Session 11

Agenda

Welcome

Hello

Logistics

Topic of today

Module 2

Step 6: Causal Relationships and Systems Thinking, Part 1

Step 7: Causal Relationships and Systems Thinking, Part 2

Open questions

Closing

Topics of Today

Step 6 - Causal Relationships and Systems Thinking, Part 1

Systems thinking is an indispensable tool for working with complex systems, such as cryptoeconomic systems.

An important step in our system design process is to identify causalities. This process helps us understand how parts of the system can influence each other.

Identifying Causalities

The next step in our system design process is to identify causalities. This important process leads to an understanding of how different inputs or events will influence other parts and the overall state of the system, giving strong intuition about how the states may change over time.

This step is good for qualitative understanding. When we link causes and effects at this stage, it still does not tell us the magnitude of the relationship. We also need to do different types of quantitative modeling, usually later in the design phase.

How can we clearly define these causalities?

In systems thinking, a system is broken down into constituent parts, which are then connected by their relationships to one another. These relations can be modeled using a causal loop diagram.

There are four steps to creating a Causal Loop Diagram.

Step 1

Define Variables Present in the System

For each variable, we create a node (circle) representing that node.

Step 2

Assign Arrows Between the Variables

Arrows should go from the cause to the effect.

Step 3

Determine Sign of Cause

Attach a sign (+/-) to every arrow, reflecting whether there is a positive or negative impact.

Step 4

Recognize and Label Feedback Loops

Also put a sign in the middle of the diagram that represent the overall polarity of the feedback loop. A loop can be reinforcing or balancing.

This property is determined based on the amount of negative signs found in the loop.

An even number will mean that the loop is reinforcing, and an odd number means that the loop is balancing and will therefore stabilize itself.

The Benefits and Limitations of Causal Loop Diagrams

Causal loop diagrams are especially important in the discovery phase of the modeling process, since they so clearly reveal the constituent elements. However, such a diagram cannot display the amount of impact (positive or negative) one element has on another.

Further along in the process, such impacts will need to be quantified with defined metrics for this purpose.

Repeatedly talking through the loops guarantees that the story the diagram tells is consistent with reality. These diagrams are a thinking tool that will also ensure that no important causalities are neglected and that the whole story can be presented in a clear manner.

Like any tool, causal loop diagrams have limitations, and it's important to be aware of some risks:

1. Using and trusting the diagram without testing and simulation.

2. Failure to distinguish between information and non-information flow.

3. They account only for the feedback and not the dynamics.

4. Inability to represent system parameters, hidden loops, and non-linear relationships within the system.

Systems and Feedback Loops

It's important to understand the difference between open and closed systems, and the different kinds of feedback loops that occur in a closed system.

Step 1: Open Systems

In an open system, the inputs influence the outputs, but not vice versa.

Step 2: Closed System

In a closed system, the outputs can exert influence on the inputs, leading to feedback loops.  These loops are characterized in two types: balancing and reinforcing.

Step 3: 

Step 4:

Step 5: Balancing Feedback Loops

Negative feedback loops instead have stabilizing effects, helping to reach the desired state of the system. While these have stronger resilience towards shocks, they can sometimes cause systems to oscillate.

Analysis of an AMM from the Causal Loop Perspective

Let's apply the tools we're discussing to analysis of an Automated Market Maker. We can identify the following variables that may impact a particular Liquidity Pool:

Fees Charged By the Pool

Trading Volume in the Pool

Return on Investment for Liquidity Providers

Liquidity in the Pool

Amount of Slippage

Thinking verbally through the cause-and-effect relationships, we would have the following two scenarios:

"As fees go up, ROI for Liquidity Providers will also go up, which will lead to more liquidity, which will lead to less slippage, which would tend to lead more to trading volume."

"As fees go up, trading volume will tend go down, which will lead to less ROI for Liquidity Providers, which will lead to less liquidity, which will lead to higher slippage, which will lead to less trading volume."

One advantage of looking at cause-and-effect modeling through tools like Causal Loop Diagrams is that there are certain patterns that we learn to recognize.

One common pattern for balancing feedback loops is oscillation.

Let's take a moment to look at types of oscillation.

Types of Oscillation in Balancing Feedback Loops

There are four major types of oscillation we see in balancing feedback loops. Thinking about the type of behavior you expect to see from a system will help to make sure your representations of the system are helpful and accurate.

Step1:

Step 2:

Step 3:

Step 4:

Step 7 - Causal Relationships and Systems Thinking, Part 2

There are many types of diagrams used to represent systems. 
In addition to Causal Loop Diagrams, other types are Stock-and-Flow Diagrams and Block Diagrams.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Converting Causal Loop Diagrams to Stock-and-Flows

If we have done causal mapping, we can often convert Causal Loop Diagrams to Stock-and-Flow Diagrams. There is a well-established process for doing this, which we summarize from this article.

Identify the units of measurement for all variables in the Causal Loop Diagram.

Identify and create the stocks by looking at variables from the Casual Loop Diagram.

Develop flows between stocks. If a variable in the Causal Loop Diagram involves time or can be expressed as a rate, that is a clue that it could represent a flow. Another way to identify a flow is to look for variables that cause an increase or decrease in other variables.

Now, connect the flows to stocks and vice versa. Remember that a positive effect on the stock will be represented as an inflow, while a negative impact of the stock corresponds to an outflow. In some cases you may need to connect stocks to flow, this is necessary if the stock influences the flows through an information link.

Define the stocks and flows and check units.

Then you add and link any remaining CLD variables, if they were not already identified in previous steps. These are constant variables that does not change over time and also variables that are only representing calculations of stocks and flows. Connect these to the rest of the model and keep in mind that these variables cannot affect stocks. The diagram is now complete, but may need to be iterated to identify additional stocks and flows.

Another way to look at system dynamics is through the use of 
block diagrams.

Block Diagrams

Block diagrams are used to visualize control systems and provide comprehensive yet simple overview of the system. These diagrams serve as a summary of the system, as they provide information that can be used to define the state space and its transitions.

The main components of the block diagram are:

blocks

summing points

take-off points

Within blocks, transfer functions can be represented. These transfer functions theoretically model the output of (sub-)systems for all possible inputs.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Session 11

Agenda

Welcome

Hello

Logistics

Topic of today

Module 2

Step 6: Causal Relationships and Systems Thinking, Part 1

Step 7: Causal Relationships and Systems Thinking, Part 2

Open questions

Closing

Topics of Today

Step 6 - Causal Relationships and Systems Thinking, Part 1

Systems thinking is an indispensable tool for working with complex systems, such as cryptoeconomic systems.

An important step in our system design process is to identify causalities. This process helps us understand how parts of the system can influence each other.

Identifying Causalities

The next step in our system design process is to identify causalities. This important process leads to an understanding of how different inputs or events will influence other parts and the overall state of the system, giving strong intuition about how the states may change over time.

This step is good for qualitative understanding. When we link causes and effects at this stage, it still does not tell us the magnitude of the relationship. We also need to do different types of quantitative modeling, usually later in the design phase.

How can we clearly define these causalities?

In systems thinking, a system is broken down into constituent parts, which are then connected by their relationships to one another. These relations can be modeled using a causal loop diagram.

There are four steps to creating a Causal Loop Diagram.

Step 1

Define Variables Present in the System

For each variable, we create a node (circle) representing that node.

Step 2

Assign Arrows Between the Variables

Arrows should go from the cause to the effect.

Step 3

Determine Sign of Cause

Attach a sign (+/-) to every arrow, reflecting whether there is a positive or negative impact.

Step 4

Recognize and Label Feedback Loops

Also put a sign in the middle of the diagram that represent the overall polarity of the feedback loop. A loop can be reinforcing or balancing.

This property is determined based on the amount of negative signs found in the loop.

An even number will mean that the loop is reinforcing, and an odd number means that the loop is balancing and will therefore stabilize itself.

The Benefits and Limitations of Causal Loop Diagrams

Causal loop diagrams are especially important in the discovery phase of the modeling process, since they so clearly reveal the constituent elements. However, such a diagram cannot display the amount of impact (positive or negative) one element has on another.

Further along in the process, such impacts will need to be quantified with defined metrics for this purpose.

Repeatedly talking through the loops guarantees that the story the diagram tells is consistent with reality. These diagrams are a thinking tool that will also ensure that no important causalities are neglected and that the whole story can be presented in a clear manner.

Like any tool, causal loop diagrams have limitations, and it's important to be aware of some risks:

1. Using and trusting the diagram without testing and simulation.

2. Failure to distinguish between information and non-information flow.

3. They account only for the feedback and not the dynamics.

4. Inability to represent system parameters, hidden loops, and non-linear relationships within the system.

Systems and Feedback Loops

It's important to understand the difference between open and closed systems, and the different kinds of feedback loops that occur in a closed system.

Step 1: Open Systems

In an open system, the inputs influence the outputs, but not vice versa.

Step 2: Closed System

In a closed system, the outputs can exert influence on the inputs, leading to feedback loops.  These loops are characterized in two types: balancing and reinforcing.

Step 3: 

Step 4:

Step 5: Balancing Feedback Loops

Negative feedback loops instead have stabilizing effects, helping to reach the desired state of the system. While these have stronger resilience towards shocks, they can sometimes cause systems to oscillate.

Analysis of an AMM from the Causal Loop Perspective

Let's apply the tools we're discussing to analysis of an Automated Market Maker. We can identify the following variables that may impact a particular Liquidity Pool:

Fees Charged By the Pool

Trading Volume in the Pool

Return on Investment for Liquidity Providers

Liquidity in the Pool

Amount of Slippage

Thinking verbally through the cause-and-effect relationships, we would have the following two scenarios:

"As fees go up, ROI for Liquidity Providers will also go up, which will lead to more liquidity, which will lead to less slippage, which would tend to lead more to trading volume."

"As fees go up, trading volume will tend go down, which will lead to less ROI for Liquidity Providers, which will lead to less liquidity, which will lead to higher slippage, which will lead to less trading volume."

One advantage of looking at cause-and-effect modeling through tools like Causal Loop Diagrams is that there are certain patterns that we learn to recognize.

One common pattern for balancing feedback loops is oscillation.

Let's take a moment to look at types of oscillation.

Types of Oscillation in Balancing Feedback Loops

There are four major types of oscillation we see in balancing feedback loops. Thinking about the type of behavior you expect to see from a system will help to make sure your representations of the system are helpful and accurate.

Step1:

Step 2:

Step 3:

Step 4:

Step 7 - Causal Relationships and Systems Thinking, Part 2

There are many types of diagrams used to represent systems. 
In addition to Causal Loop Diagrams, other types are Stock-and-Flow Diagrams and Block Diagrams.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6:

Converting Causal Loop Diagrams to Stock-and-Flows

If we have done causal mapping, we can often convert Causal Loop Diagrams to Stock-and-Flow Diagrams. There is a well-established process for doing this, which we summarize from this article.

Identify the units of measurement for all variables in the Causal Loop Diagram.

Identify and create the stocks by looking at variables from the Casual Loop Diagram.

Develop flows between stocks. If a variable in the Causal Loop Diagram involves time or can be expressed as a rate, that is a clue that it could represent a flow. Another way to identify a flow is to look for variables that cause an increase or decrease in other variables.

Now, connect the flows to stocks and vice versa. Remember that a positive effect on the stock will be represented as an inflow, while a negative impact of the stock corresponds to an outflow. In some cases you may need to connect stocks to flow, this is necessary if the stock influences the flows through an information link.

Define the stocks and flows and check units.

Then you add and link any remaining CLD variables, if they were not already identified in previous steps. These are constant variables that does not change over time and also variables that are only representing calculations of stocks and flows. Connect these to the rest of the model and keep in mind that these variables cannot affect stocks. The diagram is now complete, but may need to be iterated to identify additional stocks and flows.

Another way to look at system dynamics is through the use of 
block diagrams.

Block Diagrams

Block diagrams are used to visualize control systems and provide comprehensive yet simple overview of the system. These diagrams serve as a summary of the system, as they provide information that can be used to define the state space and its transitions.

The main components of the block diagram are:

blocks

summing points

take-off points

Within blocks, transfer functions can be represented. These transfer functions theoretically model the output of (sub-)systems for all possible inputs.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 6: