Dec 15, 2010
The Idea of Fairness
If we were asking questions of the children in a classroom, we wouldn't ask just one person over and over, right? We would want to spread the questioning around. Or if we were running a class debate, we wouldn't let just one student speak for the entire session, right? We would want to ensure that a number of different voices were heard.
We wouldn't design our tests so that only one person could pass. We wouldn't organize our library so that books were only available to one student. In a social endeavour like learning, there is a principle of equity at work. Though we may not always follow it perfectly or completely, we tend to try to make our classrooms fair: fairness in learning, fairness in assessment, fairness in reward.
There is growing recognition that there might be something to this principle. One significant observation from the recently released international assessment of student learning, PISA, is that countries that address social inequalities demonstrate better learning outcomes, while countries that ignore them remain stationary or begin to drop in the rankings.
The United States came out only in the middle of the PISA rankings. Why? As Kevin Carey wrote, "One of the reasons Canada is our biggest trading partner is that it has a stable democratic government and a highly-developed economy... And if you run down the list of our closest higher education competitors -- Finland, New Zealand, Norway, Japan -- one can make similar observations. By contrast, none of our competitors are destabilizing their respective regions or miring UN troops in internecine warfare or letting large segments of their populations starve. That's probably not a coincidence."
As the PISA authors noted, poverty itself wasn't the problem. A country could be rich or poor and do more or less well in the rankings. What mattered was the division of wealth in the society, and correspondingly, the sense that "we're all in this together." Even conservative authors, such as the National Post's Jonathan Kay, are beginning to see this. He writes, "creeping income inequality is a menace to the economies and social fabric of western countries, and that some form of redistributionist policies eventually are going to be a necessary antidote."
All of that said, while it is all very well to appeal to some sort of principle of fairness, the fact remains that there is no widely accepted economy of fairness. Usually they are thought of as opposites. This is important to underline. If a person simply does not care about fairness, and does not think that it, as a principle, has any causal efficacy, then appeals to the principle will fail. "Life is unfair," he will respond, with apparently equal empirical support.
Efforts to ground the principle in moral or philosophical arguments are equally futile. We frequently hear, for example, appeals to the Golden Rule as the common moral foundation of society, the guarantee that ensures fairness. But in practice, it does no such thing: the rich are perfectly happy to have people 'vote with their dollars'; the strong allow that people should fight for their principles; the intelligent are always willing to let disputes be resolved through a battle of wits.
The Golden Rule allows the powerful to legitimize their power, and does not promote fairness at all. Applied a certain way, it puts everybody into the position of the powerful and then asks them to derive a mechanism for decision. Creating an artificial blindness, in an attempt to find a common understanding of fairness, as in the case of John Rawls's 'veil of ignorance', does not, contrary to his argument, produce a principle of justice as fairness. People don't vote according to their situation, they vote according to their aspirations.
If there are grounds for fairness, then, what are those grounds? The fact that inequity actually produces harmful results -- that it reduces educational outcomes, and lowers the health of a society -- provides some clue. Inequality is some sort of structural deficit that operates independently of the attitudes of the people living in such a system, while fairness is, by contrast, a structural virtue. But how can we cash that out?
Network stability and network death
In a previous post, "Two Kinds of Knowledge," I argued that both personal knowledge and social knowledge are based on organizations of entities, whether the connections are between neural cells or between people or between theories, methods, feelings, values and skills. Viewing knowledge and society as a network (as opposed to something with inherent qualities, or as opposed to something knowable as a quantity or mass) provides us with a certain perspective on it.
We could say a great deal about the idea of knowledge and society as network, but I would like to focus on one facet for now: network stability and network death.
The idea of a network is that it is composed of many discrete entities, and that these entities are connected together. There are different ways to talk about networks. We might, as when we talk about the Internet, talk about pages (or people) and links. Or we might, if we are using graph theory, talk about nodes and edges. Or we might, if we are talking about artificial intelligence, talk about neurons and connections. No matter what vocabulary we use, the underlying principles are the same.
One principle observed in our largest network, the Internet, is the phenomenon of the 'power law'. If we count the number of links each website has, and then line up all the websites one by one, ordered by the number of links it has, we get a characteristic graph. On the left, we have what might be called the 'big spike', consisting of a few websites that have millions or even billions of links pointing to it -- sites like Google, Facebook, Yahoo and Microsoft. On the right we see everybody else, the 'long tail' of millions of websites with only a few links pointing to them.
We get the sense, reading about the power law, that it is natural and common. And if we read the sociology and mathematics behind social network and graph theory, we see that a power law emerges of its own accord when we build networks randomly. And when we analyze the creation of these networks, we understand that it is a result of preferential attachment: people want to link to a site that already has links. And this phenomenon of 'the rich get richer' seems to hold in networks generally. It makes more sense to invest in people who are already wealthy, because they are more likely to succeed. It makes sense to give new knowledge to the person who already knows the most, because they can make the best use of it.
The shape of the network that forms as a result of preferential attraction is the now-familiar hub-and-spoke network. When we look at maps of the Internet, we see hubs and spokes. If we were to map the history of philosophy, we would see some great hubs, like Rene Descartes and Immanuel Kant, and spokes of lesser philosophers surrounding them. If we were to map the network of airlines, or bus terminals, or urban geography, we see again this form of hub and spoke organization. And everywhere we see a hub-and-spoke network, we see a power law: the hubs constitute the big spikes, and everything else constitutes the long tail.
The problem with the hub-and-spoke network is that it is less stable. Let me be clear: if it is the target of random failures, then it is more stable, because a random failure is not very likely to hit a hub, and with a little redundancy the network can be protected from the failure of a single hub. But if a hub-and-spoke network is subject to a directed attack, or if a once-in-a-lifetime event takes out a single point of failure, it will collapse completely. If the hubs are corrupted, the network becomes corrupted. Communication between the nodes will cease. A living network can adapt, can change, can learn, and can grow, can resist corruption. But in a dead network, there is no communication taking place between the nodes. There is organization, but it is static and inert.
A stable network, therefore, is one that resists failure at the hubs. It is one that distributes the central function performed by the hub across a larger number of nodes. If we draw a map of such a network, it looks like a mesh or a grid. If we graph the connectivity of such a network, the big spike disappears and the importance of each entity in the long tail is increased a little. In such a network, there is no single point of failure. If one node becomes corrupted, the vigour of the nodes surrounding it restrain that corruption. Communication continues, the network grows, adapts and learns. It remains living.
By fairness, then, I mean the set of principles that tend to move knowledge or society to a more mesh-like, less hub-and-spoke-like, organization. I mean mechanisms that limit the growth of entities in the big spike and augment the importance of entities in the long tail. Intuitively, we talk about, say, giving each entity a relatively equal number of links, or an equitable voice, or a degree of power. But scientifically, methodologically, we mean the principles that promote this result, as a means to ensuring network stability.
The Principles of Democracy
There are two major ways to transform a hub-and-spoke network into a mesh network. The first is to limit the growth of the big spike. The second is to augment the growth of the long tail. In practice, the first amounts to the creation of structural, or syntactic, limitations. A syntactic principle. And the second amounts to intentional, or semantic, empowerments. A semantic principle.
If we look at networks in physical systems, such as airports, bus stations, forests and friends, we do not see the prevalence of the big spike. True, some airports are more important than others -- but there is a limit to how important the large airports can get, because you can only fly so many planes in and out of the airport, and you can only travel a certain distance to take a flight. There are tall trees and short trees, but one tree is not a million times taller than its neighbor, because there is a limit to how tall a tree can grow. There's a limit to the number of (real) friends you can have.
The syntactic principles of democracy work in the same way. They are physical limits created by the construction of the network. I first outlined these principles in a presentation in Palermo five years ago (though to be sure they are not unique to me). Networks should be decentralized. They should be distributed. Communications between entities should be disintermediated. Components of the network should not be dependent on each other; structures should be dis-integrated. Control should not be imposed one one entity from another. The network should be dynamic and changeable. And the network should be global; silos should be desegregated.
These principles can be implemented in a network structure in a variety of ways. In a legislature, the limitation of one vote to each person is a syntactic principle. In a financial network, the imposition of taxation and tariffs work in the same way. In a sport, we place limits on the number of players each team can field. In a highway system, we limit the width of a road and create alternative routes to create a variety of options.
These principles have already been applied, to some degree at least, to the education system. School systems are typically decentralized, with control residing in regional school boards or even local schools. The system is distributed; there is not a central school or university, but rather, smaller entities spread across a country or a city. Schools or universities are typically independent of one another; students of one school do not have to attend a certain university, and students at a university do not have to come from a certain school. Each has only limited influence over the management, standards and curriculum of the other. And schools are not segregated, nor organized into stand-alone clusters.
But syntactic principles are not enough. Simply limiting the growth of certain nodes is insufficient. If individual nodes have no resistance to damage or corruption spreading from other nodes, it doesn't matter how the network is structured. Networks need not only to be resistant to structural failure, they need also to be able to grow. There is therefore also needed the empowerment of individual entities in the network. This is the semantic principle.
To my mind, there are four elements to the semantic principle, each with wide-ranging and practical implications.
Autonomy -- each entity in a network should employ its own internal mechanisms, its own criteria and its own principles, in the governance of its own actions, including the assessment and management of incoming signals. Autonomy creates the capacity for judgement and resistance. It ensures that a signal propagates only if it satisfies a wide range of assessments, rather than a single, and potentially fallible, test.
In the education system, programs and resources should be structured so as to maximize autonomy. Wherever possible, learners should be guided, and able to guide themselves, according to their own goals, purposes, objectives or values. It is a recognition that, insofar as a person shares values with other members of a community, and associates with those members, it is a sharing freely undertaken, of their own volition, based on the evidence, reason and beliefs they find appropriate.
Diversity -- the entity is composed of many different entities, rather than many copies of the same type of entity; minimally, each entity has its own set of connections and inputs, creating a unique perspective, rather than the same set of connections and inputs as the others. This ensures a variety of perspectives, a variety of points of view, and therefore a more multi-dimensional and reliable perception of phenomena.
In the education system resources should be structured so as to maximize diversity. The intent and design of such a system should not be to in some way make everybody the same, but rather to foster creativity and diversity among its members, so that each person in a society instantiates, and represents, a unique perspective, based on personal experience and insight, constituting a valuable contribution to the whole.
Openness -- the network should have inputs and outputs, content should flow freely through the system, constrained only by the individual decisions of the entities, and entities themselves should flow freely into and out of connective relationships with others. Openness enables the possibility of perception by the network, and fluidity of connection enables the possibility of learning and adaptation.
The system of education and educational resources should be structured so as to maximize openness. People should be able to freely enter and leave the system, and there ought to be a free flow of ideas and artifacts within the system. This is not to preclude the possibility of privacy, not to preclude the possibility that groups may wish to set themselves apart from the whole; openness works both ways, and one ought to be able to opt out as well as in. But it is rather to say that the structure of the system does not impede openness, and that people are not by some barrier shut out from the system as a whole.
Interactivity -- networks should adapt and grow by means of interactions between its members. Interactivity is the creation of knowledge, not the propagation of knowledge. Networks that support and sustain interactivity are able to learn; networks that limit and stifle interaction are unable to learn.
The system of education and educational resources should be structured so as to maximize interactivity. This is a recognition both that learning results from a process of immersion in a community or society, and second that the knowledge of that community or society, even that resulting from individual insight, is a product of the cumulative interactions of the society as a whole. Jut as a language represents the collective wisdom of a society, so also an insight represented in that language is based on that collective insight.
Much more could be said of these four elements, of course, and what has been described in this article is just a sketch, a framework for understanding the elements of learning theory within a wider context. And for the purpose of the present discussion, what we have done is not only to highlight the importance of fairness and equity in education, but also to explain the role of fairness and equity through an understanding of network stability and network death, and to approach a definition of fairness and equity, through a description of the mechanisms that enable them and the structural and semantic changes they engender.
Fairness and equity are not just things that are nice to have if we can afford them. They are the foundation of prosperity in a society, the elements that help a society learn and keep a society healthy. To the extent we abandon fairness and equity, we abandon society itself, and any of the benefits we as individuals draw from it in turn.
If we were asking questions of the children in a classroom, we wouldn't ask just one person over and over, right? We would want to spread the questioning around. Or if we were running a class debate, we wouldn't let just one student speak for the entire session, right? We would want to ensure that a number of different voices were heard.
We wouldn't design our tests so that only one person could pass. We wouldn't organize our library so that books were only available to one student. In a social endeavour like learning, there is a principle of equity at work. Though we may not always follow it perfectly or completely, we tend to try to make our classrooms fair: fairness in learning, fairness in assessment, fairness in reward.
There is growing recognition that there might be something to this principle. One significant observation from the recently released international assessment of student learning, PISA, is that countries that address social inequalities demonstrate better learning outcomes, while countries that ignore them remain stationary or begin to drop in the rankings.
The United States came out only in the middle of the PISA rankings. Why? As Kevin Carey wrote, "One of the reasons Canada is our biggest trading partner is that it has a stable democratic government and a highly-developed economy... And if you run down the list of our closest higher education competitors -- Finland, New Zealand, Norway, Japan -- one can make similar observations. By contrast, none of our competitors are destabilizing their respective regions or miring UN troops in internecine warfare or letting large segments of their populations starve. That's probably not a coincidence."
As the PISA authors noted, poverty itself wasn't the problem. A country could be rich or poor and do more or less well in the rankings. What mattered was the division of wealth in the society, and correspondingly, the sense that "we're all in this together." Even conservative authors, such as the National Post's Jonathan Kay, are beginning to see this. He writes, "creeping income inequality is a menace to the economies and social fabric of western countries, and that some form of redistributionist policies eventually are going to be a necessary antidote."
All of that said, while it is all very well to appeal to some sort of principle of fairness, the fact remains that there is no widely accepted economy of fairness. Usually they are thought of as opposites. This is important to underline. If a person simply does not care about fairness, and does not think that it, as a principle, has any causal efficacy, then appeals to the principle will fail. "Life is unfair," he will respond, with apparently equal empirical support.
Efforts to ground the principle in moral or philosophical arguments are equally futile. We frequently hear, for example, appeals to the Golden Rule as the common moral foundation of society, the guarantee that ensures fairness. But in practice, it does no such thing: the rich are perfectly happy to have people 'vote with their dollars'; the strong allow that people should fight for their principles; the intelligent are always willing to let disputes be resolved through a battle of wits.
The Golden Rule allows the powerful to legitimize their power, and does not promote fairness at all. Applied a certain way, it puts everybody into the position of the powerful and then asks them to derive a mechanism for decision. Creating an artificial blindness, in an attempt to find a common understanding of fairness, as in the case of John Rawls's 'veil of ignorance', does not, contrary to his argument, produce a principle of justice as fairness. People don't vote according to their situation, they vote according to their aspirations.
If there are grounds for fairness, then, what are those grounds? The fact that inequity actually produces harmful results -- that it reduces educational outcomes, and lowers the health of a society -- provides some clue. Inequality is some sort of structural deficit that operates independently of the attitudes of the people living in such a system, while fairness is, by contrast, a structural virtue. But how can we cash that out?
Network stability and network death
In a previous post, "Two Kinds of Knowledge," I argued that both personal knowledge and social knowledge are based on organizations of entities, whether the connections are between neural cells or between people or between theories, methods, feelings, values and skills. Viewing knowledge and society as a network (as opposed to something with inherent qualities, or as opposed to something knowable as a quantity or mass) provides us with a certain perspective on it.
We could say a great deal about the idea of knowledge and society as network, but I would like to focus on one facet for now: network stability and network death.
The idea of a network is that it is composed of many discrete entities, and that these entities are connected together. There are different ways to talk about networks. We might, as when we talk about the Internet, talk about pages (or people) and links. Or we might, if we are using graph theory, talk about nodes and edges. Or we might, if we are talking about artificial intelligence, talk about neurons and connections. No matter what vocabulary we use, the underlying principles are the same.
One principle observed in our largest network, the Internet, is the phenomenon of the 'power law'. If we count the number of links each website has, and then line up all the websites one by one, ordered by the number of links it has, we get a characteristic graph. On the left, we have what might be called the 'big spike', consisting of a few websites that have millions or even billions of links pointing to it -- sites like Google, Facebook, Yahoo and Microsoft. On the right we see everybody else, the 'long tail' of millions of websites with only a few links pointing to them.
We get the sense, reading about the power law, that it is natural and common. And if we read the sociology and mathematics behind social network and graph theory, we see that a power law emerges of its own accord when we build networks randomly. And when we analyze the creation of these networks, we understand that it is a result of preferential attachment: people want to link to a site that already has links. And this phenomenon of 'the rich get richer' seems to hold in networks generally. It makes more sense to invest in people who are already wealthy, because they are more likely to succeed. It makes sense to give new knowledge to the person who already knows the most, because they can make the best use of it.
The shape of the network that forms as a result of preferential attraction is the now-familiar hub-and-spoke network. When we look at maps of the Internet, we see hubs and spokes. If we were to map the history of philosophy, we would see some great hubs, like Rene Descartes and Immanuel Kant, and spokes of lesser philosophers surrounding them. If we were to map the network of airlines, or bus terminals, or urban geography, we see again this form of hub and spoke organization. And everywhere we see a hub-and-spoke network, we see a power law: the hubs constitute the big spikes, and everything else constitutes the long tail.
The problem with the hub-and-spoke network is that it is less stable. Let me be clear: if it is the target of random failures, then it is more stable, because a random failure is not very likely to hit a hub, and with a little redundancy the network can be protected from the failure of a single hub. But if a hub-and-spoke network is subject to a directed attack, or if a once-in-a-lifetime event takes out a single point of failure, it will collapse completely. If the hubs are corrupted, the network becomes corrupted. Communication between the nodes will cease. A living network can adapt, can change, can learn, and can grow, can resist corruption. But in a dead network, there is no communication taking place between the nodes. There is organization, but it is static and inert.
A stable network, therefore, is one that resists failure at the hubs. It is one that distributes the central function performed by the hub across a larger number of nodes. If we draw a map of such a network, it looks like a mesh or a grid. If we graph the connectivity of such a network, the big spike disappears and the importance of each entity in the long tail is increased a little. In such a network, there is no single point of failure. If one node becomes corrupted, the vigour of the nodes surrounding it restrain that corruption. Communication continues, the network grows, adapts and learns. It remains living.
By fairness, then, I mean the set of principles that tend to move knowledge or society to a more mesh-like, less hub-and-spoke-like, organization. I mean mechanisms that limit the growth of entities in the big spike and augment the importance of entities in the long tail. Intuitively, we talk about, say, giving each entity a relatively equal number of links, or an equitable voice, or a degree of power. But scientifically, methodologically, we mean the principles that promote this result, as a means to ensuring network stability.
The Principles of Democracy
There are two major ways to transform a hub-and-spoke network into a mesh network. The first is to limit the growth of the big spike. The second is to augment the growth of the long tail. In practice, the first amounts to the creation of structural, or syntactic, limitations. A syntactic principle. And the second amounts to intentional, or semantic, empowerments. A semantic principle.
If we look at networks in physical systems, such as airports, bus stations, forests and friends, we do not see the prevalence of the big spike. True, some airports are more important than others -- but there is a limit to how important the large airports can get, because you can only fly so many planes in and out of the airport, and you can only travel a certain distance to take a flight. There are tall trees and short trees, but one tree is not a million times taller than its neighbor, because there is a limit to how tall a tree can grow. There's a limit to the number of (real) friends you can have.
The syntactic principles of democracy work in the same way. They are physical limits created by the construction of the network. I first outlined these principles in a presentation in Palermo five years ago (though to be sure they are not unique to me). Networks should be decentralized. They should be distributed. Communications between entities should be disintermediated. Components of the network should not be dependent on each other; structures should be dis-integrated. Control should not be imposed one one entity from another. The network should be dynamic and changeable. And the network should be global; silos should be desegregated.
These principles can be implemented in a network structure in a variety of ways. In a legislature, the limitation of one vote to each person is a syntactic principle. In a financial network, the imposition of taxation and tariffs work in the same way. In a sport, we place limits on the number of players each team can field. In a highway system, we limit the width of a road and create alternative routes to create a variety of options.
These principles have already been applied, to some degree at least, to the education system. School systems are typically decentralized, with control residing in regional school boards or even local schools. The system is distributed; there is not a central school or university, but rather, smaller entities spread across a country or a city. Schools or universities are typically independent of one another; students of one school do not have to attend a certain university, and students at a university do not have to come from a certain school. Each has only limited influence over the management, standards and curriculum of the other. And schools are not segregated, nor organized into stand-alone clusters.
But syntactic principles are not enough. Simply limiting the growth of certain nodes is insufficient. If individual nodes have no resistance to damage or corruption spreading from other nodes, it doesn't matter how the network is structured. Networks need not only to be resistant to structural failure, they need also to be able to grow. There is therefore also needed the empowerment of individual entities in the network. This is the semantic principle.
To my mind, there are four elements to the semantic principle, each with wide-ranging and practical implications.
Autonomy -- each entity in a network should employ its own internal mechanisms, its own criteria and its own principles, in the governance of its own actions, including the assessment and management of incoming signals. Autonomy creates the capacity for judgement and resistance. It ensures that a signal propagates only if it satisfies a wide range of assessments, rather than a single, and potentially fallible, test.
In the education system, programs and resources should be structured so as to maximize autonomy. Wherever possible, learners should be guided, and able to guide themselves, according to their own goals, purposes, objectives or values. It is a recognition that, insofar as a person shares values with other members of a community, and associates with those members, it is a sharing freely undertaken, of their own volition, based on the evidence, reason and beliefs they find appropriate.
Diversity -- the entity is composed of many different entities, rather than many copies of the same type of entity; minimally, each entity has its own set of connections and inputs, creating a unique perspective, rather than the same set of connections and inputs as the others. This ensures a variety of perspectives, a variety of points of view, and therefore a more multi-dimensional and reliable perception of phenomena.
In the education system resources should be structured so as to maximize diversity. The intent and design of such a system should not be to in some way make everybody the same, but rather to foster creativity and diversity among its members, so that each person in a society instantiates, and represents, a unique perspective, based on personal experience and insight, constituting a valuable contribution to the whole.
Openness -- the network should have inputs and outputs, content should flow freely through the system, constrained only by the individual decisions of the entities, and entities themselves should flow freely into and out of connective relationships with others. Openness enables the possibility of perception by the network, and fluidity of connection enables the possibility of learning and adaptation.
The system of education and educational resources should be structured so as to maximize openness. People should be able to freely enter and leave the system, and there ought to be a free flow of ideas and artifacts within the system. This is not to preclude the possibility of privacy, not to preclude the possibility that groups may wish to set themselves apart from the whole; openness works both ways, and one ought to be able to opt out as well as in. But it is rather to say that the structure of the system does not impede openness, and that people are not by some barrier shut out from the system as a whole.
Interactivity -- networks should adapt and grow by means of interactions between its members. Interactivity is the creation of knowledge, not the propagation of knowledge. Networks that support and sustain interactivity are able to learn; networks that limit and stifle interaction are unable to learn.
The system of education and educational resources should be structured so as to maximize interactivity. This is a recognition both that learning results from a process of immersion in a community or society, and second that the knowledge of that community or society, even that resulting from individual insight, is a product of the cumulative interactions of the society as a whole. Jut as a language represents the collective wisdom of a society, so also an insight represented in that language is based on that collective insight.
Much more could be said of these four elements, of course, and what has been described in this article is just a sketch, a framework for understanding the elements of learning theory within a wider context. And for the purpose of the present discussion, what we have done is not only to highlight the importance of fairness and equity in education, but also to explain the role of fairness and equity through an understanding of network stability and network death, and to approach a definition of fairness and equity, through a description of the mechanisms that enable them and the structural and semantic changes they engender.
Fairness and equity are not just things that are nice to have if we can afford them. They are the foundation of prosperity in a society, the elements that help a society learn and keep a society healthy. To the extent we abandon fairness and equity, we abandon society itself, and any of the benefits we as individuals draw from it in turn.
