffusion rate is faster as more agents learn because there are typically more total expressions- even if they are less effective per expression. This is an interesting lead, which may be worth looking

into in future experiments.

Stanford Prison Experiment Summary

Overall, the Stanford Prison Experiment simulation has provided a number of interesting avenues for future research. Firstly, it has demonstrated an effective simulation of a real-life scenario. Secondly, it has demonstrated the ability to extend classical diffusion of innovation simulation. This simulation takes into account both physical and social environments, combining social influence and physical barriers (such as shift change) into a common framework. Thirdly, this simulation has shown unique capabilities beyond typical diffusion-of-ideas research. This fine-grained analysis allowed identifying the different phases of adoption for individuals, as well as to determine their relative level of output value. This is very different from a classical diffusion model, which seldom models the background actions that agents can take instead of expressing a meme.

Finally, it has opened new avenues of simulation and empirical research. For example, the internal validity analysis showed that novelty correlates negatively with attention in a complex environment. While initially counter-intuitive, this is a useful finding that appears likely to be reproducible within an experimental setting. The internal validity analysis on attention also highlighted the ability of an agent-based model to help explore how situational factors could affect trends in data. This demonstrated the ability of the model to be a test-bed for mocking up an experimental condition.