<p>I think the Investopedia article does not use clear terminology which leads to confusion.</p>
<p>In Economics, utility can be split across two categories as <em>ordinal</em> and <em>cardinal</em> utility.</p>
<p>In the case of ordinal utility assigning numeric values is meaningless. For example, if A is proffered to B, assigning 200 utils to A and 100 utils to B is meaningless because that would imply that A is twice as good as B, but the ordinal utility can only measure preferences, not intensity.</p>
<p>In the case of cardinal utility, which measures both preference ordering and their intensity it is completely valid to assign some value like <span class="math-container">$u(A)=200$</span> utils or <span class="math-container">$u(B)=100$</span> utils. In this case, the numerical values can be assigned and they are, mathematically,  'true' numerical values.</p>
<p>However, from my reading of the Investopedia article, they seem to be referring to the measurability problem.  That is an old discussion in economic theory that revolves around whether utility can be actually measured in some way (i.e. can we somehow scan a person's brain to measure precisely utility).</p>
<p>Now from a purely practical perspective whether the utility is measurable or not we definitely cannot measure in any direct way presently. Right now we can only observe people's choices and their revealed preference which is only solid basis for ordinal utility, not cardinal utility. However, this does not mean that utility would be immeasurable. In fact, famously  Von Neumann and Morgenstern (1944) in their Theory of Games and Economic Behavior argued that utility even if we cannot measure it yet is measurable. The authors argued that utility can be viewed the same way as temperature in physics. Temperature also originally could not be measured beyond just saying it is getting colder or warmer but developments in thermodynamic theory later allowed us not just to cardinally measure temperature, but even allowed us to recognize that there is actually some absolute zero and absolute units temperature (presently even <a href="https://en.wikipedia.org/wiki/Celsius" rel="noreferrer">Celsius scale</a> is actually a derived measure in terms of Kelvins).</p>
<p>Consequently, in the view of  Von Neumann and Morgenstern utility should also be measurable and their view is quite influential although not accepted by all. If utility is measurable then there is a 'true' underlying measurable utility value to any choice. Whether we actually have instruments to do the measurements or not is irrelevant for the problem.</p>
<p>However, from my reading of the Investopedia article I think that what Investopedia refers to is the present practical inability to directly measure utility. I cannot see any indication from the article that it is taking stance on the measurability problem itself. Economists definitely don't go around hooking jumper cables to peoples heads and directly measuring utility from their choices (yet). Consequently, it is an accurate statement from a present-day practical perspective but not necessarily valid statement from the perspective of measurability problem.</p>
<p><strong>Response to second question after edit:</strong></p>
<p>The issue here is that true numerical value does not necessarily depend on measurement. As explained in this article from <a href="http://www.science-campus.com/physics/measurement/meas_3_1.html" rel="noreferrer">Science Campus</a> site:</p>
<blockquote>
<p>The measurement value (which is sometimes referred to simply as the measurement) is the value given by a measuring instrument and the true value is the actual value of the property being measured.</p>
</blockquote>
<p>Of course, there are no instruments to measure utility, however that does not mean that there are no true numerical values for it. In fact, as argued by  Von Neumann and Morgenstern (1944) in cardinal utility there will be some mapping of the underlaying preferences on the set of real numbers. Hence, cardinal utility actually does represent the 'true' values of utility (within the vNM framework at least).</p>
<p>However, Investopedia is correct in pointing out that economists do not measure it when constructing utility because (presently) there is no practically viable way that would in real life make it possible to create such mapping from the unobservable preferences onto real numbers. But just because we are not able to practically make such mapping does mean it cannot exist (again in past people were unable to map the true values of temperature onto real numbers - in fact for the  most part of the human history such mapping was impossible until technology and science advanced enough to make it possible).</p>
<p>Furthermore, of course there are economist who are pure ordinalist but from my reading of the Investopedia article they are not taking pure ordinalist position rather they mean that we are simply unable to measure utility in practical sense.</p>

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2020-10-18T19:02:49.413Z
Article states: "When economists measure the preferences of consumers, it's referred to ordinal utility. In other words, the order in which consumers choose one product over another can establish that consumers assign a higher value to the first product. Ordinal utility measures how consumers rank one product versus another. Economists take the utility-function concept one step farther by assigning a numerical value to the products that consumers choose or choose not to consume. Assigning a value of utility is called cardinal utility, and the metric used to it is called utils."
SystemTheory
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2020-10-18T19:15:25.370Z
@SystemTheory yes I read the article before I posting my post. At the beginning I provide further context which previously was not part of the question.
1muflon1
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2020-10-18T19:25:23.733Z
You state, "the numerical values can be assigned and they are, mathematically, 'true' numerical values." In a scientific or engineering measurement the numbers must be assigned according to a standard or unique measurement procedure to be a "true" measurement within the limits of statistical variation in the effort to assign numbers this way. How does the economist assign numbers in the context of measuring utility? A radian is dimensionless number yet we define this as the angle where arc length of the circle equals the radius. What procedure defines unit called utils?
SystemTheory
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2020-10-18T19:38:23.150Z
@SystemTheory you are conflating two concepts. True value and measurement value. Even in physics (and I used to study it) true value is independent of measurement. True value simply is. If the temperature of empty space is 0K that is true value whether we can measure it or not. This has nothing to do with calibration of instruments etc. vNM cardinal utility is defined in terms of true utils as it can be constructed from persons preference over different 'lotteries'. In fact if you read the book I provided as a reference you will learn that thanks to this we can theoretically...
1muflon1
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2020-10-18T19:40:52.773Z
... create precise mapping from preferences onto set of real numbers. Hence yes we can *theoretically* in vNM sense measure true values and there also exist some true values. However, unfortunately there is no practical way how to consistently do such mapping as it would also require some more precise measurement of preferences than just simply observing revealed preference in real life.
1muflon1
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2020-10-18T19:54:10.873Z
Am I conflating or are you waffling? I think you have given a good answer except for the waffling when it comes to the distinction between constructing a utility curve based on working assumptions without measurements and taking actual scientific measurements. I understand that the revealed preferences are observations used to construct the utility functions from further working assumptions.
SystemTheory
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2020-10-18T20:04:49.453Z
@SystemTheory well english is my second language so it is possible I am waffling - but if so it is unintentional. Also, just to make it clear when I say things like you are conflating this or that I do not mean to demean you I am just saying what I think is the issue, I think you raised a good question - thats why I upvoted it - but I still think you are conflating measurement of true value for true value (which is due to the way how investopedia is worded) - I just added an edit to my answer let me know if that cleared the issue or not
1muflon1
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2020-10-18T20:17:30.697Z
I gave your answer +1 vote and will likely select it as correct. For clarity I argue as follows. The concept of "true numerical value" has several potential meanings in this exchange:  (1) all numerical values are true values; or (2) no numerical value assigned by a scientific measurement method can be taken as the true value (due to measurement error and to arbitrary choice of units); or (3) utility curves are constructed without the use of scientific measurements so the economist cannot assign a true numeric value. I would say (3) is accurate utility is not a "true" measured value.
SystemTheory
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2020-10-18T20:28:50.180Z
@SystemTheory (1) is almost metaphysical view - but that is actually not what I meant (sorry if I was not clear). (2) correct but also not what I meant because even though they are not equal a perfect measurement will be mapping of true value. (3) the problem with this is that can't assign suggest that it is impossible - well it is theoretically possible to assign those values but we dont know how to do it. We can prove that in vNM framework there is some mapping so it is possible (if vNM framework is correct). If I am still not explaining myself clearly consider this.
1muflon1
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2020-10-18T20:36:42.527Z
In past it was impossible to accurately measure temperature, but would you say that a general statements scientists cannot assign true values of temperature on kelvin scale is a true statement? - I would not think it is true because that suggests that it is impossible to do so but we now know it is possible. It is only a question of developing precise instruments to do precise measurements. Of course, it is possible there is no cardinal utility as mentioned in answer there are pure ordinalists but I just dont think that is the position investopedia is taking.
1muflon1
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2020-10-18T21:00:25.663Z
or another analogy I would use is that in physics we know that it is possible to travel at 99% of speed of light - you just cannot go faster than light, but we cannot construct spaceship that would be able to reach such high speeds. But I don't think there is any physicist who would state that people cant be traveling at 99% of speed of light. We just can't practically do it in a sense that we do not know how to construct spaceship that would have enough fuel and thrust to accelerate to such speeds
1muflon1
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2020-10-18T23:47:32.847Z
So it appears that utility functions are made up or constructed from some systematic assumptions that cannot be verified by systematic measurements. In other words several economists might observe the same ordinal utility but are likely to construct distinct numerical models for a utility function. It would be like a scientist or engineer saying we can't measure temperature yet but if we could the curves in this experimental observation should look something like this constructed model.
SystemTheory
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2020-10-18T23:52:12.160Z
@SystemTheory 1. This only applies to cardinal utility. Ordinal utility is easily measurable. 2. Just because you cannot directly verify what utility looks like is not a big deal. Utility is part of wider structure of theories and you can verify that the theory based on utility works. In astrophysics (which I used to study before switching to Econ) there is an innumerable number of things we can’t directly verify. For example, it is impossible to see dark matter but we can make an induction that there should be some based on general relativity theory which itself can be verified. In a same..
1muflon1
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2020-10-18T23:54:15.593Z
way when we test economic theories that would not work without cardinal utility and test cannot reject them we can take that as a confirmation that the cardinal utility theory works and it is there.
1muflon1
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2020-10-19T01:20:45.373Z
I agree since I stated that ordinal relations or revealed preference is subject to independent verification or duplication using some standard measurement methods. I am convinced that ordinal utility means constructing an ordered set of preferences as tuples or similar logical structures; and that utility functions as math models do not assign number values via a systematic measurement procedure. I do not know how economists apply these models in a context where one can say "this model fails if (apply logic)". I want to comprehend reasoning methods in engineering, economics, and law.
SystemTheory
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2020-10-19T10:16:56.160Z
@SystemTheory “I want to comprehend reasoning methods in engineering, economics, and law” - that’s good but that is something that I think is beyond what can be done at a stack exchange. Setting the engineering and law aside, if you are interested in these big questions of metaphysics I recommend you to have a look at the Ross (2014) philosophy of economics. Hausman philosophy of economics - for a context and then MWG microeconomic theory - at least the first couple of chapters. I know those are dense books but if you wanna get answers to broad questions you will have to do some heavy lifting.
1muflon1
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2020-10-19T10:27:23.353Z
@SystemTheory SE format is tailored to more narrow questions. That’s why we have too broad as a valid option to vote to close. I think originally your Q was nice and narrow but you keep expanding it and making it more broad and less fit for SE format - I think that’s why someone decided to downvote your Q (I have high rep to see vote totals). I won’t be changing my vote retroactively and I still find your Q interesting but expanding it to question about understanding the reasoning of all methodology underpinning utility will most likely just invite negative reactions and poor answers
1muflon1
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2020-10-19T13:45:29.437Z
I understand the scope of questions and answers has a limit, however, you said "utility models work" so then my question would be according to what criteria? Also I am getting information about the revealed preferences of this community if they vote down my questions or answers which are not narrowly constrained to some particular economic tradition. I appreciate your scholarship and efforts to answer questions here to the best of your ability.
SystemTheory
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2020-10-19T13:50:26.273Z
@SystemTheory yes but that is really broad because the criteria of model working - that is by definition literally subject matter of philosophy of science (in this case economics) so you are basically asking me to describe whole field to you (I did not recommend those two books just haphazardly). The modern economics seems to be following instrumentalists/Popperian/Kuhnian view of what science is and how we evaluate models (if this does not make sense I promise after reading those books it will make sense - give it a try).
1muflon1
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2020-10-19T13:58:40.793Z
This is way beyond scope of question, I edited away the term "ideology" due to its charged implications. A Wikipedia entry states "Economic ideologies express perspectives on the way an economy should run and to what end." Pareto efficiency means people are motivated to contract for services that make them better off and no worse off. In engineering and law the person claims malpractice against the lawyer or engineer to state "I am worse off under the terms of the contract or outcome from social interaction." Does the typical economist pay for malpractice insurance?
SystemTheory
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2020-10-19T14:03:01.520Z
@SystemTheory also, I think you should consider that you are not being downvoted because of not aligning to some economic tradition. You will find ordinalists across many economic traditions - it was originally the default position of economics until the expected utility theory revolution. Next, you are asking a Q not posting an A how can Q be in some tradition? - there are upvoted (with 0 downvotes) Q about Marxian economics and that is hardly accepted tradition. Maybe at least consider that it may be due to the Q not aligning with rules of forum (eg no multiple Q per post, be narrow etc)
1muflon1
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2020-10-19T14:19:48.960Z
@SystemTheory but that Wikipedia article specifically states it is not referring to economics as science. Normative economics has nothing to do with whether utility is cardinal or not. Furthermore, in fact that is not even term used economics much if at all because even in normative economics we dont talk about economic ideologies but ideologies general  (you can look almost any book on policy economics about normative economics). That rather seems like a term from political science or maybe used in political economy and refers to the concept of ideology there as in relation with economics
1muflon1
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2020-10-19T14:21:51.717Z
Final remark - I will take a look at those references and try to conform my efforts to the format here. I will also view some videos showing how the economist takes a set of ordered preferences and then uses a number of assumptions to construct a continuous utility function. Your efforts have been helpful so thanks.
SystemTheory
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2020-10-18T17:49:11.287Z
2020-10-18T20:44:35.717Z
2020-10-18T20:44:35.717Z
1muflon1
<p>Investopedia article - What is the utility function and how is it calculated?</p>
<p><a href="https://www.investopedia.com/ask/answers/072915/what-utility-function-and-how-it-calculated.asp" rel="nofollow noreferrer">https://www.investopedia.com/ask/answers/072915/what-utility-function-and-how-it-calculated.asp</a></p>
<p>Article describes ordinal versus cardinal utility:</p>
<blockquote>
<p>When economists measure the preferences of consumers, it's referred to ordinal utility. In other words, the order in which consumers choose one product over another can establish that consumers assign a higher value to the first product. Ordinal utility measures how consumers rank one product versus another.</p>
</blockquote>
<blockquote>
<p>Economists take the utility-function concept one step farther by assigning a numerical value to the products that consumers choose or choose not to consume. Assigning a value of utility is called cardinal utility, and the metric used to it is called utils.</p>
</blockquote>
<p>Article includes the following statement under limitations and benefits of utility function:</p>
<blockquote>
<p>Of course, in reality, economists can't assign a true numerical value to a consumer's level of satisfaction from a preference or choice. Also, pinpointing the reason for the purchase can be difficult if there are many variables being considered.</p>
</blockquote>
<p>Is this an accurate description of economic reasoning? Utility functions are models  constructed by a particular economist who cannot assign a true numerical value?</p>
<p>To further develop my question, if it is not clear, in a scientific measurement there is a procedure which defines a standard unit of measure. Instruments are calibrated in terms of these procedures and then calibrated instruments are applied to assign the numbers with units in the models. Is there a standard procedure for assigning numbers to specify utils or is it constructed when the economist assigns numbers arbitrarily to the ordinal set?</p>
<p>Another article - Constructing a utility function:</p>
<p><a href="http://planning.cs.uiuc.edu/node469.html" rel="nofollow noreferrer">http://planning.cs.uiuc.edu/node469.html</a></p>
<blockquote>
<p>Unfortunately, establishing the existence of a utility function does not produce a systematic way to construct it. In most circumstances, one is forced to design <span class="math-container">$ {\cal U}$</span> by a trial-and-error process that involves repeatedly checking the preferences. In the vast majority of applications, people create utility and cost functions without regard to the implications discussed in this section. Thus, undesirable conclusions may be reached in practice. Therefore, it is important not to be too confident about the quality of an optimal decision rule.</p>
</blockquote>

CC BY-SA 4.0
2020-10-18T18:42:22.190Z
Does this answer your question? [Doesn't the concept of marginal utility speak to a cardinal utility function?](https://economics.stackexchange.com/questions/30713/doesnt-the-concept-of-marginal-utility-speak-to-a-cardinal-utility-function)
BKay
<utility><measuring-utility>
Is it accurate to state that an economist cannot assign a true numerical value for utility?
SystemTheory
# Is it accurate to state that an economist cannot assign a true numerical value for utility?

(Asked by: username_0 on 2020-10-18)

Investopedia article - What is the utility function and how is it calculated?

<https://www.investopedia.com/ask/answers/072915/what-utility-function-and-how-it-calculated.asp>

Article describes ordinal versus cardinal utility:

> When economists measure the preferences of consumers, it's referred to ordinal utility. In other words, the order in which consumers choose one product over another can establish that consumers assign a higher value to the first product. Ordinal utility measures how consumers rank one product versus another.

> Economists take the utility-function concept one step farther by assigning a numerical value to the products that consumers choose or choose not to consume. Assigning a value of utility is called cardinal utility, and the metric used to it is called utils.

Article includes the following statement under limitations and benefits of utility function:

> Of course, in reality, economists can't assign a true numerical value to a consumer's level of satisfaction from a preference or choice. Also, pinpointing the reason for the purchase can be difficult if there are many variables being considered.

Is this an accurate description of economic reasoning? Utility functions are models constructed by a particular economist who cannot assign a true numerical value?

To further develop my question, if it is not clear, in a scientific measurement there is a procedure which defines a standard unit of measure. Instruments are calibrated in terms of these procedures and then calibrated instruments are applied to assign the numbers with units in the models. Is there a standard procedure for assigning numbers to specify utils or is it constructed when the economist assigns numbers arbitrarily to the ordinal set?

Another article - Constructing a utility function:

<http://planning.cs.uiuc.edu/node469.html>

> Unfortunately, establishing the existence of a utility function does not produce a systematic way to construct it. In most circumstances, one is forced to design $ {\cal U}$ by a trial-and-error process that involves repeatedly checking the preferences. In the vast majority of applications, people create utility and cost functions without regard to the implications discussed in this section. Thus, undesirable conclusions may be reached in practice. Therefore, it is important not to be too confident about the quality of an optimal decision rule.

**Tags:** utility, measuring-utility
> **Comments:**
> **username_1**: Does this answer your question? [Doesn't the concept of marginal utility speak to a cardinal utility function?](https://economics.stackexchange.com/questions/30713/doesnt-the-concept-of-marginal-utility-speak-to-a-cardinal-utility-function)  

---

## 1 answers

### Answer by username_2 on 2020-10-18. Score: 7

I think the Investopedia article does not use clear terminology which leads to confusion.

In Economics, utility can be split across two categories as *ordinal* and *cardinal* utility.

In the case of ordinal utility assigning numeric values is meaningless. For example, if A is proffered to B, assigning 200 utils to A and 100 utils to B is meaningless because that would imply that A is twice as good as B, but the ordinal utility can only measure preferences, not intensity.

In the case of cardinal utility, which measures both preference ordering and their intensity it is completely valid to assign some value like $u(A)=200$ utils or $u(B)=100$ utils. In this case, the numerical values can be assigned and they are, mathematically, 'true' numerical values.

However, from my reading of the Investopedia article, they seem to be referring to the measurability problem. That is an old discussion in economic theory that revolves around whether utility can be actually measured in some way (i.e. can we somehow scan a person's brain to measure precisely utility).

Now from a purely practical perspective whether the utility is measurable or not we definitely cannot measure in any direct way presently. Right now we can only observe people's choices and their revealed preference which is only solid basis for ordinal utility, not cardinal utility. However, this does not mean that utility would be immeasurable. In fact, famously Von Neumann and Morgenstern (1944) in their Theory of Games and Economic Behavior argued that utility even if we cannot measure it yet is measurable. The authors argued that utility can be viewed the same way as temperature in physics. Temperature also originally could not be measured beyond just saying it is getting colder or warmer but developments in thermodynamic theory later allowed us not just to cardinally measure temperature, but even allowed us to recognize that there is actually some absolute zero and absolute units temperature (presently even [Celsius scale](https://en.wikipedia.org/wiki/Celsius) is actually a derived measure in terms of Kelvins).

Consequently, in the view of Von Neumann and Morgenstern utility should also be measurable and their view is quite influential although not accepted by all. If utility is measurable then there is a 'true' underlying measurable utility value to any choice. Whether we actually have instruments to do the measurements or not is irrelevant for the problem.

However, from my reading of the Investopedia article I think that what Investopedia refers to is the present practical inability to directly measure utility. I cannot see any indication from the article that it is taking stance on the measurability problem itself. Economists definitely don't go around hooking jumper cables to peoples heads and directly measuring utility from their choices (yet). Consequently, it is an accurate statement from a present-day practical perspective but not necessarily valid statement from the perspective of measurability problem.

**Response to second question after edit:**

The issue here is that true numerical value does not necessarily depend on measurement. As explained in this article from [Science Campus](http://www.science-campus.com/physics/measurement/meas_3_1.html) site:

> The measurement value (which is sometimes referred to simply as the measurement) is the value given by a measuring instrument and the true value is the actual value of the property being measured.

Of course, there are no instruments to measure utility, however that does not mean that there are no true numerical values for it. In fact, as argued by Von Neumann and Morgenstern (1944) in cardinal utility there will be some mapping of the underlaying preferences on the set of real numbers. Hence, cardinal utility actually does represent the 'true' values of utility (within the vNM framework at least).

However, Investopedia is correct in pointing out that economists do not measure it when constructing utility because (presently) there is no practically viable way that would in real life make it possible to create such mapping from the unobservable preferences onto real numbers. But just because we are not able to practically make such mapping does mean it cannot exist (again in past people were unable to map the true values of temperature onto real numbers - in fact for the most part of the human history such mapping was impossible until technology and science advanced enough to make it possible).

Furthermore, of course there are economist who are pure ordinalist but from my reading of the Investopedia article they are not taking pure ordinalist position rather they mean that we are simply unable to measure utility in practical sense.

> **Comments:**
> **username_0**: Article states: "When economists measure the preferences of consumers, it's referred to ordinal utility. In other words, the order in which consumers choose one product over another can establish that consumers assign a higher value to the first product. Ordinal utility measures how consumers rank one product versus another. Economists take the utility-function concept one step farther by assigning a numerical value to the products that consumers choose or choose not to consume. Assigning a value of utility is called cardinal utility, and the metric used to it is called utils."  
> **username_2**: @SystemTheory yes I read the article before I posting my post. At the beginning I provide further context which previously was not part of the question.  
> **username_0**: You state, "the numerical values can be assigned and they are, mathematically, 'true' numerical values." In a scientific or engineering measurement the numbers must be assigned according to a standard or unique measurement procedure to be a "true" measurement within the limits of statistical variation in the effort to assign numbers this way. How does the economist assign numbers in the context of measuring utility? A radian is dimensionless number yet we define this as the angle where arc length of the circle equals the radius. What procedure defines unit called utils?  
> **username_2**: @SystemTheory you are conflating two concepts. True value and measurement value. Even in physics (and I used to study it) true value is independent of measurement. True value simply is. If the temperature of empty space is 0K that is true value whether we can measure it or not. This has nothing to do with calibration of instruments etc. vNM cardinal utility is defined in terms of true utils as it can be constructed from persons preference over different 'lotteries'. In fact if you read the book I provided as a reference you will learn that thanks to this we can theoretically...  
> **username_2**: ... create precise mapping from preferences onto set of real numbers. Hence yes we can *theoretically* in vNM sense measure true values and there also exist some true values. However, unfortunately there is no practical way how to consistently do such mapping as it would also require some more precise measurement of preferences than just simply observing revealed preference in real life.  
> **username_0**: Am I conflating or are you waffling? I think you have given a good answer except for the waffling when it comes to the distinction between constructing a utility curve based on working assumptions without measurements and taking actual scientific measurements. I understand that the revealed preferences are observations used to construct the utility functions from further working assumptions.  
> **username_2**: @SystemTheory well english is my second language so it is possible I am waffling - but if so it is unintentional. Also, just to make it clear when I say things like you are conflating this or that I do not mean to demean you I am just saying what I think is the issue, I think you raised a good question - thats why I upvoted it - but I still think you are conflating measurement of true value for true value (which is due to the way how investopedia is worded) - I just added an edit to my answer let me know if that cleared the issue or not  
> **username_0**: I gave your answer +1 vote and will likely select it as correct. For clarity I argue as follows. The concept of "true numerical value" has several potential meanings in this exchange:  (1) all numerical values are true values; or (2) no numerical value assigned by a scientific measurement method can be taken as the true value (due to measurement error and to arbitrary choice of units); or (3) utility curves are constructed without the use of scientific measurements so the economist cannot assign a true numeric value. I would say (3) is accurate utility is not a "true" measured value.  
> **username_2**: @SystemTheory (1) is almost metaphysical view - but that is actually not what I meant (sorry if I was not clear). (2) correct but also not what I meant because even though they are not equal a perfect measurement will be mapping of true value. (3) the problem with this is that can't assign suggest that it is impossible - well it is theoretically possible to assign those values but we dont know how to do it. We can prove that in vNM framework there is some mapping so it is possible (if vNM framework is correct). If I am still not explaining myself clearly consider this.  
> **username_2**: In past it was impossible to accurately measure temperature, but would you say that a general statements scientists cannot assign true values of temperature on kelvin scale is a true statement? - I would not think it is true because that suggests that it is impossible to do so but we now know it is possible. It is only a question of developing precise instruments to do precise measurements. Of course, it is possible there is no cardinal utility as mentioned in answer there are pure ordinalists but I just dont think that is the position investopedia is taking.  
> **username_2**: or another analogy I would use is that in physics we know that it is possible to travel at 99% of speed of light - you just cannot go faster than light, but we cannot construct spaceship that would be able to reach such high speeds. But I don't think there is any physicist who would state that people cant be traveling at 99% of speed of light. We just can't practically do it in a sense that we do not know how to construct spaceship that would have enough fuel and thrust to accelerate to such speeds  
> **username_0**: So it appears that utility functions are made up or constructed from some systematic assumptions that cannot be verified by systematic measurements. In other words several economists might observe the same ordinal utility but are likely to construct distinct numerical models for a utility function. It would be like a scientist or engineer saying we can't measure temperature yet but if we could the curves in this experimental observation should look something like this constructed model.  
> **username_2**: @SystemTheory 1. This only applies to cardinal utility. Ordinal utility is easily measurable. 2. Just because you cannot directly verify what utility looks like is not a big deal. Utility is part of wider structure of theories and you can verify that the theory based on utility works. In astrophysics (which I used to study before switching to Econ) there is an innumerable number of things we can’t directly verify. For example, it is impossible to see dark matter but we can make an induction that there should be some based on general relativity theory which itself can be verified. In a same..  
> **username_2**: way when we test economic theories that would not work without cardinal utility and test cannot reject them we can take that as a confirmation that the cardinal utility theory works and it is there.  
> **username_0**: I agree since I stated that ordinal relations or revealed preference is subject to independent verification or duplication using some standard measurement methods. I am convinced that ordinal utility means constructing an ordered set of preferences as tuples or similar logical structures; and that utility functions as math models do not assign number values via a systematic measurement procedure. I do not know how economists apply these models in a context where one can say "this model fails if (apply logic)". I want to comprehend reasoning methods in engineering, economics, and law.  
> **username_2**: @SystemTheory “I want to comprehend reasoning methods in engineering, economics, and law” - that’s good but that is something that I think is beyond what can be done at a stack exchange. Setting the engineering and law aside, if you are interested in these big questions of metaphysics I recommend you to have a look at the Ross (2014) philosophy of economics. Hausman philosophy of economics - for a context and then MWG microeconomic theory - at least the first couple of chapters. I know those are dense books but if you wanna get answers to broad questions you will have to do some heavy lifting.  
> **username_2**: @SystemTheory SE format is tailored to more narrow questions. That’s why we have too broad as a valid option to vote to close. I think originally your Q was nice and narrow but you keep expanding it and making it more broad and less fit for SE format - I think that’s why someone decided to downvote your Q (I have high rep to see vote totals). I won’t be changing my vote retroactively and I still find your Q interesting but expanding it to question about understanding the reasoning of all methodology underpinning utility will most likely just invite negative reactions and poor answers  
> **username_0**: I understand the scope of questions and answers has a limit, however, you said "utility models work" so then my question would be according to what criteria? Also I am getting information about the revealed preferences of this community if they vote down my questions or answers which are not narrowly constrained to some particular economic tradition. I appreciate your scholarship and efforts to answer questions here to the best of your ability.  
> **username_2**: @SystemTheory yes but that is really broad because the criteria of model working - that is by definition literally subject matter of philosophy of science (in this case economics) so you are basically asking me to describe whole field to you (I did not recommend those two books just haphazardly). The modern economics seems to be following instrumentalists/Popperian/Kuhnian view of what science is and how we evaluate models (if this does not make sense I promise after reading those books it will make sense - give it a try).  
> **username_0**: This is way beyond scope of question, I edited away the term "ideology" due to its charged implications. A Wikipedia entry states "Economic ideologies express perspectives on the way an economy should run and to what end." Pareto efficiency means people are motivated to contract for services that make them better off and no worse off. In engineering and law the person claims malpractice against the lawyer or engineer to state "I am worse off under the terms of the contract or outcome from social interaction." Does the typical economist pay for malpractice insurance?  
> **username_2**: @SystemTheory also, I think you should consider that you are not being downvoted because of not aligning to some economic tradition. You will find ordinalists across many economic traditions - it was originally the default position of economics until the expected utility theory revolution. Next, you are asking a Q not posting an A how can Q be in some tradition? - there are upvoted (with 0 downvotes) Q about Marxian economics and that is hardly accepted tradition. Maybe at least consider that it may be due to the Q not aligning with rules of forum (eg no multiple Q per post, be narrow etc)  
> **username_2**: @SystemTheory but that Wikipedia article specifically states it is not referring to economics as science. Normative economics has nothing to do with whether utility is cardinal or not. Furthermore, in fact that is not even term used economics much if at all because even in normative economics we dont talk about economic ideologies but ideologies general  (you can look almost any book on policy economics about normative economics). That rather seems like a term from political science or maybe used in political economy and refers to the concept of ideology there as in relation with economics  
> **username_0**: Final remark - I will take a look at those references and try to conform my efforts to the format here. I will also view some videos showing how the economist takes a set of ordered preferences and then uses a number of assumptions to construct a continuous utility function. Your efforts have been helpful so thanks.  

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