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That's like saying 'anyone who's opposed to eugenics should pass the "Turing test for mainstream eugenics and racial hygiene" otherwise they're ill-informed'. W

by irixusr 11y ago

That's like saying 'anyone who's opposed to eugenics should pass the "Turing test for mainstream eugenics and racial hygiene" otherwise they're ill-informed'. Which is largely the argument used against opponents at the time (the opponents were ignorant "medieval obscurantists", if religious speaking from "superstition") My objections to modern economics are as follows: - utility is an ordinal quantity, not a cardinal one. I can tell you I prefer my soon-to-be-born daughter's first kiss to my sister's cheerful hello, but not by how much (how much "what"? What are the units?). - the utility function, so widely used, is an unknown function. However mathematics are performed after choosing an arbitrary functional form that has the features desired But most importantly: - It assumes utility exists and humans behave accordingly. These are fundamental objections to the field. I can talk to an economist about yield curves flipping, but that jumps over the foundational objections: they are projecting complex human behavior onto fairly outdated mathematics. And then making a mess of it.

nabla9 11y ago
>utility is an ordinal quantity, not a cardinal one. Rational choice theory assumes only complete partial ordering, transitivity and that irrelevant alternatives are independent. If preferences have continuous representation, utility function can be continuous, otherwise they are not (but can sometimes be modeled as continuous), >It assumes utility exists and humans behave accordingly. I think you are implicitly adding too much meaning into economic definitions of preference and utility. Economic definition of utility and preference assume very little. As long as people are forced to make decisions where they select one option over other you can infer underlying utilities.
- darkmighty 11y ago
  Isn't "complete partial order" the order of the ordinals? Or maybe you need the hyperreals to get the full picture (i.e. to be able to associate a number with each choice for any set of choices)? I don't know much about this stuff. But I agree utility is a model and it's conditions are quite clearly stated [1], and one may always infer an utility from the given choices as long as they obey those quite brand conditions (and I wouldn't call a choice consistent if they don't obey those -- for instance if you prefer A over B, B over C, and C over A). [1] http://en.wikipedia.org/wiki/Rational_choice_theory http://en.wikipedia.org/wiki/Rational_choice_theory
- marcosdumay 11y ago
  > Rational choice theory assumes only complete partial ordering, transitivity and that irrelevant alternatives are independent. Just that? Does it have any feature that wasn't widely disproven on real people?
deleted 11y ago
[deleted]
copsarebastards 11y ago
Yeah, it's sure terrible to want people to be informed on a subject before forming an opinion on it. /sarcasm Your post boils down to: "The models are outdated, so let's throw out the entire field." The thing is, the outdated models are predictive enough to be more useful than your complete lack of a proposed alternative. And even if you did propose a better model, you'd still have to understand the outdated models in order to prove that they are worse than the model you're proposing.
- GFischer 11y ago
  "if you did propose a better model, you'd still have to understand the outdated models in order to prove that they are worse than the model you're proposing." Maybe not. If the new model has better predictive qualities, that in itself might be a good signal :)
  - copsarebastards 11y ago
    Predictive of what? On what timescales? In which situations? And why? If I'm trying to predict, say, the price of a currency over a day, I'm going to use a different model than if I'm trying to predict the price of a currency over a year, even though it's likely I could use the same models. I'd also pick different models if I knew that oil prices had just gone up 50% than I would if I knew that the S&P had downgraded the US credit rating. Which model you choose comes from an understanding of the inputs of the model, the thinking behind the model, and the situations in which the model is suitable. There's no shortcut here. In any sufficiently complex field, people without any understanding of the field don't even know what they don't know, and therefore can't form valid opinions on the field. Intelligent people whose self-esteem is partially based on their intelligence are particularly susceptible to the Dunning-Kruger effect. Don't fall prey to that. Recognize when you don't know something, and admit it.
- NoMoreNicksLeft 11y ago
  I don't agree. If a climatologist proposes a model, good or bad, we can still use that model to make predictions and then wait for them to come true (or not). The climatologist is in no position to coerce the weather to adhere to what his models says will happen. An economist is in a position to influence the economy. And economists as a group are in a position to steer the economy in the direction of whatever their model predicts. Any predictions they make are less predictions and much closer to being promises.
zmk_ 11y ago
Your preferences are ordinal. A utility function needs to just reflect your preferences. It is ECON101 that if your preferences do not satisfy certain properties, there is no utility function that can represent them.
NoMoreNicksLeft 11y ago
I feel like comparing eugenics to economics is an unfair and disgusting comparison. Sure, eugenics is bad, but not that bad.
- irixusr 11y ago
  I didn't mean to be rude to economists. I actually like them and their field quite a lot. I compared it to the eugenics program because - Most (not enough) people today have become aghast at it. - Its biological underpinnings are actually quite sound. Intelligence has a genetic component. So does aggression. They also have a strong social component. However, eugenics is fundamentally a social theory, arriving at social conclusions. It is not a scientific theory, arriving at scientific conclusions (that would be biology and the theory of evolution) - Opposition to it at the time was large and strong (the T4 program driven underground by religious opposition; the US' program, which survived well into the 70s, was very low key). However, while opposition to a social theory was based on moral and social grounds, ignorance of largely irrelevant scientific points was used to deny standing. I feel that the OP's Turing test, while interesting and important, ultimately denies standing to most Americans. Therefore, it must be treated with caution.
collyw 11y ago
You forgot to add the fact that it relies on infinite growth.
- Symmetry 11y ago
  A lot of the basis of economics that's still used today was devised before the industrial revolution.
Symmetry 11y ago
Wait really? I'd say that I could very clearly say that the gaps in utility between some experiences are much larger than the gaps in utility between others. I'd rather bang my shin than stub my toe, but the gap between those is much smaller than the gap between a toe stub and being tortured to death. I can't give you precise numbers for all of that. But I couldn't give you the numbers involved in throwing a baseball either, yet my brain can still somehow compute the air resistance and everything else to give me the correct angle I should throw at. Just because you don't know a number doesn't mean you aren't subconsciously using it.
Sniffnoy 11y ago
> utility is an ordinal quantity, not a cardinal one. I can tell you I prefer my soon-to-be-born daughter's first kiss to my sister's cheerful hello, but not by how much (how much "what"? What are the units?). This has an answer, though, assuming you're using an appropriately strict notion of utility function. I do gather that "utility function" is used sometimes just to mean a function that reflects (deterministic) preferences, and making that cardinal has no obvious meaning. But a utility function in the more strict sense reflects preferences over gambles -- and there are theorems[0] to the effect that, given ordinal preferences over gambles satisfying appropriate conditions, these can always be represented by a cardinal (real-valued) utility function, which is unique up to positive affine transformations. In fact, the utility functions you get as a result of Savage's theorem -- which I think makes for a better foundation, personally, as it doesn't assume the notion of probability beforehand -- are always bounded. (I'm going to ignore the notion of "utility function" as used by utilitarians. That's largely unrelated -- a fact which has caused no end of confusion -- and is truly ill-defined.) Now, of course, it is true that actual humans do not have utility functions -- that is to say, they do not respect the conditions required to have one. Any agent that somehow did, however -- not that such a thing can actually be built -- would be acting exactly as if it did have one, and it would be meaningful to speak of its utility function (up to a positive affine transformation), regardless of whether such a function were explicitly programmed into it. Regardless, as I see it, if economists are getting decent results by approximating humans as having utility functions, well, good for them. That's not my area though, so I couldn't say whether they are or not. (Meanwhile, there have been attempts to modify utility theory to describe how people actually behave; prospect theory[1] is an example of this.) But as to your question -- what do the numbers mean? As I said, they reflect your (ordinal) preferences over gambles. That is to say, if you have utility function u, and u(A)=10, u(B)=1, and U(C)=0, this means that you would be indifferent between a 100% chance of B, and a gamble where you have a 10% chance of A and a 90% chance of C. Or, in other words, utility is that thing you're maximizing the expected value of (if it existed, anyway). Note that it doesn't mean that you would be indifferent between some amount of A and ten times as much of B or anything like that; the numbers are purely about probabilities. It's not clear what that would even mean in general anyway (and real things have diminishing marginal utility, you know). Note of course that no utility value is meaningful by itself -- again, utility functions are unique only up to positive affine transformations. But if you have three utility values[2] a, b, and c, then the ratio (a-c)/|b-c| is meaningful. Although, if you're dealing with bounded utility functions, then you could always normalize so that the infimum is 0 and the maximum is 1, and then the resulting numbers would be meaningful by themselves (because you'd be implicitly setting c=inf and b=sup in the above). This then (once we expand it a little) is the answer to your question "What are the units?". You ask this as if it were a strike against the notion, but in fact utility is more similar to conventional dimensioned quantities than you might realize. The biggest difference isn't, as you might suspect, that (as opposed to, say, length) it is nebulous and hard to measure -- it's that it's affine rather than linear! Let's examine the notion of "length" more closely. Here's the thing -- you can't really directly measure lengths, either! What you can do is measure ratios of lengths. That's why length is a dimensioned quantity -- when we say "this has a length of 5 meters", we mean, "the ratio of its length to the standard length 'meter' is 5". You can't just measure length and get a number; you have to pick a unit. Utilities, then, are similar, except that they're affine rather than linear -- like, say, temperature, before the discovery of absolute zero. These days of course we know that there's such a thing as absolute zero and it makes sense to measure temperature on a linear scale, hence Kelvins; but let's say we don't know that yet and we just have Celsius. This is an affine scale. Unlike meters (or Kelvins), it doesn't make sense to add two Celsius temperatures, or to multiply one of them by a (dimensionless) scalar, or to take the ratio of two of them. It does however make sense to take the difference of two Celsius temperatures, and get not a temperature but a temperature difference. (Which, again, today would be measured in Kelvins, but we're ignoring that.) It does make sense to add temperature differences, or to multiply them by scalars; and you can add a temperature difference to another temperature to get a new temperature, or you can take the ratio of two temperature differences to get a dimensionless scalar. This is exactly how utility works. Rather than picking one reference point (like a meter), you need two reference points (like the freezing and boiling points of water) -- these are the b and c in (a-c)/|b-c|. If we are measuring temperature and we set c=freezing point of water, b=boiling point of water, then when we plug in the temperature a we want to measure, we're now measuring it in... OK, not the Celsius scale, but a rescaled version that goes 0-1 instead of 0-100. (Just as with lengths, we can only measure a/|b|; and if b is the distance traveled by light in 1/299,792,458 of a second in a vacuum, we've reinvented the meter scale.) Whatever -- your reference points don't have to be 0 and 1, that's just convenient. So what units are utility measured in? Whatever you want, once you pick your two reference points. As mentioned above, if it's a bounded utility function, you have a natural two reference points in the infimum and supremum, but otherwise, use whatever two reference points you want. Of course frequently this is just implicit -- you have some function, and somewhere it's 0, and somewhere it's 1, and those are your two reference points. It's just not that important a lot of the time! A warning -- utility is often expressed in the undefined unit "utils", but personally I think this gives bad intuition, because again, utility is affine, not linear; I think "degrees utility" might be a better term. Of course, differences in utility are linear, and I don't see anything wrong with referring to those in "utils". So -- while this is far from justifying the general use of the notion of utility, which, as you say, does not actually apply to humans -- I hope this answers some of your questions and shows that it's actually on a much firmer footing than you imply (at least, as a description of abstract agents, rather than humans). By the way -- notice how when I was looking for a physical example of an affine scale, I used temperature before the discovery of absolute zero? (I mean, OK, I could have used position -- as opposed to displacement, which is a difference in positions, and thus linear -- but I wanted to keep things scalar.) The thing is that units, dimensions, are implicitly a statement of symmetry. Before the discovery of absolute zero, temperature appeared to have a symmetry (translation symmetry) that it in fact does not. When I say "You can't measure lengths, you can only measure ratios of lengths", I'm implicitly saying that if we scaled all the lengths in the universe by a constant factor, the result would be exactly the same. And that was a statement that appeared to be true when we knew less about physics. But these days, we know that's not true for speed (because of the physically significant speed c); we know that's not true for action (because of the physically significant action Planck's constant, or its reduced version); and we know that's not true for... uh, whatever the hell Newton's gravitational constant G is. And so by combining these we can see that it's not true for length, either; the Planck length forms a "natural unit", making actual lengths -- expressed in Planck units -- potentially meaningful, and not just their ratio. So when it comes to physical things, what things are affine, what are linear, and what are dimensionless, well, it depends on the physics -- in a Newtonian universe things might be different -- and our knowledge of physics has changed over time. Of course Planck lengths are not exactly convenient (and not as directly physically relevant as, for instance, c) so we continue to typically use meters despite the lack of actual symmetry; and in many ordinary cases the symmetry is still approximately there. But utility really is only unique up to positive affine transformations -- you are going to have to pick two reference values. (Though, once again, any utility you get from Savage's theorem will be bounded, making for a fairly natural choice.) Edit: Just to clarify the above point about "in a different universe things might be different" -- if we lived in a universe where the only physically relevant constants were, say, the speed of light c, the gravitational constant G, the Coulomb constant k_C, and the Boltzmann constant k, then you could double all lengths, times, masses, electrical charges, and temperatures, and get an isomorphic universe; from inside, it would appear absolutely the same -- any actual measurement you could make would have the same result. In fact, however, the Planck constant is also physically relevant, and since this change would quadruple all actions, it would not be a symmetry of our actual universe. (And of course there are other physically relevant constants with yet other dimensions as well.) [0]The VNM theorem: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenster... -- for people who already believe in probability Savage's theorem: http://lesswrong.com/lw/5te/a_summary_of_savages_foundations_for_probability/ http://lesswrong.com/lw/5te/a_summary_of_savages_foundations... -- does not assume probability, constructs it together with utility [1]https://en.wikipedia.org/wiki/Prospect_theory https://en.wikipedia.org/wiki/Prospect_theory [2]By which I mean values that "have type 'utility'", not necessarily outputs of the utility function; for instance, a supremum of outputs of the utility function would certainly count.

by irixusr 11y ago

nabla9 11y ago

>utility is an ordinal quantity, not a cardinal one. Rational choice theory assumes only complete partial ordering, transitivity and that irrelevant alternatives are independent. If preferences have continuous representation, utility function can be continuous, otherwise they are not (but can sometimes be modeled as continuous), >It assumes utility exists and humans behave accordingly. I think you are implicitly adding too much meaning into economic definitions of preference and utility. Economic definition of utility and preference assume very little. As long as people are forced to make decisions where they select one option over other you can infer underlying utilities.

darkmighty 11y ago
Isn't "complete partial order" the order of the ordinals? Or maybe you need the hyperreals to get the full picture (i.e. to be able to associate a number with each choice for any set of choices)? I don't know much about this stuff. But I agree utility is a model and it's conditions are quite clearly stated [1], and one may always infer an utility from the given choices as long as they obey those quite brand conditions (and I wouldn't call a choice consistent if they don't obey those -- for instance if you prefer A over B, B over C, and C over A). [1] http://en.wikipedia.org/wiki/Rational_choice_theory http://en.wikipedia.org/wiki/Rational_choice_theory
marcosdumay 11y ago
> Rational choice theory assumes only complete partial ordering, transitivity and that irrelevant alternatives are independent. Just that? Does it have any feature that wasn't widely disproven on real people?

deleted 11y ago

[deleted]

copsarebastards 11y ago

Yeah, it's sure terrible to want people to be informed on a subject before forming an opinion on it. /sarcasm Your post boils down to: "The models are outdated, so let's throw out the entire field." The thing is, the outdated models are predictive enough to be more useful than your complete lack of a proposed alternative. And even if you did propose a better model, you'd still have to understand the outdated models in order to prove that they are worse than the model you're proposing.

GFischer 11y ago
"if you did propose a better model, you'd still have to understand the outdated models in order to prove that they are worse than the model you're proposing." Maybe not. If the new model has better predictive qualities, that in itself might be a good signal :)
- copsarebastards 11y ago
  Predictive of what? On what timescales? In which situations? And why? If I'm trying to predict, say, the price of a currency over a day, I'm going to use a different model than if I'm trying to predict the price of a currency over a year, even though it's likely I could use the same models. I'd also pick different models if I knew that oil prices had just gone up 50% than I would if I knew that the S&P had downgraded the US credit rating. Which model you choose comes from an understanding of the inputs of the model, the thinking behind the model, and the situations in which the model is suitable. There's no shortcut here. In any sufficiently complex field, people without any understanding of the field don't even know what they don't know, and therefore can't form valid opinions on the field. Intelligent people whose self-esteem is partially based on their intelligence are particularly susceptible to the Dunning-Kruger effect. Don't fall prey to that. Recognize when you don't know something, and admit it.
NoMoreNicksLeft 11y ago
I don't agree. If a climatologist proposes a model, good or bad, we can still use that model to make predictions and then wait for them to come true (or not). The climatologist is in no position to coerce the weather to adhere to what his models says will happen. An economist is in a position to influence the economy. And economists as a group are in a position to steer the economy in the direction of whatever their model predicts. Any predictions they make are less predictions and much closer to being promises.

zmk_ 11y ago

Your preferences are ordinal. A utility function needs to just reflect your preferences. It is ECON101 that if your preferences do not satisfy certain properties, there is no utility function that can represent them.

NoMoreNicksLeft 11y ago

I feel like comparing eugenics to economics is an unfair and disgusting comparison. Sure, eugenics is bad, but not that bad.

irixusr 11y ago
I didn't mean to be rude to economists. I actually like them and their field quite a lot. I compared it to the eugenics program because - Most (not enough) people today have become aghast at it. - Its biological underpinnings are actually quite sound. Intelligence has a genetic component. So does aggression. They also have a strong social component. However, eugenics is fundamentally a social theory, arriving at social conclusions. It is not a scientific theory, arriving at scientific conclusions (that would be biology and the theory of evolution) - Opposition to it at the time was large and strong (the T4 program driven underground by religious opposition; the US' program, which survived well into the 70s, was very low key). However, while opposition to a social theory was based on moral and social grounds, ignorance of largely irrelevant scientific points was used to deny standing. I feel that the OP's Turing test, while interesting and important, ultimately denies standing to most Americans. Therefore, it must be treated with caution.

collyw 11y ago

You forgot to add the fact that it relies on infinite growth.

Symmetry 11y ago
A lot of the basis of economics that's still used today was devised before the industrial revolution.

Symmetry 11y ago

Wait really? I'd say that I could very clearly say that the gaps in utility between some experiences are much larger than the gaps in utility between others. I'd rather bang my shin than stub my toe, but the gap between those is much smaller than the gap between a toe stub and being tortured to death. I can't give you precise numbers for all of that. But I couldn't give you the numbers involved in throwing a baseball either, yet my brain can still somehow compute the air resistance and everything else to give me the correct angle I should throw at. Just because you don't know a number doesn't mean you aren't subconsciously using it.

Sniffnoy 11y ago

> utility is an ordinal quantity, not a cardinal one. I can tell you I prefer my soon-to-be-born daughter's first kiss to my sister's cheerful hello, but not by how much (how much "what"? What are the units?). This has an answer, though, assuming you're using an appropriately strict notion of utility function. I do gather that "utility function" is used sometimes just to mean a function that reflects (deterministic) preferences, and making that cardinal has no obvious meaning. But a utility function in the more strict sense reflects preferences over gambles -- and there are theorems[0] to the effect that, given ordinal preferences over gambles satisfying appropriate conditions, these can always be represented by a cardinal (real-valued) utility function, which is unique up to positive affine transformations. In fact, the utility functions you get as a result of Savage's theorem -- which I think makes for a better foundation, personally, as it doesn't assume the notion of probability beforehand -- are always bounded. (I'm going to ignore the notion of "utility function" as used by utilitarians. That's largely unrelated -- a fact which has caused no end of confusion -- and is truly ill-defined.) Now, of course, it is true that actual humans do not have utility functions -- that is to say, they do not respect the conditions required to have one. Any agent that somehow did, however -- not that such a thing can actually be built -- would be acting exactly as if it did have one, and it would be meaningful to speak of its utility function (up to a positive affine transformation), regardless of whether such a function were explicitly programmed into it. Regardless, as I see it, if economists are getting decent results by approximating humans as having utility functions, well, good for them. That's not my area though, so I couldn't say whether they are or not. (Meanwhile, there have been attempts to modify utility theory to describe how people actually behave; prospect theory[1] is an example of this.) But as to your question -- what do the numbers mean? As I said, they reflect your (ordinal) preferences over gambles. That is to say, if you have utility function u, and u(A)=10, u(B)=1, and U(C)=0, this means that you would be indifferent between a 100% chance of B, and a gamble where you have a 10% chance of A and a 90% chance of C. Or, in other words, utility is that thing you're maximizing the expected value of (if it existed, anyway). Note that it doesn't mean that you would be indifferent between some amount of A and ten times as much of B or anything like that; the numbers are purely about probabilities. It's not clear what that would even mean in general anyway (and real things have diminishing marginal utility, you know). Note of course that no utility value is meaningful by itself -- again, utility functions are unique only up to positive affine transformations. But if you have three utility values[2] a, b, and c, then the ratio (a-c)/|b-c| is meaningful. Although, if you're dealing with bounded utility functions, then you could always normalize so that the infimum is 0 and the maximum is 1, and then the resulting numbers would be meaningful by themselves (because you'd be implicitly setting c=inf and b=sup in the above). This then (once we expand it a little) is the answer to your question "What are the units?". You ask this as if it were a strike against the notion, but in fact utility is more similar to conventional dimensioned quantities than you might realize. The biggest difference isn't, as you might suspect, that (as opposed to, say, length) it is nebulous and hard to measure -- it's that it's affine rather than linear! Let's examine the notion of "length" more closely. Here's the thing -- you can't really directly measure lengths, either! What you can do is measure ratios of lengths. That's why length is a dimensioned quantity -- when we say "this has a length of 5 meters", we mean, "the ratio of its length to the standard length 'meter' is 5". You can't just measure length and get a number; you have to pick a unit. Utilities, then, are similar, except that they're affine rather than linear -- like, say, temperature, before the discovery of absolute zero. These days of course we know that there's such a thing as absolute zero and it makes sense to measure temperature on a linear scale, hence Kelvins; but let's say we don't know that yet and we just have Celsius. This is an affine scale. Unlike meters (or Kelvins), it doesn't make sense to add two Celsius temperatures, or to multiply one of them by a (dimensionless) scalar, or to take the ratio of two of them. It does however make sense to take the difference of two Celsius temperatures, and get not a temperature but a temperature difference. (Which, again, today would be measured in Kelvins, but we're ignoring that.) It does make sense to add temperature differences, or to multiply them by scalars; and you can add a temperature difference to another temperature to get a new temperature, or you can take the ratio of two temperature differences to get a dimensionless scalar. This is exactly how utility works. Rather than picking one reference point (like a meter), you need two reference points (like the freezing and boiling points of water) -- these are the b and c in (a-c)/|b-c|. If we are measuring temperature and we set c=freezing point of water, b=boiling point of water, then when we plug in the temperature a we want to measure, we're now measuring it in... OK, not the Celsius scale, but a rescaled version that goes 0-1 instead of 0-100. (Just as with lengths, we can only measure a/|b|; and if b is the distance traveled by light in 1/299,792,458 of a second in a vacuum, we've reinvented the meter scale.) Whatever -- your reference points don't have to be 0 and 1, that's just convenient. So what units are utility measured in? Whatever you want, once you pick your two reference points. As mentioned above, if it's a bounded utility function, you have a natural two reference points in the infimum and supremum, but otherwise, use whatever two reference points you want. Of course frequently this is just implicit -- you have some function, and somewhere it's 0, and somewhere it's 1, and those are your two reference points. It's just not that important a lot of the time! A warning -- utility is often expressed in the undefined unit "utils", but personally I think this gives bad intuition, because again, utility is affine, not linear; I think "degrees utility" might be a better term. Of course, differences in utility are linear, and I don't see anything wrong with referring to those in "utils". So -- while this is far from justifying the general use of the notion of utility, which, as you say, does not actually apply to humans -- I hope this answers some of your questions and shows that it's actually on a much firmer footing than you imply (at least, as a description of abstract agents, rather than humans). By the way -- notice how when I was looking for a physical example of an affine scale, I used temperature before the discovery of absolute zero? (I mean, OK, I could have used position -- as opposed to displacement, which is a difference in positions, and thus linear -- but I wanted to keep things scalar.) The thing is that units, dimensions, are implicitly a statement of symmetry. Before the discovery of absolute zero, temperature appeared to have a symmetry (translation symmetry) that it in fact does not. When I say "You can't measure lengths, you can only measure ratios of lengths", I'm implicitly saying that if we scaled all the lengths in the universe by a constant factor, the result would be exactly the same. And that was a statement that appeared to be true when we knew less about physics. But these days, we know that's not true for speed (because of the physically significant speed c); we know that's not true for action (because of the physically significant action Planck's constant, or its reduced version); and we know that's not true for... uh, whatever the hell Newton's gravitational constant G is. And so by combining these we can see that it's not true for length, either; the Planck length forms a "natural unit", making actual lengths -- expressed in Planck units -- potentially meaningful, and not just their ratio. So when it comes to physical things, what things are affine, what are linear, and what are dimensionless, well, it depends on the physics -- in a Newtonian universe things might be different -- and our knowledge of physics has changed over time. Of course Planck lengths are not exactly convenient (and not as directly physically relevant as, for instance, c) so we continue to typically use meters despite the lack of actual symmetry; and in many ordinary cases the symmetry is still approximately there. But utility really is only unique up to positive affine transformations -- you are going to have to pick two reference values. (Though, once again, any utility you get from Savage's theorem will be bounded, making for a fairly natural choice.) Edit: Just to clarify the above point about "in a different universe things might be different" -- if we lived in a universe where the only physically relevant constants were, say, the speed of light c, the gravitational constant G, the Coulomb constant k_C, and the Boltzmann constant k, then you could double all lengths, times, masses, electrical charges, and temperatures, and get an isomorphic universe; from inside, it would appear absolutely the same -- any actual measurement you could make would have the same result. In fact, however, the Planck constant is also physically relevant, and since this change would quadruple all actions, it would not be a symmetry of our actual universe. (And of course there are other physically relevant constants with yet other dimensions as well.) [0]The VNM theorem: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Morgenster... -- for people who already believe in probability Savage's theorem: http://lesswrong.com/lw/5te/a_summary_of_savages_foundations_for_probability/ http://lesswrong.com/lw/5te/a_summary_of_savages_foundations... -- does not assume probability, constructs it together with utility [1]https://en.wikipedia.org/wiki/Prospect_theory https://en.wikipedia.org/wiki/Prospect_theory [2]By which I mean values that "have type 'utility'", not necessarily outputs of the utility function; for instance, a supremum of outputs of the utility function would certainly count.