The Line Game - An Alternative Explanation to Masking Theory

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The Line Game refers to a general form of games that can be explained in the language of theory which are being used to explain social boundaries. Like most theories explained using Game Theory, this is a rather cynical explanation as it assumes everyone is acting only in their own self-interest. I do not mean to imply this is the case in reality, but merely use it as starting point to see how the line game has the potential to introduce biases into the perception of autism.

The line game is an iterative game where the goal is not to win, but for a player to achieve as many points as possible. At each step players make two actions. One action is to move to position, which is represented by a real number. Based solely on their position, the player will score a number of points. This scoring function is defined so that it is monotonically increasing, but asymptotically bound on the right - the further right the player is, the more points the player will score, but there is also a maximum number of points a player can score from this action at each step. At some number, there is also a line. If a player is to the right of the line, then all other players also lose points, while if the player is to the left of the line or on it than the other players do not lose any points for this action. The other action for a player is to punish another player. If taken, all this action does is causes the targeted player to lose points. The last stipulation is that the amount of points a player can potentially gain from crossing the line is less than the amount of points they would lose if other players punish them for crossing the line.

From this set of restrictions, it is clear that the long-term Nash equilibrium strategy of any player is to position themselves exactly on the line, and to not punish any other players. This is the maximum number of points players can make each round without invoking the ire of other players by crossing the line, and there is no reason for any player to punish another as no one is punishing anyone else or crossing the line. With such a clear Nash equilibrium, it is the best interest of any player to simply position themselves on the line. All players know this is the optimal strategy, and so that's how they try to play - if they can.

See, there is catch. Players don't actually know where the line is! Instead, they are given various signals that give them information about where the line is likely to be. We will also add in the stipulation that the location of the line changes each step according to some undefined process. This ensures that players need to interpret their signals that they get at each step to inform their strategy, rather than basing their strategy on previous experience of where the line was or knowledge of how the line moves. The actual Nash equilibrium is unclear as it depends on knowing more information about the specific model than is specified here, but it ends up being a combination of players stepping as far right as they think it is safe to do so according to weighing risk and reward, and ritualistically punishing players who step too far over the line anyway to ensure that the threat of overstepping remains. I don't know exactly how it would play out, but in many cases you'll find that there is a clear distinction between the line people are aiming for, and the line people will be punished for crossing, which is higher up to account for the variance in people's plays.

As far as the line game is concerned, the difference between autistic people and neurotypicals is that autistic people have less clear signals about where the line actually is. This estimate isn't biased in anyway though, it's just less precise. This means that if autistic people are just going to shoot for where they think the line is based on it being the most probably point, they are equally likely to undershoot it as overshoot. In both cases, the autistic person suffers for their lack of precision more than neurotypicals do. When they undershoot, they score less points, when they overshoot, they are more likely to cross the second threshold that brings about ritualistic punishment. However, because we are assuming self-interest, it is only in the case of overshooting that neurotypicals actually intervene by punishing the player.


Now it's time to step out of the world of pure game theory and look at what this means socially. First, the fact that dispute manifesting on both sides the autistic behavior only draws attention on one-side results in a perceptual bias of the behavior, causing people to perceive it as being biased towards the right when it actually isn't. For a concrete example of this effect, autistic people are often poor at controlling the volume of their voice. If someone's too quiet, they will be ignored, while if they are too loud, they will be chastised for being too loud. This leads to the perception the person as being too loud rather than of having poor control of the volume of their voice.

Second, instead of leaving them to be caught in a system of punishment, psychologists can look at the behavior of the person who steps over the bounds more frequently and more intensely than other players and note that their behavior appears to be irrational as it leads to them doing more poorly than the other players. The psychologist investigates and finds this player isn't actually acting irrationally, they just have worse information than the other players. The psychologist remedies this situation by giving the autistic person additional information in the form of rules. For the rules to achieve what the psychologist wants, they must have two properties. First, they must lead to the autistic person stepping over the line more less often, which acts in the psychologists own self-interest. Second, the rules must lead to the autistic person scoring more points than by not following it, as otherwise the autistic person would have no rational reason to follow the rules. So this is how the traditional model of autism intervention unfolds, and associated with it is a narrative that autistic people are more likely to step over the line than neurotypicals.

However, that is not necessarily the case. Based on their working model of the game, an autistic person's optimal strategy maybe to severely undershoot the line. If they aim low enough, they will actually be less likely to cross it than neurotypicals are despite having more variance. Such a pattern of behavior is still distinctly autistic as it results in a lower score for the autistic person, but since it doesn't also lead to a other outcome for those around them it does not lead to intervention. It's possible that an autistic person's working model of the game may end up in such a state due to the introduction of rules, but it's also possible for the autistic to arrive at such a strategy on their own.

One model that can be used to induce such behavior in some autistic players but not others is by adding another property to players called empathy. Note that property is meant to model behavior, not to be a statement about any concrete construct about empathy, though I hope it becomes clear why I called this property empathy once I explain what it is. We are modifying the game so that at each action, in addition to the score they would otherwise receive, player's receive an additional score proportional to the score all other player's receive (to avoid mathematical issues of compounding where scores may not converge, for now we'll only assume that the points other player's lose from crossing the line is counted towards empathy). The specific proportion is modulated by the empathy a player has, so more empathy means that player's score is more impacted by the score's of other players. Empathy varies from player to player, but we are going to assume that there is no difference in empathy between autistic and neurotypical players. This means the distribution of empathy across neurotypicals is identical to the distribution of empathy across neurotypicals.

Now, I haven't worked out all the math yet, but my hypothesis is this. Using a simple model that fits all the constraints described, a particular pattern will be observed in relation to this empathy variable. There will be some level of empathy where autistic players and neurotypicals players are equally likely to cross the line. At some level of empathy below this, autistic players will be more likely to cross the line than neurotypical players with an equal level of empathy. Conversely, at higher levels of empathy autistic people will actually be less likely to cross than neurotypicals on the same level. This should reflect a bifurcation between two strategies at the equilibrium level.

Regardless of whether this hypothesis holds, it should still hold that people with more empathy would be less likely to cross the line than those with less empathy, all else equal, since crossing the line is more of a threat to them (since they will loose more score themselves as a result of other player's losing score) so they would purposely undershoot more. If we are in some model where at some level of empathy autistic people are more likely to cross the line than neurotypicals at the same level of empathy, then it is plausible that people who cross the line with high enough frequency will be be screened for autism as it's a way they differ from their neurotypical peers at the same level of empathy. If such a threshold is defined, then it's also possible that autistic people at a higher level of empathy will miss the threshold, and thus miss screening. It's also worth noting that higher empathy inherently does not counteract the effects of autism as far as what behavior it causes it to manifest. The fact the higher empathy in this model only amplifies the effects of negative actions means higher empathy inherently results in a worse expected outcome for the player than otherwise - like with autism. A corollary of this is that it can only influence behavior in a way that would lead to worse outcomes if influence was not present, so it cannot "mask" autism even though it leads to behavior that is not identified as being the result of autism. Thus these people will be overlooked as being autistic despite being just as autistic as the people at the lower empathy levels, and will suffer just as much from misjudging where the line is.

Now that it has been established that such an a group of autistic people exists who exhibit behavior that is 1. distinctly the result of autism and 2. does not conform to expected behavior from autism, let's try to apply it to the real-world to see if we can identify a group of people who exhibit such behavior. It's important to also note that such behavior is NOT masking. Masking would be displaying the same behavior as neurotypicals while still in some sense being autistic despite this. The fact this behavior is distinctly the result of autism means it is something else. More over, I think a lot of behavior that is often attributed to masking could actually be attributed to some variation on this phenomenon.

The classic group that is believed to be underdiagnosed due to masking is women, but this could also be explained by this phenomenon instead. In many tests on empathy, women generally score higher than man do. However, empathy isn't actually what we're looking for. What we're looking for is behavior. Tests have ALSO found that women tend to factor other people into their calculations more than men do, which is enough. This could be due to some biological basis of women tending to be more empathetic, but it could also be explained that women are instead just taught to behave as such in order to be subservient to men, and there could be countless other explanations as well. The point is not the source of the phenomenon, but the phenomenon itself. The point is the phenomenon of higher empathy as described in the model as an explanation for the decisions people is present in women as a group.

In order to make the previous assumptions about the distribution of empathy being the same between autistic and non-autistic populations without qualifiers, we are also going to assume that autism rates are equal across the sexes. This does not match empirical data, as more men are diagnosed then women. However, if we assume the reason for the disparity is not that autism is actually less prevalent in women, but just underdiagnosed, then it makes no contradictions with the model. More over, the model provides an explanation for why women are underdiagnosed. The fact women tend to have higher empathy would result in autistic women being more likely to exhibit "atypical" behavior for autism, and thus fail to be picked up during screening and not receive a diagnosis.

If such a trend exists that is substantial enough to explain the disparagement in autistic diagnosis rates despite assuming it actually occurs at the same rate, it begs the question of what the distinctly autistic behavior of undiagnosed women actually looks like. After all, I postulated that such behavior exists, as it is not masking. It is not enough to merely look at trends in the behavior for women who were diagnosed vs. men, as the fact they still ended up being diagnosed means they are likely not a representative sample of the population of autistic women which is largely undiagnosed. As such, we must look elsewhere. One potential population to look at is at women with social anxiety disorder, avoidant personality disorder, and similar disorders. The behavior of these disorders is consistent with people consistently undershooting social boundaries and in turn hurting themselves. It is potential that a subset of these people are autistic and that this element of their behavior is being ignored. More people are diagnosed with social anxiety disorder than with autism, so there is plenty of room for all undiagnosed autistic women to have been diagnosed with social anxiety disorder (not that I'm claiming this is actually the case). More over, more women are diagnosed with social anxiety disorder than men, so autistic women being given that diagnosis and not autistic men could explain some of the disparity there as well. This isn't just wild conjecture either. I was recently reading about theory of mind, and found that people with social anxiety disorder are also reported as a population with theory of mind deficits, like autistic people, suggesting that despite a difference in presentation many of the underlying mechanics may be the same. As such, there is compelling reason to believe it could be one fruitful avenue to look.

If I was writing this as a paper, I would proceed to actually code up a model conforming to the restrictions I described, and try to calibrate it so it matches up with real-world data about autism. Matching up the model with empirical data would not be empirical validation of the model, but rather show that a reasonable alternative explanation exists for the empirical data, which would then inform future research where people could compare models. At the moment though, I'm not writing this as a paper as I must focus my labor elsewhere. Instead I'm just injecting this theory into the wild that explains observed phenomena in a more abstract way, and giving suggestions for what to do with it. I find this exposes a potential systemic bias in research relating to autism, and it's worth taking seriously. This systemic biases described apply not only to women, but to autistic people in general.

Even people who are autistic and were picked up by screening when they were young still suffer from these biases. As a result of failing to pick up the way autistic people suffer when the fall on the left-side of the line, autistic interventions fail to address many of the needs of autistic people. More over, this bias to only see right-side violations results in autistic people being perceived as being more aggressive than they actually are. I remember reading that Simon Baron Cohen defended his theory of autistic people being deficient in empathy against attacks from autistic introspection by saying that autistic introspection is invalid because autistic people don't pick on the times they violate social mores. I say his conclusion is exactly backwards. When autistic people violate social mores to the point it blows up in their face, THEY KNOW IT. They just don't know *why* it went that way. What SBC and other researchers don't see though is all the the times autistic people didn't act because they were afraid of stepping over the line because no one sees what does not occur. Autistic people, however, know. They know what choices they made and what choices they did not, because unlike researchers, their introspection makes them privy to such information. It is time to move past outdated theories of mindblindedness that fail under rigorous analysis, and move onto newer, more rigorous models that also take autistic perspectives into account as another source of data.

TL;DR: Autistic females aren't masking, their behavior is just as autistic as that of autistic males. It just isn't recognized as being autistic because it doesn't draw attention to itself as disordered behavior because unlike males, females are taught not to draw attention to themselves in that way. The theory behind this explains other systemic biases in autism research as well.

Interesting take.
I got a bit lost when you introduced empathy, but up to that point it seemed a reasonable hypothetical model for autistic social skills.

Without theory, you can’t have practice. So I’m not downgrading the theory, abstract aspect.

I feel like adding anecdotal illustrations, in addition to presenting the theory, would prove useful for your readers.

I’m speaking of real-life social situations.

I believe everyone “masks,” to a certain extent. Neurotypicals have to restrain themselves from revealing their base emotions—just like autistic folks restrain themselves from revealing their autistic aspects.

In it's current state it's just getting stuff out there, I did include one concrete example though, with the bias in perception of volume. Frankly I don't know what more examples to put, I'm much better with the abstract stuff, but I'd gladly work with someone who has a better idea on that side. For a general audience more anecdotes would be great, but for the sort of publications I'd be shooting for getting all the math expressed would be the highest priority. I might be able to get into some economics journals just by finding the Nash equilibrium of a more specific form of the line game without even associating it with a more concrete context than I have here. As for now though I'm working on my thesis, which while also looking at the intersection of computer science and psychology is unrelated to this particular model.

To clarify, I'm not stating that masking doesn't exist, just that some phenomena currently explained by masking might be better explained by something else. The fact better cognitive empathy makes it easier to mask has been used to discredit many overlooked populations of autistic people, so it's worth looking at alternative explanations that aren't subject to that criticism.

Well, at when I introduced empathy I was moving away from describing autistic social skills in general and towards creating a hypothesis relating to a specific phenomenon, so I understand why you'd get lost at that point.