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Published on November 29, 2007

Author: Gabir

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Decision Tree Analysis :  Decision Tree Analysis From the Deep Roots of Public Choice Ever New Branches Spring Forth… Previous Encounters With Decision Trees:  Previous Encounters With Decision Trees As you hopefully recall from our work with expected value analysis, decision trees are graphical representations of policy choices and the probable outcomes that are a function of those choices Our Old Tree From Week Nine:  Our Old Tree From Week Nine Decision Tree Notation:  Decision Tree Notation Decision nodes – the squares which indicate the choice points in a process a policy analyst may encounter Chance nodes – the circles which indicate the intervening uncertain events between choices and outcomes Probabilities – the likelihood that an outcome will occur; these are written alongside the lines emanating from a chance node Payoffs – the consequences of a given combination of choices and chances; these are written at the terminus of the lines emanating from a combination of choice nodes and chance nodes Basic Logic in Decision Depictions:  Basic Logic in Decision Depictions Each option at a node must be discreet All options for a node must be shown Options should not “flow back” into each other Probabilities must be reasonable… You can always vary them and thus employ a form of sensitivity analysis What is to Be Gained From A Tree?:  What is to Be Gained From A Tree? Decision trees are models. As such, they force us to think Delineate all reasonable possibilities It is surprisingly hard to be comprehensive Assign probabilities – not an easy task The generation of probabilities necessitates knowledge of politics, finances, and technical policy specific information Be conceptually distinct on options Forcing yourself to admit that coffee and tea are distinct options to a taste enthusiast if all you seek is a caffeine fix. Depending on the goal of the caffeine-related public policy at hand, it may or may not matter to distinguish the options Monkeying Around with Time :  Monkeying Around with Time While the logic of decision trees goes from right to left, the design of decision trees goes from left to right That’s right. We are mentally “swinging backwards though the trees” Normally we know what the outcomes are, what we generally don’t know is “how we got there” Choosing to Move:  Choosing to Move Moving is a great source of decision tree eligible choices Say I have $500.00 and I have a choice of staying in El Paso or moving to DC In El Paso the $500.00 can be used for the following 3 options: One month’s rent A new bicycle A trip to Phoenix In DC the $500.00 can be used for the following 3 options: A new home entertainment system A new washer A year’s fitness membership The Decision Tree Under Certainty:  The Decision Tree Under Certainty Made to Order… :  Made to Order… Under certainty, the decision process is easy to execute Simply order your preferences and pick the decision combination that results in the net largest preference score In this example, it is a year’s fitness membership in DC… for me, it might be otherwise for you Stokey and Zeckhauser (1978) refer to this backward mapping process as “folding back” The Decision Tree Under Uncertainty:  The Decision Tree Under Uncertainty Where to Go??? DC!:  Where to Go??? DC! According to our old EVA or as Stokey and Zeckhauser (1978) call it EMV calculations, DC beats El Paso out “big time” if we “fold backward” from the payoffs… El Paso=$55,000.00 .3($0.00)=0.00 .4($70,000.00)=$28,000.00 .3($90,000.00)=$27,000.00 DC=$104,000.00 .1($0.00)=0.00 .2($100,000.00)=$20,000.00 .7($120,000.00)=$84,000.00 Addressing Kahneman and Tversky?:  Addressing Kahneman and Tversky? Kahneman and Tversky’s (1979) Prospect Theory states that under conditions of expected gains people are risk seeking and under conditions of expected losses people are risk averse Despite the appearance of Stokey and Zeckhauser’s (1978) text on pages 216-218 the expected utility model they use derived from the Neumann and Morgenstern approach assumes context invariant utility slopes Prospect Theory Graphically:  Prospect Theory Graphically Prospect theory assumes an asymmetry in the risk behavior in gains regions versus loss regions. Classic utility theory assumes symmetrical concavity and convexity of the risk function in the regions of gains and losses See Quattrone, George, and Amos Tversky. 1988. “Contrasting Rational and Psychological Analyses of Political Choice.” American Political Science Review 82.3: 719-736. The picture is on page 721 Risk Aversion=Utility:  Risk Aversion=Utility What Stokey and Zeckhauser (1979) refer to as compensation for risk aversion is what Levin and McEwan (2001) refer to as the Variable Probability Method of measuring utility Testing, 1, 2, 3… Check Please!:  Testing, 1, 2, 3… Check Please! There is a value to testing options at a choice node, it is referred to as the value of learning What is learned is of considerable interest In most advanced political science public opinion models we design the respondents to have bayesian updating processes for new information Stokey and Zeckhauser (1978) transform the mathematical bayesian formula into a component of their folding back approach Expected Value of Perfect Information (EVPI):  Expected Value of Perfect Information (EVPI) The expected value of perfect information is the difference between the dollar or utility of testing versus not testing at the testing choice node While Stokey and Zeckhauser (1978) admit no perfect tests exist in public policy, we use the EVPI as if such perfection existed Caveat Emptor! The Quest for Mustang Sally Under Imperfect Testing:  Caveat Emptor! The Quest for Mustang Sally Under Imperfect Testing For those unaware, “Lemon” is slang for a defective automotive vehicle Buy Blind or Buy Seeing?:  Buy Blind or Buy Seeing? What becomes clear is that The used branch untested costs $27,000.00 The new branch costs $30,000.00 The used branch tested costs $24,600.00 plus the test Our value of testing is $2,400.00 If the test costs more than $2,400.00 to do, just buy the used car and hope for the best… For the computations, see http://utminers.utep.edu/dlevin/caveat1.xls Tree Flipping – Bayesian Updating the Easy Way:  Tree Flipping – Bayesian Updating the Easy Way Personally I preferred cow tipping as a collegiate pastime, but tree flipping is a better pastime for a budding policy analyst Tree flipping is how to assess the logical probability of an outcome once testing has been performed prior to actually performing the test Still Seeking Mustang Sally – Under Tree Roots?:  Still Seeking Mustang Sally – Under Tree Roots? How Do We Know What the Chances of Getting a Lemon Are After We Pass A Vehicle Test?:  How Do We Know What the Chances of Getting a Lemon Are After We Pass A Vehicle Test? Well, we need to transform the two-branch diagram to a three-branch diagram based not on whether the car works, but on the testing itself A Flipped Tree:  A Flipped Tree And the Answer Is…:  And the Answer Is… Twenty-two percent of the time a car passes the vehicle test we do prior to buying a used car, the car is still a “lemon” Other post-test probabilities are obtainable from the previous slide as well Being Sensitive About Decisions: Sensitivity Analysis:  Being Sensitive About Decisions: Sensitivity Analysis The crux of sensitivity analysis in decision trees is to find the tipping point where the decision maker will decide not to do option A versus option B For Decision Trees, the probabilities are the main thing to vary in a sensitivity analysis, thus… Does this sound familiar??? Yes, that’s right, it is essentially the mapping out of utility according to the Variable Probability Method of Levin and McEwan (2001) The End of Method and the Start of Praxis:  The End of Method and the Start of Praxis As Aslan once said at the end of C.S. Lewis’ Chronicles of Narnia (1998 edition), “Onward and Upward” At this point we disengage from the methodological explication of tools to the ethical and political discussion of the role of the policy analyst A discussion is a dialectic. As such, I expect YOU to read and engage the remaining material on your own, without my prompting and directing your thoughts via powerpoints You will now be expected to engage in a roundtable with myself and your classmates for the remaining two sessions… This should be interesting as many of us have had extensive prior public service both as budding analysts and as clients

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