The connectivity effect: Increasingly entangled in a web of issues

Indecisive 2

Too connected: Too many incoming signals complicate decision making, lead to confusion, and reluctance to take decisions (Figure: Roy Lichtenstein).

In my articles I now and then refer to the high connectivity regime of international orders, and to the connectivity effect.

In this article I explain the workings of the connectivity effect.

The connectivity effect is related to the phenomenon that due to increasing connectivity, incoming signals loose significance.

States are integral parts of issue networks (issues states have an interest in, that also produce tensions) and also experience at a certain point – the tipping point of international orders – a connectivity effect, when incoming signals – including threats – loose significance, because of the increasing number of issues these states are connected to (are integral parts of).

The connectivity effect has two important consequences: Because of the connectivity effect (1) states become increasingly stable, and (2) the release of tensions through non-systemic wars becomes increasingly problematic.

Despite their complexity, war decisions of states in fact qualify as ‘simple’ binary decisions: Ultimately, a state decides ‘to go to war‘ or ‘not to go to war‘.

 

switch
A war decision is a binary decision: War, ‘On’ or No war, ‘Off’. (Source)
Carrier, deployment Korea

A US carrier strike group now deploys towards the Korean Peninsula: President Trump decides to attack North Korea, or not.

States can be considered nodes in a network of states and issues. States – nodes in this network – can be depicted as binary switches: ‘On‘ when states to decide to go to war, and ‘Off‘ when states decide not to go to war.

States make their own considerations and ‘calculations’ regarding war decisions and take the positions – the switches – of other states into consideration.

States (mostly implicitly) use decision thresholds that ‘define’ when they switch from ‘On‘ (war) to ‘Off‘ (no war) to a positive war decision, and vice versa.

The workings of the connectivity effect can be explained with the following example:

Let’s assume a state switches to a positive war decision when a fraction of 0.6 (six out of ten) connected states (that are connected to the same issue) are switched to ‘On‘ (war). 0.6 is the decision threshold of the state. In case their are ten connections of which 5 are switched to ‘On‘,  the switch to ‘On‘ of one more state will cause the state in question to switch also to a positive war decision (‘On‘).

However, when their are not ten but 100 connections, and the same decision threshold is applied (0.6), the switch of an additional (connected) state to ‘On‘ (war) will have no effect: The fraction of ‘On‘-connections now increases from 0.50 to 0.51, but the decision threshold (0.60) is not reached.

This example explains the connectivity effect: In case of increasing connectivity, the effect of incoming signals decreases (an effect you probably also noticed, when your twitter and facebook connectivity increased).

The state in the example, in fact becomes more ‘stable’.

Watts in a series of simulations with binary networks shows that the connectivity and thresholds these nodes apply in a binary network, to a high degree determine the network’s cascade dynamics (size and frequency). Cascades in Watts’ network can be compared with non-systemic wars in the System. As is the case with Watt’s network, connectivity also is the driver of the System.

The connectivity-effect in the System concerns the network of states and issues. At a certain point during the development of an international order, the connectivity-effect ‘kicks in‘ and states in the network become more stable. I defined this point (moment) as the tipping point of the international order.

When the tipping point is reached, the average size of non-systemic wars starts decreasing (size defined as the number of Great Powers that participate in a war as a fraction of the total number of Great Powers in the System, at that point in time.). Tipping points can be visually identified in graphs that show the development of the average sizes of wars.

 

pnas-fig-6

Tipping points can be identified.

To test that these are not artificial constructs, I checked the consistency of these observations as follows: As I explained, it is possible to identify several highly consistent patterns in the war dynamics of the System, during the period 1495-1945. Four cycles – each consisting of a relatively stable period (when an international order is in place), followed by a systemic war – can be identified. During the first three international orders, a tipping point can be identified (1514, 1774, 1856); for the fourth international order (1918-1939) this is not possible, because the System only produced two non-systemic wars.

It is now possible to identify for each international order two ‘war clusters‘, a low connectivity war cluster in which non-systemic wars before the tipping point are included, and a high connectivity war cluster, in which non-systemic wars following the tipping point are included. It is possible to define six war clusters (3 x 2), during the period 1495-1945.

In below figure the average size of war clusters (non-systemic wars, including two Great Powers) are shown. The figure shows that the average size of non-systemic wars during low connectivity clusters, is in all three cases larger than the average size of non-systemic wars during high connectivity clusters (of the same international order) . Furthermore, the overall size of wars included in the successive war clusters decreases also very regularly, as is to be expected.

war clusters dev

The average sizes of war clusters develop very regularly, consistent with other patterns, and underlying mechanisms that are identified (data from Levy).

The problem is that the tensions and issues in the System still increase when the tipping point is reached, and that their release is increasingly hindered as a consequence of the connectivity effect (the increasing inability of the System to produce non-systemic wars).

Once the tipping point is reached, the buildup of tensions and issues  accelerates, because tensions and (unsolved) issues increasingly ‘feed on‘ – reinforce– each other.

The accumulation of tensions and issues is not without effect: Issues become increasingly connected, and a massive ‘underlying’ cluster of issues forms and percolates the System. At a certain point, the System becomes critical, and at that point a local event or incident produces a system-wide cascade of tension releases, a systemic war. In case of criticality, the correlation length of the System has become one, and cascades (wars) can no longer stay local, but reverberate through the (critical) system.

The decreasing average size of non-systemic wars, once the tipping point is reached, – the increasing stability of states in the network – can be misleading; not only for politicians and citizens of states but also for historians, even in hindsight.

Until now, historians try to make sense out of the First World War (the third systemic war, 1914-1918), and suggest that this war was a coincidence and could have been avoided (see for example “The Sleepwalkers, How Europe went to war in 1914“, by C, Clark). That is however, a big and persistent misunderstanding.

 

Rogers, Gilbert, 1881-1956; Gassed: 'In arduis fidelis'

Gassed: ‘In arduis fidelis’ by Gilbert Rogers (1919). No, the First World War also was not an accident. The period of relative stability that preceded the First World War, was the result of the connectivity effect, and until now is not understood by historians.

With the insights provided by this research the third – as well as the other – systemic wars could have been predicted, simply by analysing the development of the average sizes of wars. The increasing ‘stability’ of states once the tipping point is reached, is the proverbial calm before the storm.

(Even) If the United States refrains from an attack on North Korea, that ‘Off‘ decision would not be a sign that the risk for a systemic crises is averted, to the contrary. Such a decision can be attributed to the high connectivity effect: As I explained in other articles, the current international order is since 2011 in its high connectivity regime, and increasingly restricted in its ability to release tensions and solve issues.

The intensifying rivalries – with or without an attack on North Korea – between the US, China and Russia, etc. are still not resolved, and only intensify.

 

At this stage, tensions are no longer ‘only‘ about a specific issue, but increasingly linked to other issues and tensions; Issues and tensions are increasingly about the now obsolete international order, which almost collapses under the weight of its own contradictions.