This is Part I of a series of articles on mechanics of consensus.

Constructing reliable large-scale consensus is both the most important task we as humans face today and also the hardest one. If we don’t succeed at this, we will undoubtedly suffer and enact destruction everywhere — environmentally, socially, politically, and economically. The main goal of this work is to develop useful ways of thinking about consensus, to better understand its pitfalls, and to find successful strategies for building it.

What is consensus?

I define consensus as a reliable collective intention within a group of people to uphold and act upon a particular notion or plan. This definition is notably different from a more traditional understanding of consensus as universal agreement, often cited in literature on governance. This needs to be explained. Also in need of explanation is the concept of reliable collective intention. I will provide the necessary explanations shortly.

To better understand the scope of the above definition, let’s look at a few examples of consensus.

1. There is consensus that a paper rectangle of a certain kind holds a certain value. This is the basis of the notion of money and economic exchange.
2. There is consensus that, except in a few specific cases, a rule enacted through majority voting in the US Congress becomes a law in the US. There is a law (consensus) that murder is a crime and that police are empowered to use violence to prevent it and to punish it.
3. There is consensus that the word “dog” refers to a certain domestic animal that descended from another wild animal that, by consensus, is called “wolf”. The same animal in Spanish-speaking countries is, by consensus, called “perro”.
4. There is consensus with regards to the length a unit of one inch represents. Similarly, by consensus, a foot represents 12 inches.
5. There is consensus that we drive on the right side of the road and that the red traffic light means “stop”.
6. There is consensus regarding the borders that delineate one country (with its own multitude of consensus notions) from another. Such is, for example, the border between Canada and the US. There is a different consensus regarding what this specific border means for an indigenous Mohawk Nation, which is, by consensus, considered a “cross-border” nation that doesn’t recognize this border and who has unrestricted passage between the two countries.
7. Among a group of friends that are traveling together to a foreign country there is a consensus around what date they are traveling and where to.

These examples describe situations, notions, and laws which are specific to some group of people. Although many of these serve a useful purpose, none of them are universal, immutable, or inherent. In practice, consensus refers to the rules or actions enacted by people. It is inherently a social agreement.

Some examples refer to a kind of consensus typically referred to as a “social convention.” A convention is defined as a behavior (e.g. driving) or a perception (e.g. money) that is enacted repeatedly by a group of people. The repeated nature of conventions makes them a special class of consensus behaviors. As we will see shortly, both repeated and one-time situations share the same underlying dynamics: they belong to the same general phenomenon I call collectivity.

We also see from these examples that consensus is very different from universal agreement. We may concede to use inches to measure distances, but we by no means agree that we should, as the metric system is quite universally understood as better suited for engineering tasks. Similarly, we do have consensus around the laws that we enact but unless the 100% has voted “for” (which can never happen, unless you live in North Korea) there are clearly some who disagree with them.

Acting by consensus means acting together. We act by consensus because acting in a way that corresponds to the way others act is beneficial even if we think that it is somehow bad. In doing so we reap the benefits of coordinated action and avoid risks and drawbacks associated with solitary action.

Coordinated action is the answer to so-called coordination problems. Coordination problems are situations in which people must act in a corresponding fashion to achieve some common benefit that is not available to solitary or uncoordinated actors. Clearly, multiple people acting in coordination can move a large piece of furniture, build a large structure, hunt a large animal, protect each other from enemies, and so on. Without coordination none of these tasks are possible.

When we act together we take on tasks that are dangerous or expensive with the understanding that the coordinated nature of the action will mitigate the risks and expenses. For example, when hunting a large animal we come face-to-face with it, which is only safe in a well-organized group. Driving at 80 miles per hour is extremely dangerous if it is not done in coordination with other drivers.

Because of these risks it is only safe for us to act if we believe that others will carry out their part of the coordinated activity. But the same is true of others: they must be sure of us before they can act. So we can only be sure of others if we somehow know that they are sure of us. We can see that this argument can continue ad infinitum: I must be sure that you are sure that I am sure that… we will act.

This is the reliable collective intention that makes up consensus. Reliable refers to our assurance of another’s intention to act and whether it is sufficient for the risk at hand. Collective refers to the layers of upon layers of “I believe that he believes that she believes that … we will do this”. This is the game-theoretical concept of common knowledge, applied to intention.

Let’s pause here. Collectivity is very complex and warrants a deep dive. Let me explore some examples of what it means for a phenomenon to be collective.

The coordinated attack problem

This problem is heavily studied in literature related to formal analysis of computer protocols. It goes as follows (quoted from Reasoning About Knowledge by Fagin, et al.):

Two divisions of an army, each commanded by a general, are camped on two hilltops overlooking a valley. In the valley awaits the enemy. It is clear that if both divisions attack the enemy simultaneously they will win the battle, while if only one division attacks it will be defeated. As a result, neither general will attack unless he is absolutely sure that the other will attack with him. In particular, a general will not attack if he receives no messages. The commanding general of the first division wishes to coordinate a simultaneous attack (at some time the next day). The generals can communicate only by means of messengers. Normally, it takes a messenger one hour to get from one encampment to the other. However, it is possible that he will get lost in the dark or, worse yet, be captured by the enemy. Fortunately, on this particular night, everything goes smoothly. How long will it take them to coordinate an attack?

And the subsequent analysis:

Suppose that a messenger sent by General A reaches General B with a message saying “attack at dawn.” Should General B attack? Although the message was in fact delivered, General A has no way of knowing that it was delivered. A must therefore consider it possible that B did not receive the message (in which case B would definitely not attack). Hence A will not attack given his current state of knowledge. Knowing this, and not willing to risk attacking alone, B cannot attack based solely on receiving A’s message. Of course, B can try to improve matters by sending the messenger back to A with an acknowledgment. Imagine that the messenger is again successful and delivers the acknowledgment. When A receives this acknowledgment, can he then attack? A here is in a similar position to the one B was in when he received the original message. This time B does not know that the acknowledgment was delivered. Since B knows that without receiving the acknowledgment A will not attack, B cannot attack as long as he considers it possible that A did not receive the acknowledgment. Hence, A cannot attack before he ensures that B knows the acknowledgment has been delivered. […] Indeed, it is possible to show […] that no number of successful deliveries of acknowledgments to acknowledgments can allow the generals to attack. […]

The authors’ argument leads to the concept of common knowledge. Common knowledge is a state wherein a group of actors knows something, knows that they know it, knows that they know that they know it, and so on, ad infinitum. In the present situation, common knowledge is shown to be necessary for coordination to occur.

Common knowledge arises in the study of computer systems because knowledge (or, more generally, information) is what computer science is primarily focused on. In coordination of human activity it is more appropriate to speak about expectation and intention.

Intention and expectation are related. An expectation is a form of belief that some action will be performed by another person. An intention may be seen as an expectation applied to oneself. It is a belief that the one who intends will carry out the action being intended.

Let’s use the word collective with respect to intention and expectation to refer to the same principle as common in “common knowledge.” We posit that, rather than common knowledge, the generals must possess collective expectation and intention to act. Indeed, in order for General A to attack he must have a reasonable belief that General B will attack also. The same is true for General B and General A knows this. So in order for General A to attack he must also know that General B expects him to attack. Continued enough times this turns into a progression of higher order expectations of “A expects that B expects that A…”, ad infinitum. This collective intention is what we termed consensus.

Collective expectation and common (collective) knowledge are closely related. The fact that A knows the way B thinks leads A to understand that B must have a reasonable expectation of A acting before B can act. Moreover, the fact that A may expect B to act is predicated on A knowing that B wants to destroy the enemy and furthermore on the fact that B knows that A wants to destroy the enemy. Thus, it is the common knowledge of their mutual circumstances that gives rise to the generals’ need for common intention and expectation. It is their commonly known intention to destroy the enemy that allows for the consensus to occur.

The coordinated attack problem demonstrates that in order to reach consensus parties must use a communication method with certain special properties. Now, let us see how this can apply to real people.

Nonverbal signaling between people is critical to establishing a relationship between them. Nonverbal signals have meaning. In a face-to-face conversation, I am not only listening to you (that is, I know what you are saying) but also, through nonverbal signals you know that I am listening to you. Furthermore, you are not only saying something, but through nonverbal signals you let me know that you know that I am listening. This is the mutual indication of “I know that you know that…” which directly leads to establishing collectivity of our intentions and knowledge. Our understanding of consensus provides a clear explanation of why nonverbal signaling is and must be so important.

When we initially spoke about consensus we said that it is a “reliable collective intention.” Now we see that some highly risky situations require the intention to be extremely reliable. This is not universally so.

Consider the following situation. Alice and Bob are two people organizing a meeting (possibly a date). Let’s assume the meeting place is located midway between their homes, one hour from each. One hour is a long way to go and neither one of them wants to arrive at the meeting place only to find out that the other did not show up. So the argument for a reliable consensus goes along the same lines as the analysis of the coordinated attack problem. However, a one hour long journey is not the worst thing that can happen to someone and consequently mis-coordination — or a small chance of one — is an acceptable risk.

Indeed, in order to coordinate such a meeting Alice and Bob might exchange a few text messages, something like: Alice: “Meet at restaurant at 9?”, Bob: “Sure”, Alice: “Cool.” Because text messages are not perfectly reliable (one’s phone may run out of battery power or one may not be checking messages for a while) this has established only 3 levels of indirect intentionality: Alice intends to come, Bob knows that Alice intends to come, Alice knows that Bob knows that Alice intends to come. Also: Bob intends to come, Alice knows that Bob intends to come. This is far from a perfect collective intention, but it is entirely sufficient for the situation presented.

It would be rather different if Alice lived in Canada, Bob lived in Brazil and they were arranging a meeting in Paris. Intuitively we know this very well and would naturally be inclined to use a channel of communication that better supports collectivity (permits nonverbal communication), such as a telephone conversation or a video-chat. If forced to use an unreliable text-based system, we would have to have a much longer conversation. This is because we know (again, intuitively) that in order for coordination to be established to an extent sufficient to alleviate the now considerable risks of failure, a greater extent of collectivity must be established. We can do this by increasing the number of back-and-forth exchanges between us.

Driving, language and social convention

David Lewis wrote an in-depth study of social convention. Social convention per Lewis arises when people are faced with repeated coordination problems with multiple solutions.

Consider the coordination required in driving. It doesn’t matter which side we choose to drive on, as long as we all choose together. Once the choice is established, all we need is to stick by it for successful coordination to continue.

Language is another example of the same phenomenon. People must designate a specific word or idiom to mean each kind of object we face. Given our physiological abilities there is a very large possible set of sounds that a human vocal system can utter. From this set we must, together, choose one or a few sounds to mean every important feature of the physical world we live in. Thus, language is a confluence of a tremendous number of coordination problems each with a tremendous number of possible solutions.

The fact that language is a solution to a coordination problem implies that we can coordinate without communicating. Indeed, if this were not the case, then what means of communication would we use to coordinate our use of language in the first place?

Lewis writes:

Schelling has experimented with coordination problems in which the agents cannot communicate. His subjects know only that they share a common understanding of their problem — for instance, they may get instructions describing their problem and stating that everyone one gets the same instructions. It turns out that sophisticated subjects in an experimental setting can often do very well — much better than chance — at solving novel coordination problems without communicating. They try for a coordination equilibrium that is somehow salient: one that stands out from the rest by its uniqueness in some conspicuous respect. It does not have to be uniquely good; indeed, it could be uniquely bad. It merely has to be unique in some way the subjects will notice, expect each other to notice, and so on. If different coordination equilibria are unique in different conspicuous ways, the subjects will need to be alike in the relative importance they attach to different respects of comparison; but often they are enough alike to solve the problem.

How can we explain coordination by salience? The subjects might all tend to pick the salient as a last resort, when they have no stronger ground for choice. Or they might expect each other to have that tendency, and act accordingly; or they might expect each other to expect each other to have that tendency and act accordingly, and act accordingly; and so on. Or — more likely — there might be a mixture of these. Their first — and higher — order expectations of a tendency to pick the salient as a last resort would be a system of concordant expectations capable of producing coordination at the salient equilibrium.

If their expectations did produce coordination, it would not matter whether anyone really would have picked the salient as a last resort. For each would have had a good reason for his choice, so his choice would not have been a last resort.

Thus even in a novel coordination problem — which is an extreme case — the agents can sometimes obtain the concordant expectations they need without communicating. An easier, and more common, case is that of a familiar coordination problem without communication. Here the agents’ source of mutual expectations is precedent: acquaintance with past solved instances of their present a coordination problem.

A precedent can be seen as a collective phenomenon. Indeed, if we succeed in coordinating once, this fact becomes collective (common) knowledge: we each know that we have succeeded and we each know that we each know we have succeeded and so on. This, by itself, is not enough to form a collective intention to uphold a convention (consensus). After all, that some past action is commonly known to have been successful doesn’t necessarily translate into future intention. However, Lewis points out that we as people possess a tendency to follow precedent. If we are inclined to repeat actions that led to successful coordination and assume that others also do and that others assume that we do, and so on, then we have a mechanism that translates past precedent into future intention. I call this mechanism a collective tendency.

Collective here, once again, refers to the way in which a cognitive phenomenon, a tendency in this case, is known by everyone to hold, is known to be known to hold, and so on. A tendency to follow precedent must be collective in order for groups to reliably repeat behaviors when faced with the same situation repeatedly.

Competition

The last class of coordination problems that we will examine are situations that involve some kind of competition between participants. Competition arises when different solutions to coordination problems favor different participants.

Let’s say Alice and Bob want to meet. Of the two possible meeting places the Park is closest to Bob’s house while the Cafe is closer to Alice’s. Their primary motivation is to get together, so Bob would rather go with Alice to the Cafe then go to the Park alone and vice versa. The small competitive element means, however, that Bob prefers to meet in the Park while Alice wants to meet at the Cafe.

Let’s say a group of people engage in a construction project. Each is given a role — to carry cement, to lay bricks, to measure, to dig, etc. The nature of the project is such that everyone must fill a different role. There is no point for two people to bring building materials while nobody is actually laying the bricks. Distributing the roles is, then, a coordination problem with many different possible solutions. However, roles differ somewhat in the amount of effort they require. Carrying the bricks is more strenuous than laying them, which is in turn more strenuous than measuring, and so on. Consequently, while all participants’ main motivation is to complete the project, each has a marginal preference to exert less physical effort.

This type of coordination problem is where the difficulty in constructing reliable collective intention (consensus) is most pronounced. In these situations there always exists a class of participants that find themselves at a disadvantage relative to others. Having a reliable collective intention requires that these people join the consensus and are, furthermore, known to join the consensus and are, furthermore, known to be know to join the consensus and so on. Consensus breakdowns occur when the deeper layers of this structure are missing.

Consider two cars waiting to cross an intersection. Their primary motivation is to cross safely, which requires coordination between two possibilities: car 1 goes first, car 2 goes second; or car 2 goes first and car 1 goes second. Each driver wants to cross first — this is the element of competition. A solution where I cross first gives me a small advantage. The driver crossing second is at a disadvantage. While this other driver may be perfectly willing to cross second, I cannot proceed until I know this with some assurance.

Let’s say a group is hunting large game and must split into two subgroups: chasers and ambushers. Let’s say chasing is relatively safe, while ambushing is more dangerous. Those who take on the role of ambushers can be said to be in a disadvantaged role because of this relatively high risk. They might be perfectly willing to take on the risk and do the work, but until the chasers know this, their task carries a significant risk of expending physical effort to no good end.

These examples illustrate a general situation where consensus is required between parties that, essentially, disagree with each other as to what the best outcome is. Maintaining consensus in the presence of disagreement is the purpose of governance. In the case of drivers, governance presents itself in the form of a stop-sign and the rules we collectively follow: the one to come to the intersection first goes first. In other cases the governance process entails an authority which is well-known to be accepted by the community — one that can tell people to accept large risks or significant disadvantages.

Collectivity in summary

Collectivity is the bridge between individual cognition and group behavior. Even if I expect, believe, uphold, or value X, it only becomes a group expectation, belief, rule, or value if and when it acquires deeper levels of concordant perceptions between members of the group (I believe that you expect X, etc.) The property of collectivity may apply to a variety of cognitive states. It permits independent agents to form beliefs about the future actions of the rest of the group, referred to here as reliable expectations. Being able to accurately assess the intentions of others mitigates the risks and expenses of solitary action and so allows them to act in coordination.

Often collective states present themselves in a form of commonly accepted coordinating factors. There is a wide variety of such factors: cultural attitudes, social conventions, individual authority, etc. In all cases, however, a collective recognition of such factors is a necessary element of group behavior. A collective use of an observable external coordination factor allows people to independently make interdependent choices.

In almost all cases we perceive coordination factors to be external to ourselves. There are countless examples of this within cultural belief systems, where people refer to ancestors, God, stars or nature forces as external actors that have power over the group. But this can also be seen in modern social attitudes where we often perceive powers that control society as external, a “they” of one kind or another. People often refer to collective coordinating factors as “the way things are” or “the way we always do things”.

Such externalization is often a crucial piece of the puzzle in examining and understanding group behavior, which sometimes seems either irrational, unnecessary, or even disadvantageous for a group. What happens, however, is that we all believe something and know that we believe it and that makes this “something” into a coordinating factor. We perceive such factors to be of high importance because they allow us to act together. Anyone deviating from consensus created by such beliefs will incur the actual or perceived risks of acting on their own. In order to change such behaviors, we would have to change them together and simultaneously, which is hardly ever possible. This is the main reason why changing existing social structures is so difficult.

I conclude with some examples of collective phenomena. These are the attitudes, beliefs and dynamics that play into our ability to arrive at consensus under various situations.

1. Cultural myths, beliefs, and attitudes are collectively known. That they are cultural means precisely that we expect everyone to uphold them, expect everyone to expect everyone to uphold them and so on.
2. Biologically imposed attitudes. These are attitudes towards pain, pleasure, and death which we reasonably expect everyone to have and expect everyone to expect everyone to have and so on.
3. Psychological attitudes and reactions. These are attitudes and tendencies that we, similarly, expect to be collective. An example of such tendency is to repeat known behaviors, which we already saw as a major factor in constructing social norms.
4. Trust is a collective phenomenon. Trust is only then meaningful, when the one being trusted knows this and expects everyone to know this.
5. Social power is collective in that it is only meaningful if the entire group is known to respect it and is known to be known to respect it. Non-collective power is merely strength and is severely limited and expensive.
   Related to power is leadership. Leadership in its most crude form is simply a situation where a decision made by a single individual is collectively known to be consensus, such as in a hierarchical organization.

We have looked at consensus as a state in which a group of people is able to act in coordination. Consensus as a way to make group decisions through universal agreement could be naively regarded as a special case of this broader understanding. We see, however, that universal agreement may not even lead to consensus of action. Rather, what a group needs in order to act is collective intention. (See also a more academic account of this)

The ways we achieve collective intentionality can often seem irrational or counter-intuitive. Understanding the nature of collective states helps us think about these complex situations more productively. In the next article we will continue our exploration of this topic.

This concludes Part I of the Consensus Series. In Part II we will explore economic value as a consensus phenomenon.

(Alex Bulkin is a co-founder at CoinFund, a blockchain technology research firm and proprietary cryptoasset investment vehicle. CoinFund’s team brings together expertise in high technology, quantitative finance, private equity research, and social innovation research to generate insights into this exciting growth space. CoinFund provides consulting and research services to investors and companies interested in blockchain technology. Follow us on Twitter or join the discussion on our open community Slack.)