# Subjective probability

Subjective probability |
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**Subjective probability**, also known as personal probability, is a type of probability based on an individual's personal belief, opinion, or judgment regarding the likelihood of an event occurring. It is distinct from objective probability, which is based on established rules, empirical data, or scientific research. In management, subjective probability is often used to assess the probability of certain outcomes in decision-making processes. This type of probability relies heavily on the management team's judgment, experience, and intuition to weigh up the risks and opportunities of certain decisions. It is an important factor to consider, as it can influence the success of a project or course of action.

## Example of subjective probability

- An experienced entrepreneur may assess the probability of success for a business venture to be 80%, based on their past experience in similar ventures.
- A financial analyst may assess the risk of a certain stock to be medium, based on their expert analysis of the company's financial performance and market conditions.
- A political analyst may assess the probability of a certain candidate winning an election to be high, based on their knowledge of current public opinion and voting trends.
- A meteorologist may assess the probability of rain in a certain area to be low, based on their knowledge of the region's weather patterns.

## Formula of subjective probability

The formula for subjective probability is a mathematical expression of the likelihood of an event occurring, based on an individual's personal judgment. It is expressed as a number between 0 and 1, where 0 indicates that the event has no chance of occurring and 1 indicates that the event is certain to occur. The formula is given by:

Subjective Probability = $$P(E) = \frac{F + I}{F + I + U}$$

Where: P(E) is the probability of the event occurring F is the number of favorable outcomes I is the number of indifferent outcomes U is the number of unfavorable outcomes

This formula takes into account the individual's opinion of the event, as well as the number of favorable, indifferent, and unfavorable outcomes associated with it. By adding up the number of outcomes associated with each category, we can calculate the probability of the event occurring. This formula is useful for making decisions, as it allows an individual to weigh up the risks and opportunities associated with a project or decision, and make an informed choice based on their personal judgment.

## When to use subjective probability

Subjective probability can be a useful tool in decision-making, especially when dealing with situations that are uncertain or involve a high degree of risk. It is particularly useful in situations where objective probability does not provide enough information to make an accurate decision. Some of the most common applications for subjective probability include:

**Assessing the probability of a new product launch succeeding or failing in the market**: By analyzing the management team's experience, knowledge and intuition, a subjective probability can be used to assess the likelihood of a new product launch succeeding or failing in the market.**Estimating the likelihood of a project meeting its goals**: The management team can use subjective probability to estimate the likelihood of a project meeting its goals. This can be especially useful for long-term projects with uncertain outcomes.**Assessing the risk of a certain course of action**: Subjective probability can be used to assess the risk of a certain course of action, such as entering a new market or launching a new product. This can help the management team identify the potential risks and rewards of the decision.**Determining the probability of a certain event occurring**: Subjective probability can be used to help determine the probability of a certain event occurring. For example, it can be used to assess the likelihood of a certain competitor entering the market or a certain customer segment becoming more or less important.

## Types of subjective probability

Subjective probability has many forms, including:

**Intuitive Probability**: This type of subjective probability is based on the individual's gut feeling and instinct about the likelihood of an event occurring. It often relies on the individual's past experience and knowledge of the situation.**Personal Bias Probability**: This type of subjective probability is based on an individual's personal beliefs and opinions. It is often used to support a decision or opinion, and can be influenced by a person's background, values, and context.**Cognitive Bias Probability**: This type of subjective probability is based on an individual's cognitive biases, which are mental shortcuts or assumptions that affect an individual's decision-making process. These biases can be based on an individual's past experience, emotions, or beliefs.**Expert Opinion Probability**: This type of subjective probability is based on an expert's opinion, which may be based on their experience and knowledge of the situation. This type of probability is often used in business decisions and is based on the experience of a particular expert or group of experts.

## Steps of subjective probability

Subjective probability relies on an individual's personal opinion, judgment, or belief about the likelihood of an event occurring. Below are the key steps to determining subjective probability:

- Start by identifying the event or outcome you are trying to assess.
- Gather available information and data on the event and analyze it to gain a better understanding of it.
- Brainstorm potential risks and opportunities associated with the event.
- Use your experience and intuition to assess the likelihood of the event occurring.
- Gauge the impact of the event on your decision-making process.
- Assign a subjective probability score to the event.
- Compare the scores of different events to determine the most likely outcome.
- Make an informed decision based on the subjective probability scores.

## Advantages of subjective probability

Subjective probability has its advantages when used for decisions in management. These advantages include:

- Greater flexibility - Subjective probability enables managers to be more flexible in their decision-making process, as it allows for a more personalized approach to assessing risks and opportunities.
- Faster decisions - Subjective probability can lead to faster decisions, as it does not require the same amount of research and data analysis as more objective probability models.
- Improved accuracy - Subjective probability takes into account the manager's experience and intuition, which can lead to more accurate decisions.
- Better resource allocation - Subjective probability can help managers allocate resources more effectively, as it allows them to better weigh up the risks and opportunities associated with a decision.
- Increased creativity - Subjective probability encourages creativity and out-of-the-box thinking, which can lead to more innovative solutions.

## Limitations of subjective probability

Subjective probability is commonly used in decision-making processes, however it has its limitations. These include:

**Lack of objectivity**: Since subjective probability relies heavily on an individual’s opinion or judgment, it can be difficult to remain unbiased and make decisions that are free of personal bias.**Potential for inaccuracy**: Since subjective probability is based on an individual’s perceptions, there is a chance that it could be inaccurate or unreliable.**Limited scope**: Subjective probability can be limited in its scope, as it does not take into account all of the available evidence when making decisions.**Lack of quantifiable data**: Subjective probability does not provide any quantifiable data or hard evidence, making it difficult to accurately assess the probability of certain outcomes.

Subjective probability relies heavily on an individual's personal beliefs and judgments, rather than objective data or established rules. Other approaches related to subjective probability include:

**Bayesian inference**: A method for revising beliefs about a probability in light of new evidence or information.**Fuzzy logic**: A form of reasoning based on degrees of truth rather than absolute truth or false values.**Heuristics**: A problem-solving technique which uses mental shortcuts to come to a conclusion.**Intuition**: A gut feeling or instinctive sense of what is right or wrong.

Overall, subjective probability is a method of deriving a probability based on the individual's personal judgment, experience, and intuition. It is distinct from objective probability, which relies on established rules, empirical data, or scientific research. While subjective probability can be a useful tool in decision-making processes, it is important to consider other approaches such as Bayesian inference, fuzzy logic, heuristics, and intuition in order to make informed decisions.

## Suggested literature

- Anscombe, F. J., & Aumann, R. J. (1963).
*A definition of subjective probability*. Annals of mathematical statistics, 34(1), 199-205. - Kahneman, D., & Tversky, A. (1972).
*Subjective probability: A judgment of representativeness*. Cognitive psychology, 3(3), 430-454. - Machina, M. J., & Schmeidler, D. (1992).
*A more robust definition of subjective probability*. Econometrica: Journal of the Econometric Society, 745-780.