Variables, Signals, and Proxies

By the end of this lesson, you will be able to...

• Separate a target condition from the signals and proxies used to observe it.

• Explain why a metric can be useful evidence without being the thing that matters.

• Review a decision rule for proxy failure and choose a better set of signals.

Idea in one sentence: We often measure a visible stand-in for an important condition, so we must keep the stand-in separate from the thing we care about.

Core Insight

Imagine the public library from the previous lesson. The manager wants to know whether families can get timely help in the children's room on Saturday.

The manager cannot directly read “timely help” from the building. It is a condition people experience. So the team chooses numbers:

• average waiting time;
• number of people in the queue;
• requests handled per hour;
• complaints about the desk.

At first, this seems like progress. Numbers are easier to compare than a vague question about experience.

Then the team sets a rule:

If the average wait stays below ten minutes, staffing is adequate.

The number falls to seven minutes. The dashboard turns green. Yet the same afternoon, families with complex questions wait thirty minutes, and staff start closing the queue before the workshop ends so the average will not rise.

The metric was not useless. It was simply asked to carry more meaning than it could support.

This is the pressure behind the lesson:

What matters, what we can observe, what we use as a stand-in, and what we decide to do are four different things.

The Four Layers of a Measurement Model

A useful model keeps four layers separate.

1. The target condition

This is the condition or quantity we actually care about. It may be partly hidden, distributed, or difficult to define.

For the library, the target is not “seven minutes.” It is something closer to:

Families can get appropriate help within a reasonable time while the children's room remains safe and usable.

This target contains several dimensions. Waiting time matters, but so do the kind of help needed, the distribution of waits, and whether visitors leave without service.

2. A variable in the model

A variable is a quantity whose value can change in the model. The target condition can be represented by several variables, such as waiting time, queue length, completed requests, or abandoned requests.

A variable is not automatically a measurement. The model may include a variable that comes from an estimate, a classification, or a rule.

3. An observed signal

A signal is an observation that gives us information about what is happening.

The library's ticket system emits a signal when someone joins the queue. A staff member records when the request starts. A visitor survey provides another signal. Each signal shows something, but none shows the entire target condition.

4. A proxy and a decision rule

A proxy is a signal we use as a stand-in for a target that is harder to observe directly. Average wait can be a proxy for timely help.

A decision rule maps a signal or proxy to an action:

if average_wait > 10 minutes:
    move one trained staff member to the desk

The rule is not an observation. It is a choice about what to do with an observation.

Plain meaning:

The target is what matters. The signal is what we can notice. The proxy is what we choose to represent the target. The decision rule is what we do when the proxy changes.

Technical names:

This separation is a basic measurement model. It helps us avoid treating a recorded number as if it were the whole condition it was meant to describe.

Why the Proxy Is Tempting

The library team did not choose average wait because it was foolish. They chose it because it has real advantages:

• it is cheap to collect;
• it changes quickly enough to guide a shift;
• people understand minutes;
• it can be compared across Saturdays;
• it provides a visible trigger for staffing.

A target such as “appropriate help for families” is harder to store in a spreadsheet. It requires judgment, context, and perhaps several different observations.

This creates a useful trade-off. A proxy makes an invisible or expensive condition easier to discuss, but it also bends the condition into the shape of the metric.

The danger begins when the proxy silently replaces the target:

Target: families receive timely, appropriate help
Proxy: average waiting time
Rule: keep the average below ten minutes
New belief: service is good whenever the dashboard is green

The last line is not justified by the first three. It adds meaning that the proxy does not contain.

Worked Path: When a Green Metric Hides a Bad Service

Let us follow one Saturday through the four layers.

Starting point: name the target

The library wants to improve access to children's-room help. The target condition has at least three parts:

1. visitors can reach a staff member;
2. the wait is reasonable for their situation;
3. the help is suitable, not merely fast.

Step 1: Choose an observed signal

The ticket system records the time between joining and first contact. At 10:00, it reports:

12 requests
average wait: 8 minutes

This is an observation about recorded waits. It is not yet a conclusion about service quality.

Step 2: Select a proxy

The manager chooses average wait as a proxy for timely access. This is reasonable as a first approximation, as long as its limits remain visible.

Step 3: Apply the decision rule

The rule says no staffing change is needed while the average stays below ten minutes.

Step 4: Add the missing distribution

At 11:00, the records look like this:

The average is 12.5 minutes, so the dashboard turns red. But an earlier snapshot could have shown a green average while the complex requests were already accumulating.

The average compresses a distribution. It tells us one center value, not who waited, how long the longest waits were, or why they waited.

Step 5: Compare additional signals

The team adds three signals:

• the 90th-percentile wait, meaning the wait below which nine out of ten requests fall;
• the number of abandoned requests;
• the type of request and whether the assigned staff member had the required skill.

Now the model can say more:

average_wait: 12.5 minutes
90th_percentile_wait: 34 minutes
abandoned_requests: 3
complex_requests_waiting: 4
qualified_staff_available: 1

Step 6: Revise the decision rule

The revised rule is not “ignore the average.” It is:

if average_wait > 10
or 90th_percentile_wait > 20
or complex_requests_waiting >= 3:
    assign a qualified staff member or change the queue policy

The output changes from “staffing adequate” to a more cautious decision: the service has a long-wait problem concentrated in complex requests.

The naive failure was to treat one easy-to-count signal as the target. The stronger model keeps the target, observations, proxy, and action rule separate.

So far, we have seen a complete path:

target condition
-> observed records
-> selected proxy
-> decision rule
-> behavior and blind spot
-> additional signals
-> revised action

A Signal Is Not Automatically a Proxy

The words are close, so keep the distinction practical.

Suppose the ticket system records “request closed.” That is a signal. It becomes a proxy only when the team uses it to stand in for something else, such as “the visitor received a useful answer.”

Suppose a visitor says, “I found what I needed.” That is also a signal. It may be a direct report about one person's experience, but it can still be incomplete if visitors who gave up never answer the survey.

The same observation can play different roles in different models:

This is why model cards should name the question each measurement serves. A number does not carry its interpretation with it.

When the Measure Becomes the Target

Once a proxy controls rewards, staffing, or public status, people may change behavior to improve the proxy rather than the target.

The library can reduce average wait in several ways:

• answer easy questions first;
• move difficult requests to an unmeasured queue;
• close the ticket before the visitor's problem is solved;
• ask people not to join the queue near closing time.

These actions can improve the number while making service worse. This pattern is often summarized as:

When a measure becomes a target, it can stop being a good measure.

The sentence is not a reason to reject metrics. It is a reason to inspect incentives and pair a proxy with other evidence.

What This Changes

Before this distinction, a dashboard question sounds like:

Is the number good or bad?

After this distinction, ask:

1. What condition are we trying to understand?
2. What exactly did we observe?
3. Why is this observation a reasonable proxy, if it is one?
4. What does the decision rule do when the number changes?
5. Who can change behavior because the number matters?
6. Which cases might the measurement miss?

These questions turn measurement from passive reporting into model inspection.

Trade-offs and Limits

The central trade-off is that a proxy makes a difficult target measurable and actionable, but it can distort attention and behavior.

More signals can reduce blind spots. They also increase collection cost, interpretation work, and the chance that two indicators disagree. A model with ten dashboards can be less usable than one with three carefully chosen signals.

No signal guarantees access to the full target. A survey can miss people who leave silently. A queue count can show pressure without showing whether the answer was useful. A resolved ticket can show closure without showing satisfaction.

This lesson does not tell us to replace judgment with metrics. It tells us to make the measurement chain explicit. You can see the boundary when the proxy improves while direct experience, outcomes, or independent checks worsen.

Common Confusions

Confusion: A variable is the same thing as a proxy

Why it is tempting:

Both can appear as columns in a table or fields in a dashboard.

Better model:

A variable is any changing quantity represented in the model. A proxy is a variable or signal chosen to stand in for a harder target. The role depends on the question.

Confusion: More precise measurement means more truth

Why it is tempting:

The number has more decimal places, so it looks more rigorous.

Better model:

Precision describes the resolution of the record. It does not prove that the record represents the target well. A precise count of the wrong thing is still the wrong evidence.

Confusion: A metric is bad if people can game it

Why it is tempting:

Gaming reveals that the metric can be manipulated.

Better model:

Gaming is a signal about the decision rule and incentives. A useful metric may still be part of a measurement set, but it should not be treated as the whole target or the only reward.

Confusion: Qualitative evidence is not a signal

Why it is tempting:

Stories are harder to aggregate than counts.

Better model:

A conversation, observation, or complaint can be a signal. It may be less standardized, but it can reveal dimensions that a count hides.

Check Your Understanding

Check: A software team uses “number of incidents closed this week” as a proxy for reliability. The count rises after engineers close unresolved tickets as duplicates. What changed?

Think first, then reveal.

Answer: The decision pressure changed behavior around the proxy. “Closed” remains an observed signal, but it no longer supports the stronger claim that reliability improved. Add outcome signals such as recurrence, user impact, and time to recovery.

Check: A hospital reports an average waiting time of five minutes. Which extra question most directly tests whether the average hides a serious problem?

Think first, then reveal.

Answer: Ask about the distribution and the people not represented: for example, the longest waits, the 90th percentile, people who left, and differences between urgent and routine cases.

Practice: Audit a Decision Rule

Choose a metric used by a team, service, school, household, or public institution. Write a short measurement card with:

1. the target condition that matters;
2. one observed signal;
3. the proxy interpretation, if the signal is being used as one;
4. the decision rule attached to the metric;
5. one way a person could improve the number without improving the target;
6. two additional signals that would expose that failure;
7. one cost of collecting or using the additional signals.

A good answer should keep the chain visible:

what matters -> what we observe -> what we infer -> what we do -> how behavior may change

Do not try to find a perfect metric. The goal is to identify where interpretation enters and where a proxy could bend the model.

Connection to the Next Lesson

We now have a model with a target, a boundary, variables, signals, proxies, and decision rules. The next question is what happens after the decision acts on the situation:

Can today's intervention change tomorrow's observations and make the model behave differently?

That is where feedback and delayed consequences enter.

Resources

• [BOOK] The Model Thinker — Focus: Compare several representations instead of letting one metric stand for an entire situation.
• [BOOK] Thinking in Systems — Focus: Measurements, information flows, and the limits of using one visible signal to steer a system.
• [ARTICLE] Mental Models I Find Repeatedly Useful — Focus: Notice when a useful measure is mistaken for the thing it represents.

Key Takeaways

• The target condition is what matters; a signal is what we observe; a proxy is a chosen stand-in; a decision rule turns the proxy into action.
• A precise number can still be weak evidence if it measures the wrong dimension or hides important cases.
• When a proxy controls rewards or decisions, people may optimize the proxy instead of the target.
• Add signals to expose blind spots, but remember that more signals cost time and interpretation.
• A good measurement model keeps the full chain visible: target, observation, interpretation, decision, and behavioral response.