What does delay discount rate (k) mean in a target group profile?

What does it mean for a target group when a benefit today carries more weight than a larger benefit later? Delay discounting offers a way to investigate that trade-off. The target group profile includes a Delay discount rate (k) field. A useful entry needs more than a number: record the choices studied, the model used and the time unit attached to the result.

In the simple hyperbolic model, the delay discount rate k is a parameter describing how the subjective value of a delayed reward decreases with waiting time. This wording follows the model description in Kirby, Petry and Bickel (1999).

For a target group profile, Neurofactor recommends recording k together with the model, time unit, choice task and measurement date. Without an appropriate measurement, enter ‘not measured’. An interview comment about quick results remains a qualitative observation.

Time preference is used here for the broad question of how someone weighs outcomes at different times. Delay discounting describes devaluation with delay; k is a parameter within a selected mathematical model. This article uses:

V = A / (1 + kD)

Hold A and a positive D constant: a larger positive k produces a lower V. At D = 0, V = A. These are direct consequences of the equation. Do not use k as a fixed percentage discount per day, an annual interest rate or a universal 0–100 scale. The equation describes a model, not the percentage of customers who buy immediately.

Kirby and colleagues attribute this equation to James E. Mazur (1987). The contents page of the original volume lists his chapter An Adjusting Procedure for Studying Delayed Reinforcement. The available preview does not contain the chapter itself; the equation was checked in Kirby and colleagues.

Other summaries of discounting also exist. Myerson, Green and Warusawitharana (2001) describe area under the empirical curve, AUC, as a measure independent of a particular theoretical model. Keep AUC as a separate measure and do not convert it into k without justification.

Start with a specific trade-off: which reward, for whom and after how much time? A delayed personal cash reward is a different research setting from an organisation waiting for an implementation to deliver results. Do not automatically transfer a measurement from the first setting into a score for the second.

This separation is Neurofactor’s practical documentation advice. It helps prevent urgency, available resources or scheduling constraints from being stored as measured personal characteristics. The category name ‘Neuropsychological scores’ does not make k a direct brain measurement.

Use a documented procedure with multiple choices and an appropriate estimation method. Kirby and colleagues estimate k from a pattern of choices; in their model, one choice can indicate a bound without determining k exactly. See their estimation procedure.

Neurofactor proposes the following workflow for target group profiles:

1. Define the question. Describe participants, choice context, reward and intended use of the result.
2. Document the task. Record its name, version, language, amounts, currency, delays and whether rewards are hypothetical or actually payable.
3. Describe estimation. Preserve the model, procedure, any parameter bounds and the chosen time unit. A different model requires its own interpretation.
4. Check usability. Document how task comprehension, missing responses, inconsistencies and model fit are assessed. Report limitations instead of forcing a seemingly reliable number.
5. Preserve the unit of analysis. State whether you summarise individual estimates or fit a model to pooled observations. Retain participant count, dispersion and the summary method.
6. Tie conclusions to the task. A marketing application, such as changing the order of benefits, remains a separate question to investigate.

A log transformation requires the original unit, logarithm base and treatment of zero values. Log(0) is undefined. Do not silently add a small constant merely to make the system calculate. Labels such as ‘high’ require an explicit reference group and decision rule.

These are Neurofactor documentation conventions. Empty does not mean zero. Choosing every immediate or every delayed option does not authorise entering infinity or zero, respectively, without the estimation rules. A publication using a different measurement range does not automatically supply a suitable norm for your target group.

This is a fictional calculation, with no participant or research result. Assume someone finds €80 now exactly as valuable as €100 in thirty days. That assumed equivalence is the indifference point. Under the selected model:

k = (A / V − 1) / D = (100 / 80 − 1) / 30 = 1/120 ≈ 0.008333 per day.

Substituting back gives V = 100 / (1 + (1/120 × 30)) = 80.

The same delay is 30/7 weeks. To preserve exactly the same value, k per week = 7 × k per day = 7/120 ≈ 0.058333 per week.

The larger number in the second row does not indicate a stronger time preference: the unit changed. This conversion follows algebraically from the equation. It is not another measurement.

If someone merely chooses €80 now, equivalence has not been established. Do not automatically enter 0.008333. Even the assumed indifference point above only illustrates the calculation; a usable estimate requires the broader task and quality assessment.

An associative target group is a bounded group of people whose similar associations guide decisions within a specific choice context.

Use this Neurofactor working definition to investigate what ‘now’, ‘later’ or ‘try first’ means within a choice. Does someone associate waiting with care, stagnation or uncertainty? These are possible research questions, not established associations for any particular group.

Investigate associations and temporal trade-offs with appropriate methods for each. Two groups with similar k values could have different explanations or associations in your analysis; treat that as a possibility to test, not an automatic explanation. Do not infer k from an association word or an AI description.

For an application, you might investigate an early visible milestone as a hypothesis. Whether it improves trust or decision-making requires a separate test. k does not supply a formula for the right campaign or a predicted conversion percentage.

• Omitting the unit. Keep ‘per day’ or the actual unit alongside every value.
• Treating one preference as an exact indifference point. Choosing and finding options equally valuable are different observations.
• Replacing unknown with zero. Use a missing value with a recognisable status.
• Combining different tasks. Check model, reward, amounts, delays and estimation procedure before comparing.
• Applying a group number to everyone. Preserve variation and explain how the group result was calculated.
• Hiding a sales conclusion in the score. Record measurement, interpretation and application hypothesis separately.

With a usable measurement:

> k = [value] per [time unit], estimated using [model and task version] for [reward and choice context], measured on [date]; group summary [method, count and dispersion], with [quality and limitations].

Without a measurement:

> Delay discount rate (k): not measured; [qualitative observation with source] is recorded separately as a research question.

Retain the detailed method behind the concise entry. Give readers access to the measurement report or internal research reference where access permissions allow. Do not publish a fictional example value as a characteristic of an existing target group.

The value of this field lies in traceable documentation. With the model, task, unit and quality information, a researcher can assess the result. Without measurement, the field remains ‘not measured’, and an observation about time or results has its own place in the profile.