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PSY333 notes
Heuristics are mental shortcuts that people use to make decisions quickly
Lecture 1 General Intro
Bayes Formula/Bayes Theorem:
P(D/S)=[P(S/D)xP(D)]/P(S) where P=probability, D=diagnosis, S=Symptom
Stroop test:
A psychological test that measures cognitive interference showcases the delay in reaction time when the color of a word differs from the name of the color itself.
The anterior cingulate is activated during the Stroop test, which indicates its role in conflict monitoring and error detection as individuals attempt to suppress the automatic response to read the word rather than name the color.
We care about the Stroop test because it is a demonstration of the competition of two mental components/modules competing, (System 1 and System 2) from the TLS book
This competition highlights the dual-process theory of cognition, where System 1 operates automatically and quickly, while System 2 is slower and more deliberate, providing insight into how cognitive processes interact in tasks requiring attention and control.
Visual illusions:
Shepards tables- Is surface A identical to surface B?
The Gateway Arch is the same size in length and width (the largest man-made optical illusion.
Muller-Lyer illusion: the lines with arrows
Al Seckel was an artist who made art of optical illusions, showcasing how perception can be deceived through clever use of shapes and colors.
“The eye sees what it sees even when the mind knows what it knows, BUT there are illusions also outside the domain of vision.”
Lecture 2 More on Illusions
Behavioral Decision Theory studies how people make choices and decisions, focusing on the psychological influences that affect their judgments and the behaviors resulting from these decisions. It emphasizes that individuals often do not behave entirely rationally, as they can be influenced by emotions, cognitive biases, and social factors, leading to decisions that may deviate from what traditional economic models would predict.
Heuristic:
A procedure, strategy or rule we apply to solve a class of similar problems, often without being aware.
from the ancient Greek heurein(to find, to discover)
These heuristics can simplify complex decision-making processes but may lead to systematic errors or biases, such as overconfidence or anchoring.
They do not have a real justification(a rational, impeccable foundation)
Something that we do, whether we are aware of it or not
Bias:
an internal spontaneous tendency to develop specific intuitions, judgments, preferences and choices
some are okay and useful while some are not okay
Something that happens to us
These are bottom-up and modular processes. Our perceptual periphery drives our perception and pattern recognition in ways we cannot control consciously.
McGurk effect:
ear hears Ba-Ba, eye sees Ga-Ga. These combine and you perceive Da-Da.
It works only for speech, cannot be reproduced with other kinds of noises and visual percepts
The Monty Hall Problem is a probability puzzle based on a game show scenario, illustrating how intuition can often lead to incorrect conclusions regarding probability.
Three identical boxes, 100 in one of them
you don’t know where the bill is, but the dealer does
Dealer opens one box that is always empty
you decide if you stick or switch boxes
typically 95% of people stick with their first choice; however, statistical analysis shows that switching boxes increases your chances of winning to 2/3.
Lecture 3 A Bit More on Illusions
Choice Blindness
can be defined psychologically as the phenomenon where individuals are unaware of their preferences and may even reject their original choice when presented with a different option, leading to a discrepancy between their stated preferences and their actual behavior.
This phenomenon illustrates how cognitive biases can influence decision-making, often causing individuals to misinterpret their own choices and the reasons behind them.
Something escapes our attention but we want to be consistent. This inconsistency can result in a lack of awareness regarding the motivations driving our decisions, ultimately impacting our self-perception and the validity of our choices.
Overconfidence
can further exacerbate this issue, as individuals may overestimate their understanding of their own preferences, leading them to confidently endorse choices that do not align with their true inclinations. This disconnect highlights the importance of introspection and self-awareness in the decision-making process.
Warning subjects that people are often overconfident has no significant effect, nor does offering them things reward accuracy in their judgments. This suggests that simply informing individuals about the pitfalls of overconfidence may not be sufficient to alter their decision-making behavior.
In their domain of expertise people are more accurate but the increase in their over-confidence exceeds by far the increase in accuracy
Over-confidence can do a lot of damage
Choices between monetary outcomes
Where exact numbers can be monitored
Typically: choices between smaller gains with high probability and larger gains with small probability
The normative principle is that individuals tend to evaluate options based on expected utility, favoring certainty over uncertainty when making decisions. This behavior can be observed in various contexts, such as gambling and investment decisions, where individuals often prefer a guaranteed return, even if it is lower, rather than risking a loss for a potentially higher gain.
Subjective Values:
Losses loom larger than gains, usually by a factor of 2.5
Outcomes are assessed in terms of losses and gains, not in absolute values
Losses and gains are constructed with respect to a subjective baseline/reference point/status quo, not in terms of total personal assets positions or states of wealth. Typical baselines are X at best nad Y at worst.
Probabilities are weighted psychologically
Different ways of presenting the same options can have dramatic effects on decision-making and preferences
Framing effects are the phenomenon where individuals make different choices based on how options are presented, highlighting the importance of context and wording in influencing judgments.
Conclusion
I think that the conclusion I have come to for the reason that we have seen these illusions during class is to show that how information is presented can significantly alter our perceptions and choices, reinforcing the idea that awareness of these biases can enhance our critical thinking and analytical skills. Some illusions highlighted how our immediate perception of things can be easily swayed by subtle changes in context, which underscores the necessity for mindfulness in how we interpret and evaluate information. At the beginning of this class, I was honestly confused about why we were being shown optical illusions. I found it kind of irrelevant to the psychology of judgment and decision-making, but I now see that these seemingly simple things like optical illusions can actually illustrate the underlying cognitive processes that shape our perceptions and decisions by basically demonstrating how our brains can be easily influenced by context, thus reinforcing the concept of framing effects in a tangible way. The overall takeaway I have had from these lectures and our textbook readings so far is that it is important to question our immediate reactions in many situations, but at the same time, questioning everything is not sustainable, so we must have a balance in what we choose to question.
Lecture 5 Fairness Then Nudge
Fairness-
Unfair behavior activates brain regions associated with disgust
Experiments on fairness have shown that when individuals perceive an allocation of resources as unfair, a significant emotional response can influence decision-making and social interactions.
Which example sounds more friendly? examples
Lecture Overview
Course: UofA PSYC 333 - Judgment and Decision Making
Instructor: Massimo Piattelli-Palmarini
Topic: Our Probabilistic Intuitions
Quiz Results
Class average for Quiz 1: 84%
Notable low performance on one question: Only 58% correct responses.
The Three Prisoners Dilemma
Scenario: Three prisoners on death row; one prisoner will be spared by the tyrant, but only the jailer knows who.
Jailer's Role: Communicates that one will be spared but keeps the identity secret.
Prisoner 2’s Strategy: Offers a bribe to find out who will be executed.
Jailer’s Decision
Jailer tells Prisoner 2, "Prisoner 3 will be executed!"
Prisoner 2 assumes the chance of being spared went from 1/3 to 1/2.
Actual Outcome: Prisoner 2's real chance remains 1/3.
Analysis of Probabilities
Counterintuitive Results for Prisoner 1:
Chance remains 1/3 for the prisoner who didn’t negotiate (Prisoner 1).
Prisoner 3's chance of being spared is now increased to 2/3 due to the jailer's logic.
Understanding the Logic
If Prisoner 2 is spared, the jailer chooses one of the remaining prisoners to execute, which has a probability of 1/3.
If Prisoner 2 is executed, the jailer must choose the other one to execute, which has a probability of 2/3.
Cognitive Dissonance in Decision-Making
Subjects often realize intuitive errors after questioning (examples: Maternity Ward Problem, Monty Hall Problem).
Rationality is felt internally by subjects rather than being imposed externally.
Evolutionary Biases in Decision-Making
Heuristics and biases may have been adaptive historically but can lead to irrational choices today.
Critique: It's unwise to overlook the dangers of cognitive illusions while misjudging narrow rationality.
Thought Experiment: Russian Roulette
Scenario: 6 prisoners must participate in a game of Russian roulette.
Rule Setup: Only one round in a spinning cylinder; survival leads to freedom.
Freedom to choose positions in the lineup.
Survivability Analysis
Preference Order: Participants often believe being first is best; this belief is based on intuition rather than probability.
Actual Probability: All prisoners have an equal survival probability of 5/6.
Alternative Scenarios
Variant with Six Revolvers: Each with a bullet placed differently.
Consequence: Format changes perceptions but not the underlying probabilities.
Key Insights on Probabilistic Intuition
People are typically risk-averse with gains and risk-seeking with losses.
Cognitive biases can lead to dramatically different decision-making outcomes based solely on framing effects.
Case Study: Tversky and Kahneman (1981)
Decision 1: Choose between a sure gain of $240 vs. a gamble.
Decision 2: Choose between a sure loss of $750 vs. a gamble.
Findings: Strong preference for gains (A) and against losses (D).
Manipulation of Preferences
New combinations presented reversed previous preferences despite being objectively equivalent.
Example Choices:
Option E: 25% chance to win $240 vs.
Option F: 25% chance to win $250
Result: People overwhelmingly prefer option F, showing how presentation impacts choices.
Cognitive Processes Involved
Mental Editing: Difficulties in integrating losses with gains once separated.
Psychological factors influence choices beyond objective rationality.
Normative Principles in Decision-Making
Dominance Principle: Choose A if it excels over B in one area and is equal in others.
Description Invariance: Preferences should not change based on presentation if logically equivalent.
Aggregation of Gambles: Combines two gambles' expected values.
Conclusion on Cognitive Biases
These biases are systematic and resistant to intervention, independent of education and culture.
Important to recognize the role of heuristics in shaping decisions and intuitions.Lecture Overview
Course: UofA PSYC 333 - Judgment and Decision Making
Instructor: Massimo Piattelli-Palmarini
Topic: Our Probabilistic Intuitions
Quiz Results
Class average for Quiz 1: 84%
Notable low performance on one question: Only 58% correct responses.
The Three Prisoners Dilemma
Scenario: Three prisoners on death row; one prisoner will be spared by the tyrant, but only the jailer knows who.
Jailer's Role: Communicates that one will be spared but keeps the identity secret.
Prisoner 2’s Strategy: Offers a bribe to find out who will be executed.
Jailer’s Decision
Jailer tells Prisoner 2, "Prisoner 3 will be executed!"
Prisoner 2 assumes the chance of being spared went from 1/3 to 1/2.
Actual Outcome: Prisoner 2's real chance remains 1/3.
Analysis of Probabilities
Counterintuitive Results for Prisoner 1:
Chance remains 1/3 for the prisoner who didn’t negotiate (Prisoner 1).
Prisoner 3's chance of being spared is now increased to 2/3 due to the jailer's logic.
Understanding the Logic
If Prisoner 2 is spared, the jailer chooses one of the remaining prisoners to execute, which has a probability of 1/3.
If Prisoner 2 is executed, the jailer must choose the other one to execute, which has a probability of 2/3.
Cognitive Dissonance in Decision-Making
Subjects often realize intuitive errors after questioning (examples: Maternity Ward Problem, Monty Hall Problem).
Rationality is felt internally by subjects rather than being imposed externally.
Evolutionary Biases in Decision-Making
Heuristics and biases may have been adaptive historically but can lead to irrational choices today.
Critique: It's unwise to overlook the dangers of cognitive illusions while misjudging narrow rationality.
Thought Experiment: Russian Roulette
Scenario: 6 prisoners must participate in a game of Russian roulette.
Rule Setup: Only one round in a spinning cylinder; survival leads to freedom.
Freedom to choose positions in the lineup.
Survivability Analysis
Preference Order: Participants often believe being first is best; this belief is based on intuition rather than probability.
Actual Probability: All prisoners have an equal survival probability of 5/6.
Alternative Scenarios
Variant with Six Revolvers: Each with a bullet placed differently.
Consequence: Format changes perceptions but not the underlying probabilities.
Key Insights on Probabilistic Intuition
People are typically risk-averse with gains and risk-seeking with losses.
Cognitive biases can lead to dramatically different decision-making outcomes based solely on framing effects.
Case Study: Tversky and Kahneman (1981)
Decision 1: Choose between a sure gain of $240 vs. a gamble.
Decision 2: Choose between a sure loss of $750 vs. a gamble.
Findings: Strong preference for gains (A) and against losses (D).
Manipulation of Preferences
New combinations presented reversed previous preferences despite being objectively equivalent.
Example Choices:
Option E: 25% chance to win $240 vs.
Option F: 25% chance to win $250
Result: People overwhelmingly prefer option F, showing how presentation impacts choices.
Cognitive Processes Involved
Mental Editing: Difficulties in integrating losses with gains once separated.
Psychological factors influence choices beyond objective rationality.
Normative Principles in Decision-Making
Dominance Principle: Choose A if it excels over B in one area and is equal in others.
Description Invariance: Preferences should not change based on presentation if logically equivalent.
Aggregation of Gambles: Combines two gambles' expected values.
Conclusion on Cognitive Biases
These biases are systematic and resistant to intervention, independent of education and culture.
Important to recognize the role of heuristics in shaping decisions and intuitions.
Children are sensitive to fairness, but we all are.
Daniel Kahneman and his research on behavioral economics illustrates how people's feelings about fairness can lead to irrational decisions, highlighting the importance of understanding these emotional responses in both children and adults.
For instance, when children play games and feel that the distribution of rewards is unequal, they may refuse to participate further, demonstrating their innate sense of justice.
Similarly, adults may react strongly in workplace situations where they perceive favoritism or inequity, leading to conflict and dissatisfaction.
Nudge -
The concept of nudging refers to subtly guiding individuals toward making decisions that are in their best interest without restricting their freedom of choice. By framing choices that highlight fairness, nudges can promote equitable behavior and enhance cooperative interactions among individuals.
Implications of nudging in real-world scenarios include its application in policy-making, where governments can design systems that encourage fair resource distribution and promote social welfare.
Nudges can be used for negative purposes as well.
An example of this is when credit card companies tell a person that they’ll get three months free of a magazine subscription and then automatically enroll them in a paid subscription if they do not opt out, which can lead to unintended financial burdens.
The definition of a Nudge in this context is any aspect of the choice architecture that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives.
Libertarian paternalism in philosophy suggests that it is possible to influence people’s choices while still preserving their freedom to choose. This approach advocates for designing choices to promote individuals' welfare without coercion.
Freedom to accept or reject, no obligation, and the emphasis on informed decision-making are key components of this philosophy, ensuring that individuals can navigate choices without feeling pressured.
Richard Thaler, who received a Nobel Prize in Economic Sciences in 2017, is one of the foremost proponents of the nudge theory and has significantly contributed to the understanding of how subtle changes in the environment can impact decision-making.
Choice architects play a crucial role in this framework, designing the context in which decisions are made and guiding individuals toward beneficial outcomes while maintaining their autonomy.
Information disclosure is essential in this process, as it empowers individuals with the knowledge needed to make informed choices, thereby enhancing their ability to weigh options and outcomes effectively.
Moreover, the integration of behavioral insights into policy-making can lead to improved public health, financial decisions, and environmental sustainability, demonstrating the practical applications of nudge theory in everyday life.
A nudge is free to reject
Cass Sunstein, in the Obama administration, played a pivotal role in promoting the use of behavioral economics in government policies, advocating for the implementation of nudges to guide citizens toward better choices without restricting their freedom.
An example of this is the "opt-out" organ donation system, where individuals are automatically considered donors unless they explicitly choose not to participate, significantly increasing donation rates while preserving personal choice.
This approach not only respects individual autonomy but also harnesses the power of default options to influence behavior positively. By framing choices in a way that aligns with people's natural inclinations, nudges can effectively steer public behavior toward more beneficial outcomes.
A choice architect can be almost anyone in power, such as policymakers, employers, or educators, who designs the environment in which people make decisions, thereby influencing their choices without mandating them. This concept has broad applications across various sectors, including health care, finance, and education, where subtle changes in how choices are presented can lead to significant improvements in decision-making and overall well-being.
Nudges can be used to encourage people, including children, to make healthier food choices by presenting nutritious options more prominently in school cafeterias or even the type of utensil used in the cafeteria or the distance they are from the food itself.
Regret and the Decoy Effect
Connolly, Reb & Kausel, 2010 defined regret and the decoy effect as the psychological phenomenon where the presence of a less attractive option (the decoy) can influence preferences and lead individuals to choose a more favorable option, thereby enhancing their overall satisfaction with the decision. This effect can be observed in various scenarios, such as marketing strategies where introducing a high-priced option makes a more moderately priced item appear more appealing.
Regret priming eliminated the decoy effect by reducing the influence of the decoy option on decision-making, leading individuals to focus more on their true preferences rather than being swayed by the presence of the less attractive alternative.
Lecture 5: Fairness Then Nudge
Fairness:
Unfair behavior activates brain regions associated with disgust.
Experiments show emotional responses influence decision-making when individuals perceive resource allocations as unfair, contributing to conflicts and dissatisfaction in both children and adults.
Daniel Kahneman's research highlights feelings about fairness leading to irrational decisions, illustrating children, for example, may refuse to play if rewards are distributed unequally.
Nudge:
Nudging refers to subtly guiding individuals towards beneficial decisions without restricting freedom of choice.
By highlighting fairness, nudges can enhance cooperative interactions and equitable behavior.
Nudge examples include how credit card companies may exploit automatic enrollments leading to unintended burdens.
Nudges can be defined as aspects of choice architecture that predictably alter behavior without forbidding options.
Libertarian paternalism suggests influencing choices while preserving freedom.
Richard Thaler, a proponent of nudge theory, contributed insights on how small environmental changes impact decision-making.
Choice architects design decision-making environments, empowering individuals through information disclosure, which can lead to improvements in public health, finances, and sustainability.
Examples of nudges include programs to increase organ donation rates through opt-out systems and healthier food choices in schools.
Regret and the Decoy Effect:
The decoy effect influences preferences by introducing a less attractive option—enhancing satisfaction with a more favorable choice.
Regret priming can diminish this effect, allowing individuals to focus more on true preferences rather than being swayed by decoys.
Fairness:
Unfair behavior activates brain regions associated with disgust.
Experiments show emotional responses influence decision-making when individuals perceive resource allocations as unfair, contributing to conflicts and dissatisfaction in both children and adults.
Daniel Kahneman's research highlights feelings about fairness leading to irrational decisions, illustrating children, for example, may refuse to play if rewards are distributed unequally.
Nudge:
Nudging refers to subtly guiding individuals towards beneficial decisions without restricting freedom of choice.
By highlighting fairness, nudges can enhance cooperative interactions and equitable behavior.
Nudge examples include how credit card companies may exploit automatic enrollments leading to unintended burdens.
Nudges can be defined as aspects of choice architecture that predictably alter behavior without forbidding options.
Libertarian paternalism suggests influencing choices while preserving freedom.
Richard Thaler, a proponent of nudge theory, contributed insights on how small environmental changes impact decision-making.
Choice architects design decision-making environments, empowering individuals through information disclosure, which can lead to improvements in public health, finances, and sustainability.
Examples of nudges include programs to increase organ donation rates through opt-out systems and healthier food choices in schools.
Regret and the Decoy Effect:
The decoy effect influences preferences by introducing a less attractive option—enhancing satisfaction with a more favorable choice.
Regret priming can diminish this effect, allowing individuals to focus more on true preferences rather than being swayed by decoys.
Automatic savings enrollment
Automatic savings enrollment is an effective nudge designed to promote better financial behavior among individuals. In this framework, individuals are automatically enrolled in a savings program, with a percentage of their income set aside for savings unless they actively choose to opt out. This approach takes advantage of the tendency for people to stick with default options, effectively encouraging them to save without requiring additional effort or decision-making.
Research indicates that when individuals are automatically opted into a savings plan, participation rates significantly increase compared to programs that require active enrollment. This is particularly beneficial for individuals who may struggle with impulsive spending or who find it challenging to prioritize saving for future needs.
By implementing automatic savings enrollment, organizations and banks not only promote financial well-being but also help individuals build a safety net for emergencies and future investments. This practice aligns with the principles of behavioral economics, illustrating how subtle changes in the choice architecture can lead to substantial improvements in personal finance management and overall savings rates without restricting individuals' freedom to manage their money effectively.
I thought of the example of the automatic magazine subscription we learned about in class and had the idea to turn that around instead of automatically taking a person’s money when they don’t cancel a subscription, this same strategy could be used to encourage individuals to save by automatically enrolling them into a savings account with a set amount deducted each month, promoting a habit of saving without requiring active decision-making. This strategy makes sense because it does, in fact, take more effort and thought to cancel something rather than sign up for something, as shown by research indicating that people often prefer to stick with the default option due to inertia and the cognitive load associated with making active choices. This approach not only simplifies the savings process but also fosters a sense of financial security, as individuals can gradually accumulate savings without the burden of constant decision-making, ultimately leading to greater financial stability and peace of mind, which would benefit most people in today’s society.
TFS Chapter 13
The economist Howard Kunreuther, on the subject of availability, emotion, and risk, said that "people's perceptions of risk are often influenced by immediate experiences and emotional responses rather than statistical realities, leading to a misalignment between actual risk and perceived risk." This insight underscores the importance of understanding how emotional factors can shape financial decisions and behaviors.
Statistically, these perceptions can lead individuals to underestimate or overestimate risks, which ultimately affects their saving and investment choices.
Lecture 6 The Framing of Decisions
the three approaches relevant to our course are
normative: rationality, how we should decide, how we should choose
Cognitive: how we, as a matter of fact, choose and decide
Prescriptive: what we are doing here, learn about our heuristics and biases and avoid them
The cognitive explanation for anchoring is that individuals rely heavily on the first piece of information encountered (the anchor) when making decisions, which can lead to skewed judgments and choices. This reliance on anchors illustrates the importance of being aware of the initial information presented, as it can unduly influence our perception and evaluation of subsequent data.
Confirmation bias as a dominant heuristic is the tendency to search for, interpret, and remember information in a way that confirms one's pre-existing beliefs or hypotheses, often leading to faulty decision-making.
Tversky and Kahnmen performed a classic study of this in 1974, where participants were presented with different scenarios that involved making probabilistic judgments. Depending on how the questions were framed, their responses varied significantly, demonstrating the impact of anchoring and confirmation biases on decision-making.
Representativeness in heuristic view point is the tendency to judge the probability of an event based on how closely it resembles a typical case, often leading to misconceptions about likelihood and randomness.
A recurrent cognitive illusion is confusing what is more typical and what is more probable.
Lecture 7 Probability
Neglect of base rates is the tendency to disregard the overall prevalence of an event or characteristic in favor of specific information about a particular case, which can skew our judgment and lead to incorrect conclusions. and something to be avoided
The classical definition of probability is that the probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible
Pierre de Fermat, Blaise Pascal, Jakob Bernoulli and Abraham de Moivre created a mathematical theory of probability that laid the groundwork for modern probability theory, emphasizing the importance of random events and the calculation of probabilities in various contexts. This theory has since evolved, incorporating concepts such as conditional probability and the law of large numbers, which further enhance our understanding of how probabilities function in real-world scenarios.
The term favorable in the probability theory is defined by its relevance, or what its all about
It is not to be confused with odds, which is the number of favorable cases divided by the number of un-favorable cases
In the thermodynamics we have the carnot cycle(the normative model) which is a theoretical model that defines the maximum possible efficiency of a heat engine operating between two heat reservoirs, illustrating the principles of energy conservation and entropy.
The ideal ration bettor is one who understands the relationship between odds and probabilities, allowing them to make informed decisions based on the likelihood of favorable outcomes.
The notion of a fair bet is set in the threshold at which it is ration to be indifferent between accepting and refusing the best
Accepting a bet for more than the fair price is risk seeking while refusing a bet for less than the fair price is being risk-adverse
A ration person is neither of these
The value of a “fair bet” where e is the uncertain event on the occurrence of which the bet is being offered, P is the probability of e occurring, L is the fair price of the bet, W is the amount they receive if e is the case, S is the stakes of the bet
A bet is said to be fair IF, and only If P(e)=L/(W+L)
This implies that the expected utility of the bet is equal to the utility of not betting at all, which is a key principle in understanding rational decision-making in uncertain situations.
It is rational to remain indifferent in the presence of such a bet.
Accpeting it for more than L qualifies as a risk-seeker and refusing it for less than L qualifies you as risk-adverse
Expected Value(EV), also called mathematical expectation is the stakes of S multiplied by the probability of getting the stakes where EV=SxP(e) , and this calculation helps to determine the attractiveness of a gamble. In this context, if the expected value of a bet exceeds the threshold of L, it suggests a favorable outcome for the bettor, while an EV below L indicates a potential loss, guiding individuals in their decision-making process. EV is an objective quantity
Subjective Expected Utility is a decision-making framework that incorporates personal preferences and beliefs about the probabilities of various outcomes, allowing individuals to evaluate options based on their perceived satisfaction rather than solely on expected value.
A rational person accepts a fair bet for the sheer pleasure of gambling and refuses a fair bet for any reason whatsoever but not because they are authorized to suppose that there is some catch in the offer, a fair bet has no catch
The idealized subject is one that is in principle, disposed to accept some bets
Acceptance of the bet of a small stakes bet must be made before knowing which side of the bet is our side and if there is a side that is favored, then the bet is not fair
Basically, probability is the measure of our uncertainty about the occurrence of an event; there is a precise mathematical theory of how to measure that, and rational people should take that theory as the exclusive criterion in judging probabilities and making decisions based on probability. In this context, rational decision-making involves not only understanding the mathematical underpinnings of probability but also recognizing the psychological factors that influence our perceptions of risk and reward.
There are 2 interpretations of probability
subjectivist is the interpretation that views probability as a degree of belief or personal judgment about the likelihood of an event occurring, rather than an objective measure of frequency.
frequentist requentist is the interpretation that defines probability as the long-run relative frequency of an event occurring based on repeated trials or observations, emphasizing an objective approach to understanding probability.
What has impressed me the most?
So far in this course, we have learned about concepts related to heuristics, biases, and decision-making frameworks. We have seen how these frameworks can significantly influence our choices and perceptions, leading to both advantageous and detrimental outcomes in various contexts. What has impressed me the most in this class is how, in many cases, most of the participants in these studies we’ve learned about are often misled by simple cognitive biases that affect their decision-making processes, highlighting the importance of awareness and critical thinking in evaluating our own judgments. It also impresses me how routine and common this theme is within different study populations. Some parts of our readings, especially in the TFS book, ask us to come to our own conclusions for prompts similar to those in research we’ve seen, and it has led me to reflect deeply on my own thought processes and how they align or diverge from established research findings. In the beginning of this class and these thought experiments, I found myself more often in the majority, but more often than previously, I am in the minority of opinions or decisions, prompting me to reconsider my assumptions and biases. This class has encouraged me to engage more critically with the material and to seek out alternative viewpoints, thereby enhancing my understanding of the complexities involved in human decision-making.
Lecture 8 Probability: The Way We Are
Normative theories of probability is part of the axiomatic-deductive sciences which provide a structured framework for understanding how probabilities should be assigned based on logical reasoning and empirical evidence.
Descriptive(cognitive) heories are a part of the experiemental sciences
The standard position claiming that spontaneous probabilistc reasoning and spontaneous decision-making can affect the nromative theories of rationality
Each normative theory makes cognitive act, aptitude that is consider induviatyl reliable, relecant and not further composable to more elementary acts
The philosophy of probability
The extensionally axiom is a fundamental principle that asserts the consistency and coherence of probabilistic assessments across different contexts, ensuring that probabilities assigned to events are aligned with the underlying axioms of probability theory.
Lecture 11 More on Prospect Theory
decisions are made on the prospect of perceived losses and perceived gains
Prospect Theory is a behavioral economic theory that describes how individuals evaluate potential losses and gains when making decisions under risk, highlighting that people tend to weigh potential losses more heavily than equivalent gains.
losses and gains are mentally computed with respect to a baseline; this can be real or imagined
losses loom larger than gains (by a factor of the order of 2.5)
the impact of a stated probability on decisions(choices, preferences) is not the same as the objective(pure) value of that probability
subjects give a subjective weight to the probabilities
subjective weight is influenced by various cognitive biases, leading individuals to overestimate the likelihood of negative outcomes compared to positive ones.
We have
Pure (martian) normative theory: this theory posits that individuals should evaluate probabilities and outcomes based solely on objective data, without the interference of personal biases or emotions. Decide on the basis of the Expected Value(EV) and EV of receiving x with probability p=px
Classical expected utility theory(also normative) which is deciding on the basis of your subjected expected utility, the SEU of recieving the amount x with probability p is pU(x), U(x) is the utility to you of the amount x, utility depends on the subjects state of wealth. utility in the context is defined as a measure of the satisfaction or benefit derived from a particular outcome, which varies for each individual based on their personal preferences and circumstances.
prospect theory: replace p with a subjective probability weighting function W(p), it is a nonlinear function of p, subjective value function v is a nonlinear function of money, gains, and losses are computed with respect to a subjective reference point(the status quo), we separate gains from losses
The shape of a weighting function is universal
The mental non-adapatation to losses explains why individuals often experience a greater emotional impact from losses than equivalent gains, leading to risk-averse behavior when faced with potential losses.
Pairs of situations a’ la Thaler are often used to illustrate how people value outcomes differently based on their reference points, highlighting the inconsistencies in decision-making under risk. The psychological difference in subjective satisfaction is clear. This cannot be explained by the theory of expected value NOR by the theory of subjective expected utility
This discrepancy demonstrates the limitations of traditional economic theories in capturing human behavior, as individuals frequently prioritize avoiding losses over acquiring gains, leading to decisions that deviate from what would be predicted by rational choice models.
As a consequence of prospect theory we can explain the processes of: mental segregation and integration, coding and re-coding of choices, cancellation of common components and editign of the available choices
The mirror effect is: in the domain of gains, people prefer outcomes that are considered certain, relative to larger outcomes that are merely probable. in the domain of losses, people prefer outcomes that contemplate a possibility of no loss at all, and a possiblity of greater loss. relative to outcomes that impose a sure lesser loss
Main cognitive factors:
The certainity effect is the tendency for individuals to overvalue outcomes that are certain compared to those that are uncertain, leading to risk-averse behavior when faced with potential gains.
The status quo bias is the preference for maintaining the current situation or outcome rather than making a change, often resulting in resistance to new options even when they may provide better benefits.
Avoidance of ambiguity is the inclination to prefer clear and definite information over uncertain or vague options, which can significantly influence decision-making processes and lead to choices that minimize perceived risks.
Avoidance of possible regret is the tendency for individuals to steer clear of choices that could lead to feelings of remorse or disappointment, often resulting in conservative decision-making and a preference for safer, more familiar options.
Loss avoidance is the principle that individuals prefer to avoid losses rather than acquire equivalent gains, which can heavily influence risk-taking behavior and decision-making strategies.
Risk aversion is the tendency to prefer options that have lower potential for loss, even if that means forgoing opportunities for higher rewards; this behavior often reflects a deep-seated desire to maintain the status quo and avoid the discomfort associated with uncertainty.
Overweighting of small probabilities is the phenomenon where individuals give disproportionately high importance to outcomes that have a low likelihood of occurring, which can lead to irrational decision-making and an overestimation of the chances of rare events.
Under-weighting of large probabilities is the tendency for individuals to assign less significance to outcomes that are highly probable, which can result in missed opportunities and poor risk assessment in decision-making processes.
Violations of the theory of subjective expected utility are always computed internally, for the same subject.
There is no classical (normative) utility function and no consistent(normative) probability function that can jointly accommodate these preferences; this is why we need psychological theories that can explain such preferences. Prospect theory does exactly this
Risk seeking in the domain of losses and risk averse in the domain of gains
The certainity effect amplifies both our aversion to losses and our propensity to appreciate gains, in fact certainity has it’s own value. a sure gain has whatever utility we associate with the amount plus the value that we add to it for being certain. the same for losses, with an amplification due to asymmetry. BUT in that case we want to minimize negative utility so we select the option that has minimal utlity because the number is now negative
choices are among increments or decrements of wealth, not among states of wealth
there is a status quo, or reference point, or baseline
The curve of subjective estimates of probabilities in Prospect Theory, often represented as an S curve, illustrates how individuals perceive probabilities in a non-linear manner. Specifically, it shows that people tend to overweight small probabilities while underweighting larger probabilities. This means that rare events are perceived as more likely than they actually are, while highly probable outcomes receive less consideration in decision-making. The S curve reflects the asymmetry in how individuals evaluate gains and losses, with losses looming larger than gains, thus influencing their risk preferences and behaviors.
Probability zero being an outlier for the curve of subjective evaluations of probabilities means that individuals often perceive events with a probability of zero as having a chance of occurring, despite the mathematical implication that they cannot happen. This reflects a cognitive bias where people may struggle to accept the absolute impossibility of certain events, leading to irrational evaluations. Consequently, even when an event is deemed impossible, individuals may still mentally entertain the possibility, highlighting the discrepancy between objective probabilities and subjective interpretations.
I contemplate why, but I have utilized much of the information from the course in the context of gambling. I believe this approach helps me frame decision-making processes in a more relatable manner, allowing me to grasp the psychological factors at play when individuals evaluate risk and reward in gambling situations. What I found most intriguing about Prospect Theory is that, for instance, a gambler who has lost money in a betting context may be more likely to place high-risk bets in an attempt to recover their losses despite the negative expected value of such actions. On the other hand, when winning, gamblers may prefer to secure their profits rather than risk their current earnings for potentially higher rewards, highlighting the concept of loss aversion—where losses feel more significant than gains. These behavioral patterns can lead to irrational decision-making among gamblers, often resulting in a cycle of chasing losses or overconfidence during winning streaks.
Lecture 12 Two Famous Paradoxes
In this lecture, we explored two famous paradoxes that illustrate the complexities of human decision-making under uncertainty:
The Allais Paradox: This paradox demonstrates how people's preferences can violate the expected utility theory, revealing inconsistencies in risk-taking behavior when faced with different probabilistic outcomes.
The Ellsberg Paradox: This paradox highlights individuals' aversion to ambiguity, showing that people tend to prefer known risks over unknown risks, even when the expected outcomes are the same. These paradoxes underscore the importance of understanding the psychological factors that influence choices, particularly in high-stakes scenarios like gambling.
Implications for Behavioral Economics: These paradoxes challenge traditional economic models that assume rational decision-making, suggesting that human behavior is often driven by cognitive biases and emotional responses rather than purely logical calculations.
Subjective expected utility is an extension of the expected utility theory that incorporates individual beliefs about probabilities, allowing for a more nuanced understanding of decision-making under uncertainty. This approach acknowledges that personal beliefs and perceptions can significantly impact choices, leading to variations in how individuals evaluate risky options.
Prospect Theory: Developed by Daniel Kahneman and Amos Tversky, this theory further explains how people make decisions involving risk by illustrating that individuals value gains and losses differently, leading to inconsistent risk behavior.
Maurice Allais pleaded for an enlargement of the notion of economic rational in order to account for the observed discrepancies between theoretical predictions and actual human behavior, emphasizing the importance of incorporating psychological factors into economic models. His famous paradox was a key contribution to behavioral economics, illustrating how people's choices can deviate from expected utility due to framing effects and the influence of contextual factors.
Violation of SEU Theory occurs when individuals make choices that contradict the predictions of subjective expected utility, often influenced by factors such as framing effects, loss aversion, or cognitive biases. These violations highlight the limitations of traditional economic theories in accurately predicting human behavior in real-world scenarios.
The concept of loss aversion, a central tenet of Prospect Theory, suggests that losses are perceived as more significant than equivalent gains, which can lead to risk-averse behavior when faced with potential losses.
Additionally, cognitive biases such as overconfidence and anchoring can further skew decision-making processes, underscoring the need for a more nuanced understanding of economic behavior that integrates psychological insights.
Replication of Allais Paradox for ordinary gains is a key experiment that demonstrates how individuals often violate the principles of expected utility theory, as it reveals inconsistencies in choices when faced with different presentations of the same problem. These findings emphasize the importance of considering psychological factors when analyzing economic decisions, suggesting that a purely rational model may not capture the complexity of human choice.
Allias as a lottery is a thought experiment illustrating how people's choices can be influenced by the framing of options, leading to preferences that deviate from traditional economic predictions.
The principle of normative decision theory is rooted in the idea that individuals should make choices that maximize their utility based on rational calculations. Yet, empirical evidence from behavioral economics often shows that real-world decisions are influenced by heuristics and biases, challenging the assumption of purely rational behavior.
The constant column says that if that is what will happen, then the payoff is the same regardless of the probability distribution. This highlights how people's choices can be swayed by the perceived risk rather than the actual expected value, further complicating the understanding of rational decision-making in economic contexts.
When maurice allais invented this case in 1952 he made the predicition that real experiments would confirm this fact so he proposed that individuals would choose options that seem more favorable when framed in a certain way, illustrating the gap between theoretical predictions and actual behavior in decision-making.
The poor man’s Allais choice is a classic example where individuals prefer a guaranteed outcome over a probabilistic one, even when the expected value is lower, demonstrating the impact of framing effects on decision-making.
The certainity effect is a cognitive bias where individuals disproportionately favor outcomes that are certain over those that are uncertain, even if the uncertain outcomes have a higher expected value. This phenomenon underscores the influence of perceived security in choices, revealing how individuals often make decisions that contradict the principles of expected utility theory.
This effect is particularly evident in financial decisions, where investors may shy away from stocks with higher potential returns due to the risks involved, opting instead for safer, lower-yield options. Understanding these biases is crucial for economists and psychologists alike, as it can help bridge the gap between theoretical models of rationality and the actual decision-making processes observed in real-world scenarios.
The psychological value of a gain with which a given proability is associated not independent of the gains attaching to the other probabilities, psychological values are highly sensitive to distributions. This sensitivity can lead to non-linear perceptions of risk and reward, further complicating the decision-making landscape.
minimization of possible regret often drives individuals to favor options that appear less risky, even when the potential for greater gains exists. This behavior highlights the importance of emotional factors in financial decision-making, as the fear of loss can overshadow the rational assessment of expected outcomes.
in the domain of gains we opt for certaintity
when gains are far from certainity anyway, we opt for larger stakes
small differences in probabilities, if away from certainity are considered irrelevant
Ellsbergs paradox is a scenario that illustrates how individuals often prefer known risks over unknown risks, even when the expected outcomes are the same. This paradox highlights the tendency of people to avoid ambiguity in decision-making, leading to choices that may not align with traditional economic theories of rationality.
We must deal with the cognitive(descriptive) theories as a domain in itself, a domain of inquiry that. isneither independent of the normative theory, nor reducible to it. This is what has happened ever since this is our domain, of course
Lecture 13 Recap and Utility Theory
Utility theory is a normative theory that provides a framework for understanding how individuals make choices under conditions of uncertainty. Its goal is to maximize their perceived satisfaction or utility from different outcomes.
The curve of the Subjective Expected Utility is
Subjective because your curve may well not be the same as mine, numerically speaking, but it will have the same shape
Expected because it also applies to uncertain outcomes(events occurring with a certain probability)
Utility because it’s measured in utiles, not in dollars, euros, etc.
The utility theory is similar to Weber’s law, which describes a general psychological phenomenon: changes in our ability to discern the difference between two stimuli accurately (threshold goes up with magnitude). Some examples are weight, luminosity, and sound.
In this context, utility reflects not just the value of outcomes but also how we perceive and evaluate those outcomes based on their magnitude, which aligns with our subjective experiences. Additionally, the theory suggests that as the magnitude of a stimulus increases, the perceived change in utility becomes less pronounced, highlighting the diminishing returns we experience with larger gains or losses.
According to the Subjective Expected Utility theory, the intensity of personal preferences can be measured precisely with numbers
The general strategy for creating a personal SEU is to combine preferences with probabilities rigoursly and mathematically to find a set of axioms that are self-evident(preferences must be are well ordered and internally consistent), find a mathematical proof that if and only if a persons preferences obey all these axioms then there is a function(Expected Utitlity Function) for that person that maps their preferences onto real numbers. It becomes strictly rational for that person to always and only choose the option that maximizes that number
The Theory of subjective expected utility is a normative theory and the prospect theory is a cognitive(psychological) theory
Expected Value(Mathematical Expectation) is the weighted average of all possible values, where the weights are the probabilities of each outcome occurring. This concept is fundamental in decision-making processes, as it allows individuals to quantify the potential benefits of different choices based on their likelihood. This is an objective quantity
Subjective Expected Utility is SEU=U(S)xp, where U(S) represents the utility of a specific state S, and p denotes the probability of that state occurring. This formula encapsulates how individuals evaluate uncertain outcomes by integrating both their subjective preferences and the likelihood of each outcome.
The property of closure under disjunction is one of the key features of subjective expected utility, which states that if an individual prefers option A over option B, they will also prefer the combination of A with any other outcome over the combination of B with that same outcome.
An example:
The probability of rain tomorrow in Tucson is 0.2(20%)
The probability that tomorrow, my cousin will finally give me back the money he owes me is 0.4(40%)
Rain tomorrow,w AND my getting back the money is an outcome
Utility to me of rain tomorrow -5
Utility to me of getting money tomorrow is +12
-5×0.2+12×0.4=-1+4.8=3.8
The Six Axioms of the Theory are
Completeness: Preferences can be ordered and compared.
Transitivity: If A is preferred to B and B is preferred to C, then A is preferred to C.
Independence: Preferences between options should remain unchanged when presented with irrelevant alternatives.
Continuity: Preferences do not change abruptly, and small changes in options should not lead to large shifts in preference.
Non-satiation: More of a good thing is always preferred to less; consumers will always choose more of a desirable good when possible.
Substitutability: Consumers view goods as interchangeable; if the price of one good rises, they will substitute it with another good that serves a similar purpose.
If an individual’s preferences satisfy all these axioms, we can map their preferences onto a numerical function U(that individual’s Subjective Utility Function) that takes possible outcomes as its arguments and gives numbers as values
Lecture 14 Regret and Decision-Making
Lecture 15
Counterfactuals are mental representations to alternatives to the past. These alternatives allow individuals to evaluate what might have happened under different circumstances, influencing their feelings of regret and decision-making processes. They are not licesenced by true logic
if things had been different, such and such would have happened
results in regret and changes in future actions
This cognitive process allows individuals to reflect on their decisions and consider how different choices might lead to different outcomes, ultimately shaping their future behaviors and attitudes.
How close the real world to the hypothetical is affects the level of regret/sadness that a person feels when having a counterfactual thought
This relationship suggests that the more similar the hypothetical scenario is to reality, the greater the emotional response, as individuals may feel a stronger sense of loss or missed opportunity.
(Examples of a boss and lady with wine)
(Examples of two men with flights they missed)
(Examples of a young man named william going to buy a stereo system)
Counterfactual reasoning is very frequent in everyday situations, as individuals often reflect on choices and their potential outcomes. For instance, if the boss had chosen a different restaurant, or if the men had arrived on time for their flights, the consequences could have been significantly different, illustrating how our decisions shape our experiences.
The philosophical term of possible worlds is used to explore scenarios that diverge from the actual events, allowing us to analyze how different choices could lead to different outcomes.
Some counterfactuals are meaningful and some are meaningless
Counterfactuals are logicial condition, if x then y
sentential connectors are used to link these conditional statements, providing a framework for understanding the implications of each scenario. Common examples of sentential connectors include "if," "then," and "unless," which help to construct clear logical arguments in the discussion of possible worlds.
A truth table for conjunction is
P
Q
P ∧ Q
T
T
T
T
F
F
F
T
F
F
F
F
F is for the frequency of the stimulus, which plays a crucial role in understanding the perception of sound and light in psychological studies.
Nelson Goodman’s counterfactuals explore the idea of how different scenarios could lead to varying perceptions and interpretations of stimuli, emphasizing the importance of context in psychological phenomena. Furthermore, the relationship between frequency and perception can be illustrated through experiments in auditory perception, where variations in sound frequency can significantly alter our emotional and cognitive responses.
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