ObjectVision was a forms-based programming language and environment for Windows 3.x developed by Borland . The latest version, 2.1, was released in 1992.
74-453: An ObjectVision application is composed by forms designed in a graphic way that contains objects and events to provide interactivity. Forms are connected together with logic in the form of decision trees . ObjectVision applications also can interact with databases using multiple engines, like Paradox and dBase . A finished project is saved as an OVD file, that is executed by an interpreted runtime that can be freely distributed. ObjectVision
148-519: A social welfare function . Instead of giving actual numbers over different bundles, ordinal utilities are only the rankings of utilities received from different bundles of goods or services. For example, ordinal utility could tell that having two ice creams provide a greater utility to individuals in comparison to one ice cream but could not tell exactly how much extra utility received by the individual. Ordinal utility, it does not require individuals to specify how much extra utility he or she received from
222-715: A coin flip comes up heads or tails), each branch represents the outcome of the test, and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represent classification rules. In decision analysis , a decision tree and the closely related influence diagram are used as a visual and analytical decision support tool, where the expected values (or expected utility ) of competing alternatives are calculated. A decision tree consists of three types of nodes: Decision trees are commonly used in operations research and operations management . If, in practice, decisions have to be taken online with no recall under incomplete knowledge,
296-416: A consumption set of R + L {\displaystyle \mathbb {R} _{+}^{L}} , and each package x ∈ R + L {\displaystyle x\in \mathbb {R} _{+}^{L}} is a vector containing the amounts of each commodity. For the example, there are two commodities: apples and oranges. If we say apples is the first commodity, and oranges
370-445: A cup of water equal to 1-p. One cannot conclude, however, that the cup of tea is two thirds of the goodness of the cup of juice, because this conclusion would depend not only on magnitudes of utility differences, but also on the "zero" of utility. For example, if the "zero" of utility was located at -40, then a cup of orange juice would be 160 utils more than zero, a cup of tea 120 utils more than zero. Cardinal utility can be considered as
444-415: A cup of water has a utility of 40 utils. With cardinal utility, it can be concluded that the cup of orange juice is better than the cup of tea by exactly the same amount by which the cup of tea is better than the cup of water. Formally, this means that if a person has a cup of tea, he or she would be willing to take any bet with a probability, p, greater than .5 of getting a cup of juice, with a risk of getting
518-406: A decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). So used manually they can grow very big and are then often hard to draw fully by hand. Traditionally, decision trees have been created manually – as the aside example shows – although increasingly, specialized software is employed. The decision tree can be linearized into decision rules , where the outcome
592-485: A decision tree model with the same data the model is tested with. The ability to leverage the power of random forests can also help significantly improve the overall accuracy of the model being built. This method generates many decisions from many decision trees and tallies up the votes from each decision tree to make the final classification. There are many techniques, but the main objective is to test building your decision tree model in different ways to make sure it reaches
666-633: A decision tree should be paralleled by a probability model as a best choice model or online selection model algorithm . Another use of decision trees is as a descriptive means for calculating conditional probabilities . Decision trees, influence diagrams , utility functions , and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods. These tools are also used to predict decisions of householders in normal and emergency scenarios. Drawn from left to right,
740-672: A decision tree. I gain ( s ) = H ( t ) − H ( s , t ) {\displaystyle I_{\textrm {gain}}(s)=H(t)-H(s,t)} This is the phi function formula. The phi function is maximized when the chosen feature splits the samples in a way that produces homogenous splits and have around the same number of samples in each split. Φ ( s , t ) = ( 2 ∗ P L ∗ P R ) ∗ Q ( s | t ) {\displaystyle \Phi (s,t)=(2*P_{L}*P_{R})*Q(s|t)} We will set D, which
814-413: A good's marginal utility is positive, additional consumption of it increases utility; if zero, the consumer is satiated and indifferent about consuming more; if negative, the consumer would pay to reduce his consumption. Rational individuals only consume additional units of goods if it increases the marginal utility. However, the law of diminishing marginal utility means an additional unit consumed brings
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#1732800788109888-445: A lower marginal utility than that brought by the previous unit consumed. For example, drinking one bottle of water makes a thirsty person satisfied; as the consumption of water increases, he may feel begin to feel bad which causes the marginal utility to decrease to zero or even become negative. Furthermore, this is also used to analyze progressive taxes as the greater taxes can result in the loss of utility. Marginal rate of substitution
962-400: A marginal returns table, analysts can decide how many lifeguards to allocate to each beach. In this example, a decision tree can be drawn to illustrate the principles of diminishing returns on beach #1. The decision tree illustrates that when sequentially distributing lifeguards, placing a first lifeguard on beach #1 would be optimal if there is only the budget for 1 lifeguard. But if there
1036-416: A positive linear transformation (multiplying by a positive number, and adding some other number); however, both utility functions represent the same preferences. When cardinal utility is assumed, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity. For example, suppose a cup of orange juice has utility of 120 "utils", a cup of tea has a utility of 80 utils, and
1110-408: A sample has a particular mutation it will show up in the table as a one and otherwise zero. Now, we can use the formulas to calculate the phi function values and information gain values for each M in the dataset. Once all the values are calculated the tree can be produced. The first thing to be done is to select the root node. In information gain and the phi function we consider the optimal split to be
1184-413: A sample is positive or negative for the root node mutation. The groups will be called group A and group B. For example, if we use M1 to split the samples in the root node we get NC2 and C2 samples in group A and the rest of the samples NC4, NC3, NC1, C1 in group B. Disregarding the mutation chosen for the root node, proceed to place the next best features that have the highest values for information gain or
1258-478: A set of samples through the decision tree classification model. Also, a confusion matrix can be made to display these results. All these main metrics tell something different about the strengths and weaknesses of the classification model built based on your decision tree. For example, a low sensitivity with high specificity could indicate the classification model built from the decision tree does not do well identifying cancer samples over non-cancer samples. Let us take
1332-415: A tree that accounts for most of the data, while minimizing the number of levels (or "questions"). Several algorithms to generate such optimal trees have been devised, such as ID3 /4/5, CLS, ASSISTANT, and CART. Among decision support tools, decision trees (and influence diagrams ) have several advantages. Decision trees: Disadvantages of decision trees: A few things should be considered when improving
1406-413: A utility function ranks preferences concerning a set of goods and services. Gérard Debreu derived the conditions required for a preference ordering to be representable by a utility function. For a finite set of alternatives, these require only that the preference ordering is complete (so the individual is able to determine which of any two alternatives is preferred or that they are indifferent), and that
1480-462: Is u (nothing) = 0, u (1 apple) = 1, u (1 orange) = 2, u (1 apple and 1 orange) = 5, u (2 apples) = 2 and u (2 oranges) = 4. Then this consumer prefers 1 orange to 1 apple, but prefers one of each to 2 oranges. In micro-economic models, there are usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. This gives
1554-409: Is a budget for two guards, then placing both on beach #2 would prevent more overall drownings. Much of the information in a decision tree can be represented more compactly as an influence diagram , focusing attention on the issues and relationships between events. Decision trees can also be seen as generative models of induction rules from empirical data. An optimal decision tree is then defined as
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#17328007881091628-464: Is a conceptual error in the "Proceed" calculation of the tree shown below; the error relates to the calculation of "costs" awarded in a legal action. Analysis can take into account the decision maker's (e.g., the company's) preference or utility function , for example: The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference coefficients (greater than $ 400K—in that range of risk aversion,
1702-401: Is a function from choices to the real numbers: which assigns a real number to every outcome in a way that represents the agent's preferences over simple lotteries. Using the four assumptions mentioned above, the agent will prefer a lottery L 2 {\displaystyle L_{2}} to a lottery L 1 {\displaystyle L_{1}} if and only if, for
1776-502: Is a major concept in welfare economics . While preferences are the conventional foundation of choice theory in microeconomics , it is often convenient to represent preferences with a utility function . Let X be the consumption set , the set of all mutually-exclusive baskets the consumer could conceivably consume. The consumer's utility function u : X → R {\displaystyle u\colon X\to \mathbb {R} } ranks each possible outcome in
1850-425: Is a measure of the satisfaction that a certain person has from a certain state of the world. Over time, the term has been used in at least two different meanings. The relationship between these two kinds of utility functions is highly controversial among both economists and ethicists . Consider a set of alternatives among which a person has a preference ordering. A utility function represents that ordering if it
1924-399: Is indeed proportional to log of income.) The first important use of the expected utility theory was that of John von Neumann and Oskar Morgenstern , who used the assumption of expected utility maximization in their formulation of game theory . In finding the probability-weighted average of the utility from each possible outcome: Von Neumann and Morgenstern addressed situations in which
1998-408: Is not always better when optimizing the decision tree. A deeper tree can influence the runtime in a negative way. If a certain classification algorithm is being used, then a deeper tree could mean the runtime of this classification algorithm is significantly slower. There is also the possibility that the actual algorithm building the decision tree will get significantly slower as the tree gets deeper. If
2072-422: Is one way to display an algorithm that only contains conditional control statements. Decision trees are commonly used in operations research , specifically in decision analysis , to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning . A decision tree is a flowchart -like structure in which each internal node represents a "test" on an attribute (e.g. whether
2146-423: Is possible for rational preferences not to be representable by a utility function. An example is lexicographic preferences which are not continuous and cannot be represented by a continuous utility function. Economists distinguish between total utility and marginal utility. Total utility is the utility of an alternative, an entire consumption bundle or situation in life. The rate of change of utility from changing
2220-550: Is possible to assign a real number to each alternative in such a manner that alternative a is assigned a number greater than alternative b if and only if the individual prefers alternative a to alternative b . In this situation someone who selects the most preferred alternative is necessarily also selecting the alternative that maximizes the associated utility function. Suppose James has utility function U = x y {\displaystyle U={\sqrt {xy}}} such that x {\displaystyle x}
2294-448: Is preferred over B. It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer relative utilities from observed choice. These 'revealed preferences', as termed by Paul Samuelson , were revealed e.g. in people's willingness to pay: Utility is assumed to be correlative to Desire or Want. It has been argued already that desires cannot be measured directly, but only indirectly, by
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2368-424: Is the contents of the leaf node, and the conditions along the path form a conjunction in the if clause. In general, the rules have the form: Decision rules can be generated by constructing association rules with the target variable on the right. They can also denote temporal or causal relations. Commonly a decision tree is drawn using flowchart symbols as it is easier for many to read and understand. Note there
2442-562: Is the depth of the decision tree we are building, to three (D = 3). We also have the following data set of cancer and non-cancer samples and the mutation features that the samples either have or do not have. If a sample has a feature mutation then the sample is positive for that mutation, and it will be represented by one. If a sample does not have a feature mutation then the sample is negative for that mutation, and it will be represented by zero. To summarize, C stands for cancer and NC stands for non-cancer. The letter M stands for mutation , and if
2516-430: Is the number of apples and y {\displaystyle y} is the number of chocolates. Alternative A has x = 9 {\displaystyle x=9} apples and y = 16 {\displaystyle y=16} chocolates; alternative B has x = 13 {\displaystyle x=13} apples and y = 13 {\displaystyle y=13} chocolates. Putting
2590-417: Is the slope of the indifference curve, which measures how much an individual is willing to switch from one good to another. Using a mathematic equation, M R S = − d x 2 / d x 1 {\displaystyle MRS=-\operatorname {d} \!x_{2}/\operatorname {d} \!x_{1}} keeping U ( x 1 , x 2 ) constant. Thus, MRS is how much an individual
2664-424: Is willing to pay for consuming a greater amount of x 1 . MRS is related to marginal utility. The relationship between marginal utility and MRS is: Expected utility theory deals with the analysis of choices among risky projects with multiple (possibly multidimensional) outcomes. The St. Petersburg paradox was first proposed by Nicholas Bernoulli in 1713 and solved by Daniel Bernoulli in 1738, although
2738-432: The optimal attainable value of a given utility function, which depends on the prices of the goods and the income or wealth level that the individual possesses. One use of the indirect utility concept is the notion of the utility of money. The (indirect) utility function for money is a nonlinear function that is bounded and asymmetric about the origin. The utility function is concave in the positive region, representing
2812-505: The Swiss mathematician Gabriel Cramer proposed taking the expectation of a square-root utility function of money in an 1728 letter to N. Bernoulli. D. Bernoulli argued that the paradox could be resolved if decision-makers displayed risk aversion and argued for a logarithmic cardinal utility function. (Analysis of international survey data during the 21st century has shown that insofar as utility represents happiness, as for utilitarianism , it
2886-428: The above example, it would only be possible to say that juice is preferred to tea to water. Thus, ordinal utility utilizes comparisons, such as "preferred to", "no more", "less than", etc. If a function u ( x ) {\displaystyle u(x)} is ordinal and non-negative, it is equivalent to the function u ( x ) 2 {\displaystyle u(x)^{2}} , because taking
2960-401: The accuracy of the decision tree classifier. The following are some possible optimizations to consider when looking to make sure the decision tree model produced makes the correct decision or classification. Note that these things are not the only things to consider but only some. Increasing the number of levels of the tree The accuracy of the decision tree can change based on the depth of
3034-421: The accuracy of the decision tree. For example, using the information-gain function may yield better results than using the phi function. The phi function is known as a measure of “goodness” of a candidate split at a node in the decision tree. The information gain function is known as a measure of the “reduction in entropy ”. In the following, we will build two decision trees. One decision tree will be built using
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3108-423: The assumption that utility can be measured by quantifiable characteristics, such as height, weight, temperature, etc. Neoclassical economics has largely retreated from using cardinal utility functions as the basis of economic behavior. A notable exception is in the context of analyzing choice with conditions of risk (see below ). Sometimes cardinal utility is used to aggregate utilities across persons, to create
3182-567: The combinations of commodity X and Y along the same indifference curve are regarded indifferently by individuals, which means all the combinations along an indifference curve result in the same value of utility. Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively. When coupled with production or commodity constraints, by some assumptions these functions can be used to analyze Pareto efficiency , such as illustrated by Edgeworth boxes in contract curves . Such efficiency
3256-400: The company would need to model a third strategy, "Neither A nor B"). Another example, commonly used in operations research courses, is the distribution of lifeguards on beaches (a.k.a. the "Life's a Beach" example). The example describes two beaches with lifeguards to be distributed on each beach. There is maximum budget B that can be distributed among the two beaches (in total), and using
3330-618: The confusion matrix below. The confusion matrix shows us the decision tree model classifier built gave 11 true positives, 1 false positive, 45 false negatives, and 105 true negatives. We will now calculate the values accuracy, sensitivity, specificity, precision, miss rate, false discovery rate, and false omission rate. Accuracy: A c c u r a c y = ( T P + T N ) / ( T P + T N + F P + F N ) {\displaystyle Accuracy=(TP+TN)/(TP+TN+FP+FN)} Utility function In economics , utility
3404-402: The consumption set. If the consumer strictly prefers x to y or is indifferent between them, then u ( x ) ≥ u ( y ) {\displaystyle u(x)\geq u(y)} . For example, suppose a consumer's consumption set is X = {nothing, 1 apple,1 orange, 1 apple and 1 orange, 2 apples, 2 oranges}, and his utility function
3478-405: The decision tree. In many cases, the tree’s leaves are pure nodes. When a node is pure, it means that all the data in that node belongs to a single class. For example, if the classes in the data set are Cancer and Non-Cancer a leaf node would be considered pure when all the sample data in a leaf node is part of only one class, either cancer or non-cancer. It is important to note that a deeper tree
3552-438: The function itself, and which plot the combination of commodities that an individual would accept to maintain a given level of satisfaction. Combining indifference curves with budget constraints allows for derivation of individual demand curves . A diagram of a general indifference curve is shown below (Figure 1). The vertical axes and the horizontal axes represent an individual's consumption of commodity Y and X respectively. All
3626-566: The function needs to be defined for fractional apples and oranges too. One function that would fit these numbers is u ( x apples , x oranges ) = x apples + 2 x oranges + 2 x apples x oranges . {\displaystyle u(x_{\text{apples}},x_{\text{oranges}})=x_{\text{apples}}+2x_{\text{oranges}}+2x_{\text{apples}}x_{\text{oranges}}.} Preferences have three main properties : Assume an individual has two choices, A and B. By ranking
3700-413: The highest performance level possible. It is important to know the measurements used to evaluate decision trees. The main metrics used are accuracy , sensitivity , specificity , precision , miss rate , false discovery rate , and false omission rate . All these measurements are derived from the number of true positives , false positives , True negatives , and false negatives obtained when running
3774-401: The individual prefers bundle A to bundle C. (If a ≥ b and b ≥ c , then a ≥ c for all ( a , b , c )). If a bundle A contains all the goods that a bundle B contains, but A also contains more of at least one good than B, then the individual prefers A over B. If, for example, bundle A = {1 apple,2 oranges}, and bundle B = {1 apple,1 orange}, then A
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#17328007881093848-480: The model using information gain we get one true positive, one false positive, zero false negatives, and four true negatives. For the model using the phi function we get two true positives, zero false positives, one false negative, and three true negatives. The next step is to evaluate the effectiveness of the decision tree using some key metrics that will be discussed in the evaluating a decision tree section below. The metrics that will be discussed below can help determine
3922-437: The mutation that produces the highest value for information gain or the phi function. Now assume that M1 has the highest phi function value and M4 has the highest information gain value. The M1 mutation will be the root of our phi function tree and M4 will be the root of our information gain tree. You can observe the root nodes below Now, once we have chosen the root node we can split the samples into two groups based on whether
3996-422: The next steps to be taken when optimizing the decision tree. Other techniques The above information is not where it ends for building and optimizing a decision tree. There are many techniques for improving the decision tree classification models we build. One of the techniques is making our decision tree model from a bootstrapped dataset. The bootstrapped dataset helps remove the bias that occurs when building
4070-413: The nodes and the right tree is what we obtain from using the phi function to split the nodes. Now assume the classification results from both trees are given using a confusion matrix . Information gain confusion matrix: Phi function confusion matrix: The tree using information gain has the same results when using the phi function when calculating the accuracy. When we classify the samples based on
4144-465: The number D as the depth of the tree. Possible advantages of increasing the number D: Possible disadvantages of increasing D The ability to test the differences in classification results when changing D is imperative. We must be able to easily change and test the variables that could affect the accuracy and reliability of the decision tree-model. The choice of node-splitting functions The node splitting function used can have an impact on improving
4218-484: The outcomes of choices are not known with certainty, but have probabilities associated with them. A notation for a lottery is as follows: if options A and B have probability p and 1 − p in the lottery, we write it as a linear combination: More generally, for a lottery with many possible options: where ∑ i p i = 1 {\displaystyle \sum _{i}p_{i}=1} . By making some reasonable assumptions about
4292-467: The outward phenomena which they cause: and that in those cases with which economics is mainly concerned the measure is found by the price which a person is willing to pay for the fulfillment or satisfaction of his desire. Utility functions , expressing utility as a function of the amounts of the various goods consumed, are treated as either cardinal or ordinal , depending on whether they are or are not interpreted as providing more information than simply
4366-575: The phenomenon of diminishing marginal utility . The boundedness represents the fact that beyond a certain amount money ceases being useful at all, as the size of any economy at that time is itself bounded. The asymmetry about the origin represents the fact that gaining and losing money can have radically different implications both for individuals and businesses. The non-linearity of the utility function for money has profound implications in decision-making processes: in situations where outcomes of choices influence utility by gains or losses of money, which are
4440-404: The phi function in the left or right child nodes of the decision tree. Once we choose the root node and the two child nodes for the tree of depth = 3 we can just add the leaves. The leaves will represent the final classification decision the model has produced based on the mutations a sample either has or does not have. The left tree is the decision tree we obtain from using information gain to split
4514-408: The phi function to split the nodes and one decision tree will be built using the information gain function to split the nodes. The main advantages and disadvantages of information gain and phi function This is the information gain function formula. The formula states the information gain is a function of the entropy of a node of the decision tree minus the entropy of a candidate split at node t of
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#17328007881094588-459: The preference order is transitive . If the set of alternatives is not finite (for example because even if the number of goods is finite, the quantity chosen can be any real number on an interval) there exists a continuous utility function representing a consumer's preferences if and only if the consumer's preferences are complete, transitive and continuous. Utility can be represented through sets of indifference curve , which are level curves of
4662-437: The preferred bundle of goods or services in comparison to other bundles. They are only required to tell which bundles they prefer. When ordinal utilities are used, differences in utils (values assumed by the utility function) are treated as ethically or behaviorally meaningless: the utility index encodes a full behavioral ordering between members of a choice set, but tells nothing about the related strength of preferences . For
4736-459: The properties of the agent's preference relation over 'simple lotteries', which are lotteries with just two options. Writing B ⪯ A {\displaystyle B\preceq A} to mean 'A is weakly preferred to B' ('A is preferred at least as much as B'), the axioms are: Axioms 3 and 4 enable us to decide about the relative utilities of two assets or lotteries. In more formal language: A von Neumann–Morgenstern utility function
4810-520: The quantity of one good consumed is termed the marginal utility of that good. Marginal utility therefore measures the slope of the utility function with respect to the changes of one good. Marginal utility usually decreases with consumption of the good, the idea of "diminishing marginal utility". In calculus notation, the marginal utility of good X is M U x = ∂ U ∂ X {\displaystyle MU_{x}={\frac {\partial U}{\partial X}}} . When
4884-569: The rank ordering of preferences among bundles of goods, such as information concerning the strength of preferences. Cardinal utility states that the utilities obtained from consumption can be measured and ranked objectively and are representable by numbers. There are fundamental assumptions of cardinal utility. Economic agents should be able to rank different bundles of goods based on their own preferences or utilities, and also sort different transitions of two bundles of goods. A cardinal utility function can be transformed to another utility function by
4958-449: The second, then the consumption set is X = R + 2 {\displaystyle X=\mathbb {R} _{+}^{2}} and u (0, 0) = 0, u (1, 0) = 1, u (0, 1) = 2, u (1, 1) = 5, u (2, 0) = 2, u (0, 2) = 4 as before. For u to be a utility function on X , however, it must be defined for every package in X , so now
5032-710: The square is an increasing monotone (or monotonic) transformation . This means that the ordinal preference induced by these functions is the same (although they are two different functions). In contrast, if u ( x ) {\displaystyle u(x)} is cardinal, it is not equivalent to u ( x ) 2 {\displaystyle u(x)^{2}} . In order to simplify calculations, various alternative assumptions have been made concerning details of human preferences, and these imply various alternative utility functions such as: Most utility functions used for modeling or theory are well-behaved. They are usually monotonic and quasi-concave. However, it
5106-408: The tree-building algorithm being used splits pure nodes, then a decrease in the overall accuracy of the tree classifier could be experienced. Occasionally, going deeper in the tree can cause an accuracy decrease in general, so it is very important to test modifying the depth of the decision tree and selecting the depth that produces the best results. To summarize, observe the points below, we will define
5180-458: The two choices, one and only one of the following relationships is true: an individual strictly prefers A (A > B); an individual strictly prefers B (B>A); an individual is indifferent between A and B (A = B). Either a ≥ b OR b ≥ a (OR both) for all ( a , b ) Individuals' preferences are consistent over bundles. If an individual prefers bundle A to bundle B, and prefers bundle B to bundle C, then it can be assumed that
5254-456: The utility function characterizing that agent, the expected utility of L 2 {\displaystyle L_{2}} is greater than the expected utility of L 1 {\displaystyle L_{1}} : Of all the axioms, independence is the most often discarded. A variety of generalized expected utility theories have arisen, most of which omit or relax the independence axiom. An indirect utility function gives
5328-403: The values x , y {\displaystyle x,y} into the utility function yields 9 × 16 = 12 {\displaystyle {\sqrt {9\times 16}}=12} for alternative A and 13 × 13 = 13 {\displaystyle {\sqrt {13\times 13}}=13} for B, so James prefers alternative B. In general economic terms,
5402-423: The way choices behave, von Neumann and Morgenstern showed that if an agent can choose between the lotteries, then this agent has a utility function such that the desirability of an arbitrary lottery can be computed as a linear combination of the utilities of its parts, with the weights being their probabilities of occurring. This is termed the expected utility theorem . The required assumptions are four axioms about
5476-476: Was not used broadly except in some niche segments, but the visual programming ideas were the basis for Borland Delphi . This programming-tool -related article is a stub . You can help Misplaced Pages by expanding it . Decision tree A decision tree is a decision support recursive partitioning structure that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility . It
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