Decisions often involve a sequence of acts, events, and outcomes. First comes the act of making the decision and implementing it. Next comes the event which is out of the control of the decision maker. Following that is the outcome, which is a result of the decision made and the event that followed. Depending on the details of the situation, second, third, or more act-event-outcome sequences may follow the first.

Decision trees are a means to logically layout the structure and architecture of single- or multiple-sequence decisions. Decision trees produce prescriptive solutions to multi-stage decisions and indicate in advance the optimum strategy to be taken and optimal decisions to be made based on unfolding events.

Prospect theory is a descriptive model that was developed by behavioral researchers Daniel Kahneman and Amos Tversky. According to prospect theory, people will subjectively value a loss of a fixed amount as more than a gain of the same amount. Gains and losses are not perceived in absolute value, but instead are determined based on a perceived reference or zero point.

According to prospect theory, when offered a gain, people will prefer a sure gain to a risky gain with the same expected value, but when facing a loss, they will prefer a risky loss to a sure loss of the same expected value. People will overweight low probabilities and therefore overestimate the utility expected (positive or negative) of low-probability events.

Decision theory and decision making are multidisciplinary topics. Decision theory includes psychology, especially cognitive psychology, because decisions are cognitive processes. Decision theory also includes math, especially probability, as people often make decisions based on likelihood. Decision making is an applied topic pertaining to business, engineering, science, politics, other disciplines, and of course to personal decisions.

Descriptive models of decision theory explain decisions as cognitive processes, how and why people make the choices they do. Normative decision models describe how people should conceptualize a decision. Prescriptive models include mathematically based analyses that provide actionable solutions to real-world problems.

Decisions are made in one of three environments. Under certainty, the decision maker can make a choice and be sure what the outcome will be. Under risk, the decision maker will make a choice knowing in advance the probabilities of various outcomes. Under uncertainty, the possible outcomes and probabilities are unknown.

When we make decisions, we base them on a combination of the current state of reality and our memories of past events. The research of Elizabeth Loftus and her colleagues demonstrated that human memories of past events are not simply stored in an unchangeable form when events occur to be retrieved later when they are needed. Instead, memories can be shaped by subsequent events, including conversations, questions asked, similar events, and even the grammar and choice of words in how a question is formulated. People can conflate the memory of one event with previous or subsequent events. Loftus’s research demonstrates that the memories of eyewitnesses who testify in court can be contaminated by events that occurred between the time of the crime and the trial. When we retrieve what we think is a memory, and make a decision based on that memory, we are probably retrieving and reconstructing something that changed while it was stored in memory.

Decisions are often made in an environment of risk, where the decision maker considers probabilities and possible outcomes. But in order to make a decision under risk, the decision maker must first determine the probabilities of the possible outcomes.

Through experience and observation, people estimate the probability of future events. The probability of an event can be determined as the number of instances of the particular event divided by the total number of possible events. With the tossing of a coin, there are two possible outcomes – a head or a tail – and the probability of either one is ½ or .5. Games of chance, including roulette and lotteries, provide clear examples of how probabilities can be calculated.

When probabilities and outcomes are known, expected value can be calculated and decision makers can use expected value when they analyze possible courses of action and make a decision.

The two-systems descriptive model of human decision making was popularized by Daniel Kahneman in his book Thinking Fast and Slow ( 2011). System 1 is on whenever we are awake, requires almost no deliberate effort, and is quick. When System 1 detects that a question or decision requires more thoughtful or deliberate analysis, it will call in System 2. However, System 1 can sometimes be impetuous and overconfident and make snap decisions before System 2 has had the opportunity to review what System 1 is doing. System 2, while capable of more deliberate thinking, can often be lazy and simply accept the conclusion that System 1 has reached. This descriptive model explains how people will sometimes arrive quickly at a conclusion with no effort, and how a more thorough analysis will be conducted if and when System 2 engages.

Decision makers are often faced with situations where they have several choices from which to select, and each will produce a different outcome based on an external event. There are several prescriptive strategies that can be implemented in such situations depending on the desired outcome.

The strategy of expected value will produce the highest long-term-average results when the situation is repeated many times. If the decision maker wishes only to have the opportunity for the highest payoff one time, no matter what the risk, the maximax strategy will make that possible. If the goal is to avoid the worst-case outcome, the maximin strategy will be best. With pairwise comparisons, inadmissible alternatives can be eliminated. By calculating the expected value of perfect information, the decision maker can determine the upward limit on what they should be willing to pay to know the future with certainty.

How do people determine if they are hearing a faint sound or if they are hearing only background noise? How do people differentiate between important information and distractions? Signal detection theory was first developed as a model for understanding and interpreting electronic signals in early radar. The model was quickly adopted to explain people’s perception and sensation of light and sound.

Signal detection theory, with a …criterion or detection threshold that separates hits from misses and correct non-detections from false alarms… is a model for any decision-making setting that requires the decision maker to make a binary decision based on the presence or absence of the signal. Signal detection is explicitly understood and used in medical testing, fire detection, spam detectors, shoot/don’t shoot decisions by police and the military, psychophysics, artificial-intelligence algorithms, and in a variety of other settings.

Heuristics are quick rules-of-thumb and easy-to-use tools that people often use to make decisions. Heuristics have been identified by research psychologists to describe and explain behavior.

With the representative heuristic, people will estimate the likelihood or probability of an event based on how similar it is to other known situations. With the heuristic of ignoring base rates, people will ignore hard data and will instead estimate probabilities based on narratives, even if the narratives are lacking in relevant details. With the availability heuristic, people estimate likelihood based on how quickly and easily something comes to mind. With anchoring and adjustment, people will first anchor an initial estimate based on the first number indicated, and they will adjust their estimate up or down from there. With satisficing, people will look for an acceptable solution that meets minimum requirements, but will not invest additinoal resources in seeking a perfect or optimum solution. Regression toward the mean explains why initial outliers move closer to the average with subsequent repetition.