<p>There are not just rules but whole theories. Namely cardinal utility allows you to make interpersonal utility comparisons (as opposed to ordinal utility). A common cardinal utility framework is the one based on  von Neumann-Morgenstern.</p>
<p>Von Neumann-Morgenstern cardinal utility requires that axioms of completeness, transitivity, continuity and independence are satisfied (see von Neumann-Morgenstern (1944) Theory of Games and Economic Behavior), so you can view them as 'conditions' for interpersonal utility comparison (although there are also other approaches to cardinal utility that might have different conditions).</p>
<p>Furthermore, note these rather necessary conditions for interpersonal utility comparisons not sufficient ones, as mentioned in the comments a good book that discusses this in greater detail is Roemer Theories of Distributive Justice.</p>

CC BY-SA 4.0
2021-02-12T14:40:07.313Z
How do you make interpersonal welfare comparisons using vNM-expect utility representations?
Michael Greinecker
CC BY-SA 4.0
2021-02-12T14:45:00.567Z
@MichaelGreinecker by comparing cardinal utilities across individuals - at least that is what almost the whole field of public economics and optimal taxation/redistribution is based on...
1muflon1
CC BY-SA 4.0
2021-02-12T14:54:08.020Z
Uhm, not really. Suppose you have $n$ individuals and $(v_1,\ldots,v_n)$ is a profile of Bernoulli functions for all individuals. Let $(\alpha_1,\ldots,\alpha_n)\in\mathbb{R}^n_{++}$. Then $(\alpha_1 v_1,\ldots,\alpha_n v_n)$ is another profile of Bernoulli functions for all individuals that represents the same preferences over lotteries, but it is possible that $\sum_{i=1}^n v_i(x)>\sum_{i=1}^n v_i(y)$ but $\sum_{i=1}^n \alpha_i v_i(x)<\sum_{i=1}^n \alpha_i v_i(y)$. The uniqueness in the vNM representation up to positive affine transformations is not enough to make utilitarianism work.
Michael Greinecker
CC BY-SA 4.0
2021-02-12T15:03:18.067Z
@MichaelGreinecker you are right that this is an issue - and this is what often is brought up by the people who criticize the whole field, but the point is cardinal utility actually in principle allows you to make such comparisons if you assume government can use the same metric for everyone - which is not possible with ordinal utility at all.
1muflon1
CC BY-SA 4.0
2021-02-12T15:07:28.680Z
I'm not saying that utilitarian comparisons make no sense, my point is that one needs more information than is contained in the risk preferences of people. There is a huge literature on the informational requirements of certain welfare-comparisons; the book "Theories of Distributive Justice" by John Roemer has a nice survey.
Michael Greinecker
CC BY-SA 4.0
2021-02-12T15:39:12.470Z
@MichaelGreinecker oh that’s your point, well I agree what is above are necessary conditions rather than sufficient ones. I edited my answer to make that clear - thanks for your insightful comments
1muflon1
CC BY-SA 4.0
2021-02-13T09:56:20.503Z
@KennyLJ well then according to you whole literature of public economics is nonsense I guess.. Muller Public Choice III discusses cardinal utility as prerequisite for interpersonal comparisons.  Hammond (1989) - the book actually criticizes interpersonal comparisons but paradoxically makes good review of literature:  [on approach to make interpersonal utility comparison] "The first concerns the **construction of a cardinal utility function to represent each individual’s preferences,
which is clearly necessary if one is to make ICUD’s.** [interpersonal comparisons of utility differences]
1muflon1
CC BY-SA 4.0
2021-02-13T09:59:47.810Z
The second aspect is the comparison of different individual’s utility functions as such, once they have been cardinalized. The most common suggestion for cardinalizing individual utility functions
before comparing their differences interpersonally is to use NMUF’s [Neumann-Morgenstern utility function]." I am sorry if you think this is nonsense - but it is accepted by public econ. literature that interpersonal utility comparisons: 1. as require cardinalization of utility. 2. vNM utility is the most common way how to achieve that
1muflon1
CC BY-SA 4.0
2021-02-13T10:03:41.760Z
@KennyLJ you stated: "The conditions in vNM's expected utility theorem do not provide any basis for interpersonal utility comparison; and nor are they necessary."  - as shown in Hammond that is clearly false and vNM utility provides basis for interpersonal utility comparison and cardinal utility is *necessary*, at least for approaches used in econ, (or at least people in literature claim so Hammond himself criticizes any interpersonal comparisons)... my answer is based on this literature. Or is my answer nonsense just because it is written by me and your personal antipathy towards me?
1muflon1
CC BY-SA 4.0
2021-02-12T14:09:14.423Z
2021-02-12T15:38:17.570Z
2021-02-12T15:38:17.570Z
1muflon1
<p>What are the criteria which have been proposed to deal with the problem of interpersonal comparison of utility?</p>

CC BY-SA 4.0
2021-02-12T14:05:57.100Z
This is a topic on which one can write many books and on which, indeed, many books have been written. I would recommend "Theories of Distributive Justice" by John Roemer as a starting point for technically trained economists.
Michael Greinecker
<utility><welfare>
Interpersonal comparison of utility
Shantel
# Interpersonal comparison of utility

(Asked by: username_0 on 2021-02-12)

What are the criteria which have been proposed to deal with the problem of interpersonal comparison of utility?

**Tags:** utility, welfare
> **Comments:**
> **username_1**: This is a topic on which one can write many books and on which, indeed, many books have been written. I would recommend "Theories of Distributive Justice" by John Roemer as a starting point for technically trained economists.  

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## 1 answers

### Answer by username_2 on 2021-02-12. Score: 1

There are not just rules but whole theories. Namely cardinal utility allows you to make interpersonal utility comparisons (as opposed to ordinal utility). A common cardinal utility framework is the one based on von Neumann-Morgenstern.

Von Neumann-Morgenstern cardinal utility requires that axioms of completeness, transitivity, continuity and independence are satisfied (see von Neumann-Morgenstern (1944) Theory of Games and Economic Behavior), so you can view them as 'conditions' for interpersonal utility comparison (although there are also other approaches to cardinal utility that might have different conditions).

Furthermore, note these rather necessary conditions for interpersonal utility comparisons not sufficient ones, as mentioned in the comments a good book that discusses this in greater detail is Roemer Theories of Distributive Justice.

> **Comments:**
> **username_1**: How do you make interpersonal welfare comparisons using vNM-expect utility representations?  
> **username_2**: @MichaelGreinecker by comparing cardinal utilities across individuals - at least that is what almost the whole field of public economics and optimal taxation/redistribution is based on...  
> **username_1**: Uhm, not really. Suppose you have $n$ individuals and $(v_1,\ldots,v_n)$ is a profile of Bernoulli functions for all individuals. Let $(\alpha_1,\ldots,\alpha_n)\in\mathbb{R}^n_{++}$. Then $(\alpha_1 v_1,\ldots,\alpha_n v_n)$ is another profile of Bernoulli functions for all individuals that represents the same preferences over lotteries, but it is possible that $\sum_{i=1}^n v_i(x)>\sum_{i=1}^n v_i(y)$ but $\sum_{i=1}^n \alpha_i v_i(x)<\sum_{i=1}^n \alpha_i v_i(y)$. The uniqueness in the vNM representation up to positive affine transformations is not enough to make utilitarianism work.  
> **username_2**: @MichaelGreinecker you are right that this is an issue - and this is what often is brought up by the people who criticize the whole field, but the point is cardinal utility actually in principle allows you to make such comparisons if you assume government can use the same metric for everyone - which is not possible with ordinal utility at all.  
> **username_1**: I'm not saying that utilitarian comparisons make no sense, my point is that one needs more information than is contained in the risk preferences of people. There is a huge literature on the informational requirements of certain welfare-comparisons; the book "Theories of Distributive Justice" by John Roemer has a nice survey.  
> **username_2**: @MichaelGreinecker oh that’s your point, well I agree what is above are necessary conditions rather than sufficient ones. I edited my answer to make that clear - thanks for your insightful comments  
> **username_2**: @KennyLJ well then according to you whole literature of public economics is nonsense I guess.. Muller Public Choice III discusses cardinal utility as prerequisite for interpersonal comparisons.  Hammond (1989) - the book actually criticizes interpersonal comparisons but paradoxically makes good review of literature:  [on approach to make interpersonal utility comparison] "The first concerns the **construction of a cardinal utility function to represent each individual’s preferences, which is clearly necessary if one is to make ICUD’s.** [interpersonal comparisons of utility differences]  
> **username_2**: The second aspect is the comparison of different individual’s utility functions as such, once they have been cardinalized. The most common suggestion for cardinalizing individual utility functions before comparing their differences interpersonally is to use NMUF’s [Neumann-Morgenstern utility function]." I am sorry if you think this is nonsense - but it is accepted by public econ. literature that interpersonal utility comparisons: 1. as require cardinalization of utility. 2. vNM utility is the most common way how to achieve that  
> **username_2**: @KennyLJ you stated: "The conditions in vNM's expected utility theorem do not provide any basis for interpersonal utility comparison; and nor are they necessary."  - as shown in Hammond that is clearly false and vNM utility provides basis for interpersonal utility comparison and cardinal utility is *necessary*, at least for approaches used in econ, (or at least people in literature claim so Hammond himself criticizes any interpersonal comparisons)... my answer is based on this literature. Or is my answer nonsense just because it is written by me and your personal antipathy towards me?  

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