Cardinal Vs Ordinal Utility

11 Key excerpts on "Cardinal Vs Ordinal Utility"

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  Philosophy, Politics, and Economics

  An Introduction

  • Gerald Gaus, John Thrasher(Authors)
  • 2021(Publication Date)
  • Princeton University Press

    (Publisher)

  We also must not lose sight of the fact that the axioms are ways to generate cardinal measures out of ordinal preferences. This means that ordered ordinal preferences over outcomes and lotteries are all that are required. This is an especially elegant idea, but the very idea of cardinal utility does not depend on it. We should expect that doing something as neat as deriving the cardinal from the ordinal may invoke some contestable axioms. Although it is sometimes claimed that all uses of cardinal utility measures implicitly rely on the existence of the von Neumann–Morgenstern axioms, in practice economists and game theorists are quite happy to appeal directly to the idea of a cardinal scale on which outcomes can be placed.

  Indeed, John Pollock has developed a computationally realistic model of rational decision-making according to which cardinal, not ordinal, utility is fundamental.2 Pollock argues that a cognitive system that stored its basic values in an ordinal ranking would have to relate to so many possible pairs of options that it would be unable to function—essentially such an agent would require an infinite data structure. Pollock shows that a person who used pairwise comparisons to relate every possible state of the world over which she might choose would have more comparisons than the number of elementary particles in the universe! Thus, rather than taking ordinal data as basic and trying to show how we might derive cardinal data from it, Pollock argues that real agents store their utility information in cardinal form. Some cognitive scientists and philosophers of mind also argue that preferences, as they are represented in the mind, are cardinal, not ordinal.

  Representation of Utility

  One of the problems we noted with simple ordinal utility was that we could not sensibly add the utility of different people into an overall, aggregate measure of utility. Think back again to the discussion of ordinal utility. Given the very different sets of numbers that represent the same preference structure, it was clear that ordinal utility functions do not lend themselves to addition. To add we need a cardinal measure. Now suppose that in Alf’s utility function option y gives him, say, .7 utility and y gives Betty .5. Can we proceed to add these nice cardinal numbers together and say that the total utility of y is 1.2? Can we say that Alf gets more utility than Betty from y

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  Hayek: A Collaborative Biography

  Part IV, England, the Ordinal Revolution and the Road to Serfdom, 1931-50

  • R. Leeson(Author)
  • 2015(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  any increasing transformation of U(x), i.e., with any f[U(x)] such that f’>0.

  3. Classically measurable utility is associated with proportional transformations of U(x ) that do not modify the zero point of utility, i.e., with transformations of the form αU(x ), where α>0.

  4. See in particular Hayek (1934), Morgenstern (1941), Rothbard (1956), and High and Bloch (1989).

  5. On the relationships between marginal and total ordinal utility, see McCulloch (1977).

  6. This section largely draws on Moscati (2013a).

  7. Since this is the first quotation of the chapter, it is useful to illustrate here how I dealt with the original texts in German and their English translations. Whenever possible, I checked the existing English translations with the original texts in German. If I found any inaccuracies in a translation, I corrected them but maintained the reference to the translation and its page numbers. However, I refrained from specifying each time how and why I modified the translation. When no translation of the original texts was available, the translation is mine.

  8. On the reception of Menger’s work and the rise of the Austrian school, see Howey (1960).

  9. For instance, if the two quantities consist of 9 and 10 units, and the marginal utilities of the 9th and 10th units are associated with figures 6 and 5 respectively, then the economic value of 9 units (9×6=54) is larger than the economic values of 10 units (10×5=50). But if the marginal utility numbers are ordinal in nature, the marginal utilities of the 9th and 10th units could also be associated with figures 12 and 11 respectively. In that case, however, 9 units have a smaller economic value (9×12=108) than 10 units (10×11=110).

  10. Neumann was an important member of the Historical School, whose purely descriptive approach to economic analysis was attacked by Menger in his Investigations into the Method of the Social Sciences ([1883] 1985). Menger’s attack initiated a famous and lasting methodological dispute, the so-called Methodenstreit, between the Historical School, which dominated economic research in Germany at that time, and the rising Austrian School. Böhm-Bawerk’s response to Neumann’s criticism can also be seen as a minor episode of the Methodenstreit. (On the Methodenstreit, see Bostaph 1978; Caldwell 2004 and Chapter 2

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  Patrick Suppes, Economics, and Economic Methodology

  • John B. Davis, D. Wade Hands, John B. Davis, D. Wade Hands(Authors)
  • 2018(Publication Date)
  • Taylor & Francis

    (Publisher)

  It appears to have stabilized before than the de fi nition of a cardinal utility function did. Even relatively late in the twentieth century, neoclassical writers often adopted different words and different ideas to capture the more-than-ordinal features of a utility function. PATRICK SUPPES, ECONOMICS, AND ECONOMIC METHODOLOGY 33 They said not only ‘ cardinal ’ , but also ‘ numerical ’ , ‘ measurable ’ and ‘ quantitative ’ , being quite vague – and no doubt disagreeing between themselves – on the kind of mathematical uniqueness they had in view for the utility function. 3 As Hicks (1939, p. 18) writes, we have now to inquire whether a full theory of consumer ’ s demand ( … ) cannot be built up from the assumption of a scale of preference . In constructing such a theory it will be necessary every time to reject any concept which is at all dependent on quantitative utility, so that it cannot be derived from the indifference map alone. Beside testifying to the vagueness of ideas concerning ‘ quantitative utility ’ , this com-ment is instructive in the following way: while Hicks means his explication to restrict the utility concept, it also turns out to restrict the preference concept. Preference is taken here to be a mere disposition to rank the objects of interest (or to classify them as being indifferent, which we include in our notion of a ranking). As Hicks goes on, ‘ we start off from the indifference map alone; nothing more can be allowed ’ . Among other things, this implies that unlike in some earlier approaches, there will be no room in the new theory for comparisons of the type ‘ i prefers more intensely hot chocolate to coffee, than he prefers tea to herbal tea ’ . Such comparisons are unde fi ned because they do something else than ranking options. Samuelson ’ s Foundations (1947) exempli-fi es the glide, which we emphasize here, from the claim that utility is exclusively ordi-nal to the claim that preference also is.

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  Microeconomics

  A Global Text

  • Judy Whitehead(Author)
  • 2020(Publication Date)
  • Routledge

    (Publisher)

  Consumers are assumed to have full knowledge of the available commodities and their prices in the market, and to know their income limit. Consumers plan to spend their income to attain the highest possible satisfaction (utility) within these parameters. In general, there are considered to be two major approaches to the theory of utility maximization: The Cardinal theory and the Ordinal theory. A third approach, the Revealed Preference theory, is usually viewed as an addendum or upgrade to the THEORY OF THE CONSUMER C H A P T E R 2 Ordinal theory but may be considered a theory in its own right. The Ordinal theory is buoyed by the Revealed Preference theory. The study of the consumer traces the utility theories from the Classical utility theory, through the Ordinal utility theory to the modification brought to the Ordinal utility theory by the Revealed Preference theory. As the study proceeds, it may be observed that all three approaches lead to the same conclusion or testable hypothesis: that, normally, as the price of a good falls, the quantity demanded increases. This becomes known as the Law of Demand and is applied throughout economics and Business/Management Studies. It may also be observed that the revisions of utility theory over time are due to concerns with the assumptions of the theory, as discussed under the methodology of microeconomic theory (see Chapter 1), even though the predictions have already been found acceptable. The study of utility maximization begins with the Cardinal utility theory. 2.2 THE CARDINAL UTILITY THEORY The Cardinal utility theory is considered to be the oldest version of utility theory. Central to the Cardinal theory is the concept of measurable utility. The assumption is that utility or satisfaction is measurable on a cardinal scale (i.e. a scale with zero as the origin). It was believed that this measurement could be done in money, or in the older vintages, in subjective units called Utils.

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  Risk Management in Supply Chains

  Using Linear and Non-linear Models

  • Mohammad Heydari, Kin Keung Lai, Zhou Xiaohu(Authors)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  2     Risks in economics

  2.1   Utility theory

  The concept of utility and its relationship with the value of goods and services. Consumer satisfaction, which results from the consumption of goods and services, is called utility by economists.

  Professor Jermain Bentham of English first introduced the term utility. Nevertheless, neither her nor the economists of her age understood the relationship between the value of goods and the utility they derive from the consumption of goods.

  Adam Smith recognized the relationship between the value of the use and the value of the commodity’s exchange and described his famous example of water and diamonds. Diamonds have a high price, but its value for life is low, while water prices (exchange value) are small but essential for life, and they have a very high value.

  2.1.1   Cardinal Theory of Utility

  The usefulness of cardinal theory suggests that utility is measured just as much as the price and amount. This means that we can determine the amount of utility of each commodity. In this theory, both utility and ultimate utility can be measured. Economists who believed that cardinality was desirable can be divided into two groups:

  1. 1   Those who believed that the utility was acceptable.
  2. 2   Those who believed that utility could not be comprehensible.

  To better understand the subject of this theory, consider the following article that is provided by J. Singh.

  2.1.2   Consumer’s Behavior. Cardinal Utility Analysis (Explained with Diagram)

  From time to time, different theories have been advanced to explain consumer’s demand for a good and to derive a valid demand theorem.

  Cardinal utility analysis is the oldest theory of demand which provides an explanation of consumer’s demand for a product and derives the law of demand which establishes an inverse relationship between price and quantity demanded of a product.

  The price of a product depends upon the demand for and the supply of it. In this part of the book, we are concerned with the theory of consumer’s behavior, which explains his demand for a good and the factors determining it. Individual’s demand for a product depends upon the price of the product, the income of the individual and the prices of related goods.

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  Principles of Agricultural Economics

  • Andrew Barkley, Paul W. Barkley(Authors)
  • 2020(Publication Date)
  • Routledge

    (Publisher)

  USDA-ERS Economic Research Report No. ERR-100 ., U.S. Department of Agriculture, Economic Research Service, July 2010.

  Okrent, A. M., & Alston, J. M. (2012). The effects of farm commodity and retail food policies on obesity and economic welfare in the United States. American Journal of Agricultural Economics , 94(3), 611–646.

  US. BLS. (2009) National Longitudinal Surveys. USDA/ERS (2007) National Health and Nutrition Examination Survey (NHANES).

  USDA/ERS (2009) Access to Affordable and Nutritious Food: Measuring and Understanding Food Deserts and Their Consequences AP-036. Washington DC: USDA, June.

  These scientists and scholars soon found that assigning utils was impossible. People cannot assign a meaningful value to the level of satisfaction because the measures of satisfaction differ among individuals and are not observable. Since science requires accurate and measurable observations, the early scholars concluded that they could not use cardinal utility measures to quantify an individual’s feelings or level of satisfaction. Once economists and others realized that measuring utility was impossible, they turned attention to ordinal utility , or ranking goods in order of preference (A is preferred to B, B is preferred to C, C is preferred to D, etc.). Ordinal utility replaced the earlier concept of cardinal utility.

  • • Ordinal Utility = a way of considering consumer satisfaction in which goods are ranked in order of preference: first, second, third, etc.

  Ordinal preferences do not depend on specific numbers or values. Instead, the rankings of goods and services with respect to the satisfaction they provide relative to other goods allow economists to observe consumers and develop principles of human behavior to help understand consumer choices. Cardinal utility continues to provide examples of how consumer behavior works, as shown in the next section.

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  The Economics of Resource Allocation in Health Care

  Cost-utility, social value, and fairness

  • Andrea Klonschinski(Author)
  • 2016(Publication Date)
  • Taylor & Francis

    (Publisher)

  The quantity can be conceived of in hedonic terms so that a cardinally measurable, hedonic utility concept would indicate the intensity of a feeling and allows for “measuring one gain or loss in well-being [in terms of pleasure] relative to another” (Mandler 1999: 82), whereas an ordinal hedonic utility concept only indicates more or less pleasure. Despite their logical independence, psychologically, “cardinalism and hedonism are natural partners,” as Mandler (1999: 84) points out. This is because “hedonism provides the most common psychological justification for cardinality; and in order to be plausible, cardinality requires some account of how agents make judgments of preference intensity” (ibid.). But even in the case of ordinal utilities, it is actually hard to come up with a quantity behind the preference rankings other than certain sensations. Alternatively, the assumption of the existence of an underlying quantity can be dropped altogether and this is in fact what happens in the course of the formalist revolution. Suffice it to carve out at this point that the aspects of the quantitative nature of utility, the underlying psychology, and the measurability of utilities are logically independent from each other. As will become clear in the following, several combinations of these elements have been proposed throughout the history of economics. Against the background of these conceptual remarks, two different interpretations of Pareto’s contribution can be discerned in the literature, both of which exerted a major influence on the discipline of economics and its utility concept. According to the first, which was already appealed to above, Pareto regarded utility as a quantity of pleasure, albeit a cardinally immeasurable one

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  Game Theory

  A Modeling Approach

  • Richard Alan Gillman, David Housman(Authors)
  • 2019(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  2.2Make a list of four or five weekend leisure activities (or use a list provided by your instructor). Let an outcome be engaging in one of these activities for free. Determine your ordinal utilities among these outcomes. Determine one other person’s ordinal utilities among these four or five outcomes. By doing all of the necessary pairwise comparisons, check to see whether your utilities and the other person’s utilities truly are ordinal. If both are ordinal utility functions, are they the same utility function?

  2.3Consider the last time you registered for classes and the thousands of schedules that were available to you. Clearly, you did not consider every one of them. Create an ordinal utility function that assigns a utility to every possible schedule and reflects your preferences over them.

  2.4Suppose there are m outcomes to a game.

  a.We can construct an ordinal utility function for any player as we did for Scarlett in the Ice Cream Parlor scenario: First present all possible outcomes, assign a utility to the player’s choice, remove that outcome from the list, present the remaining outcomes, assign a smaller utility to the player’s choice at this step, and continue until all outcomes have been chosen and utilities have been assigned. What is the maximum number of subsets that we will present to the player to make a choice?

  b.To verify that Scarlett has ordinal preferences, we presented 11 subsets of two or more outcomes. How many subsets need we present to the player facing m outcomes to verify that they have ordinal preferences?

  c.Make a table to compare the previous two formulas with m = 3, 4, 5, 6.

  d.What do you observe about the relative growths of the two formulas?

  2.5In the text, we assigned negative numbers to Scarlett’s ordinal preferences so that u (o ) = −k if outcome o was ranked k th best by Scarlett. Later, we emphasized the fact that the specific values of the numbers did not matter, but rather the ordering of them. Why might one pick a particular set of numbers to represent ordinal preferences over another set of numbers?

  2.6Andreoni and Miller [3

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  Welfare Economics

  Towards a More Complete Analysis

  • Y. Ng(Author)
  • 2003(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  The only acceptable alter- native is to reject either Individualism or Ordinalism. Most people would find it reasonable to take some chocolates from J (who has all 100 units) and give them to K because otherwise K will starve. The chocolates given to K will meet a more urgent need than if they are consumed by J. But this is speaking in terms of cardinal utility. In purely ordinal utility terms, we cannot distinguish whether individuals prefer 50 units to no units more strongly than they prefer 100 units to 50 units. However for those (myself included) who find it sensible to speak in terms of intensity of preference, it is quite sensible to use the cardinal utility approach. It is the pure ordinalists who cannot accept this. Is there an alternative way out of the Kemp–Ng impossibility? Yes, by rejecting Individualism. Social preference then need not be based only on individual preferences (cardinal or ordinal). In particular social preference may depend on the objective specification of social states, such as the amount of commodities consumed by individuals. For example the social state (50, 50) – that is 50 units of chocolates for each individual – can be selected as the best alternative based on the objective amount of chocolates consumed and not on the cardinal utility approach of urgent versus not urgent need mentioned in the previous paragraph. But it is clearly unreasonable to base social choice on the objective specification of social states irrespective of individual preferences.

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  Game Theory Basics

  • Bernhard von Stengel(Author)
  • 2021(Publication Date)
  • Cambridge University Press

    (Publisher)

  5.6. Cardinal Utility Functions and Simple Lotteries 115 practice a good approximation of a player’s preference, and choosing its weights may help the player to clarify the necessary tradeoffs. (Exercise 5.1 relates to such an “additive” utility function.) A utility function  that represents a preference for deterministic outcomes as in (5.8) has a lot of freedom for its shape. Namely, for the comparison of outcomes that occur with certainty, only the ordinal comparison between values of  matters, that is, whether ( ) is less than, greater than, or equal to (  ). This implies that ( ) can also be replaced by a (( )) for a strictly increasing function  (also called a transformation of the utility function). For example, if  is “personal wealth” and always  > 0, then the preference    can either be represented by the wealth itself, that is, if and only if  ≤  , or, for example, by the logarithm of that wealth, namely log  ≤ log  , where the strictly increasing transformation is given by  = log. The represented preference (a higher personal wealth is strictly preferred) is exactly the same. A utility function for decisions under certainty is therefore also called an ordinal utility function. 5.6 Cardinal Utility Functions and Simple Lotteries As soon as a utility function represents a preference for risky choices, its values cannot be transformed by an arbitrary strictly increasing transformation. Suppose a player can choose between the following two lotteries  and . Lottery  gives with probability 1 2 either 100 dollars or 400 dollars, whereas lottery  gives 240 dollars for certain. If the utility for receiving  dollars is just  , then the expected utility for  is 1 2 100 + 1 2 400 = 250 whereas for  it is 240, so the player strictly prefers  to .

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  Social Limits to Economic Theory

  • Jonathan D Mulberg(Author)
  • 2005(Publication Date)
  • Routledge

    (Publisher)

  This movement towards behaviouralism began with the new definition of economics developed by Lionel Robbins (Robbins 1935 [1932]). This change in definition, which has become common currency throughout the discipline since the 1930s, was couched in positivist terms. All traces of the discipline's utilitarian past were discarded; legitimacy now lay in the claim to ‘scientific’ truth in positivist terms. Economics was no longer to look at wealth, as the classical economists did, or material welfare, as did the neo-classics. Robbins' definition concerned itself with behaviour, with ‘rational choice’. In fact, Robbins considers not Marshall's ‘men of flesh and blood’, but rather an abstract, ‘rational’ human. All that is necessary for a science of behaviour, Robbins asserts, is for actors to be able to choose between given alternatives. As long as these choices are transitive (and it would be strange for an individual to hold intransitive preferences), then it is possible to show (by the same indifference analysis as used by Pareto) that an equilibrium can occur at which each individual's utility is maximised. Robbins replaced a cardinally measurable utility with an ordinal utility, based on the idea of rational choice.

  Robbins's definition (and, as we shall see, much of his substantive analysis) reflects his Austrian background, and is a curious mixture of positivism and Austrian praxeology. Although his theory is couched in behavioural terms, Robbins explicitly denies that economic theory can be based solely on observational concepts (Robbins 1935 p. 87). He believes that

  After all, our business is to explain certain aspects of conduct. And it is very questionable whether this can be done in terms which involve no psychical element. It is quite certain that whether it be pleasing or no to the desire for the maximum austerity, we do in fact understand terms such as choice, indifference, preference and the like in terms of inner experience.

  (Robbins 1935 p. 87; emphasis in original)

  Robbins also specifically denied interpersonal comparisons of utility. Again, this affected the discipline boundary, in that it effectively excluded statements concerning redistribution (Cooter and Rappoport 1984 p. 521). The move to ordinalism therefore appears neatly to sidestep the distributional conclusions of the diminishing marginal utility of money. However, the cost of this move was high.

  Ordinal utility theory gives the appearance of allowing us to reach similar conclusions to Marshall, but without the distributional implications attached to the theory.23 It also laid the foundation for a positivist, behavioural economics.

  Robbins assembled the elements of a new conceptual framework by joining together the scarcity definition of economics, the positivist conception of method, and the ordinalist view of utility. The only piece missing from the modern view was a behaviourist interpretation of ordinal utility, and that was supplied by others (Cooter and Rappoport 1984 p. 523).

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