<p>Utility functions provide identical orderings of bundles of consumption under positive monotonic transformations. Therefore, if an individual's preferences are representable with a utility function then there are (uncountably) infinitely many other utility functions that would provide the same ordering of all bundles and therefore the same preferences. Even in finance, where we care about the cardinality of utility (though we're warned in graduate micro 101 not to do that: &quot;the only important thing about utility functions is their ordinal character&quot;) and not just the ordinality, preference orderings are preserved under positive affine transformations of utility functions. In that case too, there are infinitely many utility functions that represent the same preferences.</p>

CC BY-SA 4.0
2022-02-09T16:14:28.580Z
You are right. I should have asked: how many preference rankings can a person have?
Erel Segal-Halevi
CC BY-SA 4.0
2022-02-09T16:37:18.703Z
You could ask that as a different question. But if there are two or more goods, they  are consumable in arbitrary quantities, and utility functions are monotonic and non-satiable, I think you can have infinitely many possible reference rankings.
BKay
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2022-02-09T17:00:12.047Z
Do you mean infinitely many preferences rankings? Why?
Erel Segal-Halevi
CC BY-SA 4.0
2022-02-09T18:49:33.820Z
I'm saying that since utility functions allow arbitrary orderings of preferences over bundles, the set of possible preferences should allow near arbitrary ranking of bundles (even requiring completeness, monotonic preferences, goods not bads, etc)
BKay
CC BY-SA 4.0
2022-02-09T13:35:12.107Z
2022-02-09T15:13:29.973Z
2022-02-09T15:13:29.973Z
BKay
<p>Classical choice theory assumes that each person has a utility function, and chooses from each set of options an option that maximizes this utility. There are many empirical studies that refute this theory, showing that human choice cannot be explained by maxizing a utility function. Such results can be explained by assuming that each person has <em>multiple</em> utility functions, corresponding to different &quot;frames&quot;. For example: a frame for each endowment, a frame for each status-quo, a frame for each time, etc.. The agent always maximizes one of these utility functions, depending on the active frame (see e.g. <a href="https://pubs.aeaweb.org/doi/abs/10.1257/aer.97.2.464" rel="noreferrer">Bernhaim and Rangel</a> and many others).</p>
<p>Apparently, every human choice can be explained by assuming an unbounded number of utility functions (e.g. a utility function for each moment in time), but a more meaningful explanation would involve a bounded number of utility functions.</p>
<p>My question is: from empirical evidence, is there some lower bound on the number of utility functions that humans hold simultaneously? For example: are there choice experiments that cannot be explained as maximizing one of two utility functions, but can be explained as maximizing one of three utility functions?</p>

CC BY-SA 4.0
2022-02-09T12:24:08.103Z
I don't know about multiple utility functions. But I can conceive that there is a single function and multiple reference points (endogenous or exogenous, context dependent, etc). That would imply looking at the question from a different angle.
Fulcanelli
<behavioral-economics><empirical-evidence>
How many utility functions can a person have?
Erel Segal-Halevi
# How many utility functions can a person have?

(Asked by: username_0 on 2021-11-18)

Classical choice theory assumes that each person has a utility function, and chooses from each set of options an option that maximizes this utility. There are many empirical studies that refute this theory, showing that human choice cannot be explained by maxizing a utility function. Such results can be explained by assuming that each person has *multiple* utility functions, corresponding to different "frames". For example: a frame for each endowment, a frame for each status-quo, a frame for each time, etc.. The agent always maximizes one of these utility functions, depending on the active frame (see e.g. [Bernhaim and Rangel](https://pubs.aeaweb.org/doi/abs/10.1257/aer.97.2.464) and many others).

Apparently, every human choice can be explained by assuming an unbounded number of utility functions (e.g. a utility function for each moment in time), but a more meaningful explanation would involve a bounded number of utility functions.

My question is: from empirical evidence, is there some lower bound on the number of utility functions that humans hold simultaneously? For example: are there choice experiments that cannot be explained as maximizing one of two utility functions, but can be explained as maximizing one of three utility functions?

**Tags:** behavioral-economics, empirical-evidence
> **Comments:**
> **username_1**: I don't know about multiple utility functions. But I can conceive that there is a single function and multiple reference points (endogenous or exogenous, context dependent, etc). That would imply looking at the question from a different angle.  

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## 1 answers

### Answer by username_2 on 2022-02-09. Score: 3

Utility functions provide identical orderings of bundles of consumption under positive monotonic transformations. Therefore, if an individual's preferences are representable with a utility function then there are (uncountably) infinitely many other utility functions that would provide the same ordering of all bundles and therefore the same preferences. Even in finance, where we care about the cardinality of utility (though we're warned in graduate micro 101 not to do that: "the only important thing about utility functions is their ordinal character") and not just the ordinality, preference orderings are preserved under positive affine transformations of utility functions. In that case too, there are infinitely many utility functions that represent the same preferences.

> **Comments:**
> **username_0**: You are right. I should have asked: how many preference rankings can a person have?  
> **username_2**: You could ask that as a different question. But if there are two or more goods, they  are consumable in arbitrary quantities, and utility functions are monotonic and non-satiable, I think you can have infinitely many possible reference rankings.  
> **username_0**: Do you mean infinitely many preferences rankings? Why?  
> **username_2**: I'm saying that since utility functions allow arbitrary orderings of preferences over bundles, the set of possible preferences should allow near arbitrary ranking of bundles (even requiring completeness, monotonic preferences, goods not bads, etc)  

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