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Outline. Fundamentals of Introduction Decision analysis Behavioral decision making Game theory Negotiation analysis. Introduction. Four approaches to making decisions: How an individual should and could make decisions (Prescriptive)
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Outline • Fundamentals of • Introduction • Decision analysis • Behavioral decision making • Game theory • Negotiation analysis
Introduction • Four approaches to making decisions: • How an individual should and could make decisions (Prescriptive) • Psychology of how individuals actually make decisions (Descriptive) • How individuals should make separate interactive decisions (Normative) • How groups should and could make joint decisions (Prescriptive) • Raiffa’s book is intended to help us make better decisions and takes all these approaches into consideration
Decision Analysis • Generic Decisions • PrOACT • Uncertainty and Risk • Risk Profiles • Ordinal Ranking • EMV (Expected Monetary Value) • EDV (Expected Desirability Value) • Expected Utility Value
Generic Decisions • Choices, Occasions, Situations: • Decide to negotiate • What if the negotiations fail? • Go to court or accept a settlement • Whom do you negotiate with? • Use an arbitrator? • Choose a style of negotiation • Lesson – Learn the theory and practice prescriptive decision making
PrOACT • Identify the Problem • Clarify the Objectives • Generate creative Alternatives • Evaluate the Consequences • Make Tradeoffs • Lesson – as opposed to reactive: waiting for the other party to do something
Types of errors • When someone makes a statement to you, there are four possible results • You accept the statement as true and it is indeed true • You do not accept the statement and it is false • You accept the statement and it is false • You do not accept the statement and it is true • There is no error for the first two cases • In case three you make an error of the second kind, often called a beta error • In case four you make an error of the first kind or alpha error • Some refer to solving the wrong problem as the third kind of error
Some advice about identifying problems • Think about what caused you to realize that you had to make a decision • Consider solving problems other than the immediate one you face • Question constraints (That’s impossible, I can’t do that, she’ll never go for it, etc.) • Get advice
Objectives • Objectives and interests are synonymous • Think about them broadly rather than narrowly • People have a tendency to look at only a few ramification of what they want to get out of a situation • Why do you want this outcome? • What do mean by your stated objective? • Lesson – brainstorm a list, then whittle it down
Creative Alternatives • There are many ways to get to most objectives • The more of them you consider, the more likely you are to achieve your objectives • Here again, brainstorming lists is very good, but don’t forget to reduce them as well • Alternatives are external to negotiations, options are internal
Evaluating consequences • How good is alternative X with regard to objective Y? • Remember that you have multiple objective and a given alternative will have different effects on each • Construct a matrix as on page 19 of Raiffa – this is called conditional analysis • If we see that one alternative is at least as good or better than another with respect to all objectives, we say that it dominates. (PPP dominates QQQ)
Evaluating consequences – Making Tradeoffs • If it is possible to express all objectives with one measure, we call it costing out. This makes a direct comparison possible. Quite frequently, the one measure is money. • Suppose we assign values to the evaluations in the previous table OK = 1, Fair = 2, Good = 3, Great = 4 and a point for each $200K: • This would allow us to choose a clear winner
Evaluating consequences – Making Tradeoffs • Trade off between objectives, as in the example, sometimes prestige is more important than money (or the prestige will eventually lead to money in subsequent situations!)
Uncertainty and Risk • Usually you do not know the consequences of most alternatives precisely • Risk profiles: • Attach a risk profile to each alternative: • Possible outcomes • Probability of each outcome • Resulting consequences • Caution – separate your judgments about uncertainties from judgments about values
Uncertainty and Risk • A risk profile for one alternative, using qualitative assessments: • Adding numerical assessments:
Expected Monetary value • I have included a portion of a second lecture from a course in Statistical Decision Making that you may find useful (See the Course notes or Course Documents (DEN) sections. • Simply put, the expected monetary value or expected value equals • Probability of occurrence x Value • EMV is the mean of the expected distribution of the payoffs • If a lottery distributes 1,000,000 ticket from which it draws a winner and the winner gets $2,000,000, then • Expected Monetary Value = (1/1,000,000) x $2,000,000 = $2 • Another way to look at EMV as a weighted average • Caution – EMV’s assume that increments in money have uniform intrinsic values
Expected Desirability Value • This measure is intended to capture on how strongly or intensely we feel about something • How do you assign these values? • Without extensive consideration – assign a portion to each • Conditionally – comparing desirability on some scale • Monetary value converted to a desirability value • Let’s look at the book’s example:
Expected Desirability Value - continued • The desirability values were derived as follows • The lowest to highest outcomes are 0 and $2M. The objective is to decide how important each increment in money is. Let’s start with: • From $0 to $500,000 = 50 points • From $500,000 to $2,000,000 = 50 points, that is • The judgmental mid-desirability point between 0 an 2M is 500K • Making two more judgements • The judgmental mid-desirability point between 0 an 500K is 200K • The judgmental mid-desirability point between 500K and 2M is 1M • We can now put this into a table and graph on the next slide:
Expected Desirability Value - continued • From this graph we find the individual desirability values
Expected Utility Values • The previous two measures can be quite useful, but do not take into consideration the attitude towards risk • EUV can be a useful summary value • Definition BRLT = Basic Reference Lottery Ticket • Note that this particular ticket has an EMV of $500,000
Expected Utility Values - continued • I have put the following formula in a cell in Excel and when I put an equal sign in front of it, it will determine whether we win or not • How do we use this? • Select L and W from your risk profiles (the book’s example had 0 and $2M) • BRLT’s will be chosen with monotonicity and continuity (as in math analysis) • They are also substitutable – If we don’t care whether we get outcome B or a 0.6 BRLT, we can substitute one for the other
Expected Utility Values - continued • As with desirability midpoints, we establish mid risk points • How much would you be satisfied with if the outcome was certain as compared to a 50 – 50 chance of zero and the max? • In our example • 0 to 2M : 400K • 0 to 400K: 150K • 400K to 2M: 800K
Behavioral Decision Making • How do real people make decisions? • Most people, most of the time, do not follow the advice of theorists • What are the most frequent deviations from rational decisions?
Behavioral Decision Making - Decision traps • Anchoring – Relying on a first impression • Status Quo – stick with the past • Sunk Cost – throwing good money after bad • Confirming Evidence – we tend to pay more attention to evidence that supports our position • Wrong problem – influencing the response with the question – recent story about automobile death rates
Behavioral Decision Making - Prediction Anomalies • Thinking probabilistically – most people don’t bother • likely, probably, maybe, more than likely, rarely, likelyhood. Possibility, good chance • Lesson – be more precise • Conditional ambiguities - P(A|B) vs. P(B|A), Monty Hall • Overconfidence – using confidence intervals that are too tight • Lesson - practice • Conjunction fallacy - P(A and B) > P(A). This must be false, but when you substitute real events, people do make the mistake
Behavioral Decision Making - Prediction Anomalies • Mutually distinct – no union or P(A and B) = 0 • Exhaustive – all possible events are included in the probability space P(A) + P(B) +….+P(X) = 1 • Prior odds – the probabilities of A and B as given • When new information (NI) is added, (and assume that it is distinct) we get posterior probabilities P(A|NI), P(B|NI) • For example: P(A) = 0.3, P(B) = 0.4, P(NI) = 0.2, then P(A|NI) = 0.3/(1-0.2) = 0.375 and P(B(NI) = 0.4/(1-0.8) = 0.5, that is the odds on A and B have increased because part of the space has been taken up by NI • P(A)/P(B) = 0.75, but P(A|NI)/P(B|NI) = 0.75, because we assumed that NI was in our probability space and exclusive
Behavioral Decision Making - Prediction Anomalies • In general, this is not the case and • P(A|NI)/P(B|NI) = P(A)/P(B) x P(NI|A)/P(NI|B) The last term is the likelihood ratio • Bayes’ theorem • Example If 30% of students in a class of 50 got A’s and 35% in A class of 60 got A’s, what is the percentage of A’s? There are 15 in the first class and 21 in the second class for a total of 36 A’s out of 110 students = (15+21)/(50+60) = 0.327 • But let’s ask the question in reverse – If a student got an A, what is the probability that she/he came from the first class? How many A’s in the first class? 15. How many total A’s? 36, therefore (0.3)(50)/[(0.3)(50) + (0.35)(60)] = 0.417
Behavioral Decision Making - Prediction Anomalies • Base rate fallacy – the base is the probability ratio P(A)/P(B) • People confuse the base rate with the likelihood ratio • Underestimating the value of sample evidence • Example in book about green and white bags • Census discussion in Congress in 1990’s • Getting mystical about coincidences I bet you each have a story about a coincidence • Suppose I flip a coin 15 time in a row and get the following result HHTTHHHTHTHTTTH. Note that there are 7 T’s and 8 H’s, not an unusual result. So this particular sequence of events is not particularly unusual. However, if I view it from the perspective that this particular sequence has occurred, the odds are 215 = 32768:1!!! • People resist changing their mind once they have come to a conclusion
Game Theory • “How rational actors ought to behave when their separate choices interact to produce payoffs to each player” • Consider it from the perspective of what it tells us about negotiation because it offers us powerful insight • Helps us consider how the other party will respond to our offers • Basics: • You have to act (doing nothing is considered an act) • Payoffs depend on what each party does • You don’t know what they will do, but know what they could do • They do not know what you will do, but know what you could do
Negotiation Analysis • Joint decision making • Organizing an approach
