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Arrow's impossibility theorem is not applicable and your bringing it up is meaningless nerdery. Providing value to society is not the same problem as selecting

Arrow's impossibility theorem is not applicable and your bringing it up is meaningless nerdery. Providing value to society is not the same problem as selecting a single candidate from a set of candidates using a series of ranked preferences. For starters, value could be a function mapping preferences to a real number or random variable, called "utility," as opposed to individual ranked preferences. (Also, even if it were relevant in any sense to talk about ranked preferences, they could still be consistently aggregable into a group preference -- Arrow's Impossibility Theorem merely says they might not be. It depends on what people's rankings are. Also, even if you replace the continuous set of options on how to provide value to society with a finite, discrete set of options, and then if you talk about a marginal penny of spending instead of spending at large, so that you can finally get people talking about a set of ranked preferences, you'll find that as you iterate elections of how to spend the marginal penny on a penny by penny basis, people's preferences change from election to election as laws of diminishing returns set in. For example, if you had five discrete option on how to spend money and assuming any reasonable degree of smoothness, such a series of elections would result in a spending distribution such that no simple majority thinks that the next marginal penny should be spent on a given option. ) I really can't understand how you could possibly bring up Arrow's impossibility theorem unless you're just trying to "win" an argument by bringing up some obscure mathematical reference that nobody wants to bother understanding so that they can respond to you. Because bring Arrow's theorem into a question like this is just flagrantly pure unadulterated bullshit.

yummyfajitas 12y ago
Defining value is the same problem as creating a set of ranked preferences on reachable world states (rather than candidates). You agree with this in your third sentence - a ranked preference implies a utility function exists and vice versa (provided the set of states is countable). Arrow's Theorem says that you can't construct a set of ranked preferences from individual utility functions in a reasonable way. Throwing in extra assumptions (like cardinal preferences) allows you to do so. But if you scroll up, you'll see that Retra was arguing against a price-based (i.e. cardinal) construction. I claim that if Retra ever actually bothers to write down his definition of value to society it will be unreasonable. But given his unwillingness so far, I think he's just using "value to society" as a meaningless feel-good phrase to justify whatever policy he likes. The easiest way to prove me wrong would be to actually clearly state your definition of "value to society". Strangely, no one is willing to do that.
- Retra 12y ago
  "What is valuable to a society is not some specific state, but the ability to rapidly converge to better states as more information is obtained." Right from my other post. It is flexible decision-making capability. You simply get to the "top of the hill" because from there you can move most readily to any other place should you learn it is a better place to be.
  - yummyfajitas 12y ago
    I'm asking you how you define "better". All you've told me is that it's good to be able to get there more quickly, which is almost tautological.
    - Retra 12y ago
      No, that is not what you were asking. I'd have been glad to answer that for you, but it really has little to do with my point. Regardless, I don't think your attitude indicates that it would be worth my time to explain. I'm not going to write an academic paper for your convenience. >All you've told me is that it's good to be able to get there more quickly, which is almost tautological. http://en.wikipedia.org/wiki/Recursive_definition http://en.wikipedia.org/wiki/Recursive_definition
- SamReidHughes 12y ago
  Arrow's Theorem is irrelevant because you don't need to have a way of voting for some group preference that meets its criteria in order to have an approximate notion of what "value to society" means. Formulating a precise definition of "value to society" is irrelevant to the discussion. Gosh, maybe it means there's benefit to people other than the direct recipient of the education! Because, you know, if you look at the way people use that phrase, that's what they use it to mean. > But if you scroll up, you'll see that Retra was arguing against a price-based (i.e. cardinal) construction. Price people are paying is not the same thing as "utility", good job misreading Retra's comment.

yummyfajitas 12y ago

Defining value is the same problem as creating a set of ranked preferences on reachable world states (rather than candidates). You agree with this in your third sentence - a ranked preference implies a utility function exists and vice versa (provided the set of states is countable). Arrow's Theorem says that you can't construct a set of ranked preferences from individual utility functions in a reasonable way. Throwing in extra assumptions (like cardinal preferences) allows you to do so. But if you scroll up, you'll see that Retra was arguing against a price-based (i.e. cardinal) construction. I claim that if Retra ever actually bothers to write down his definition of value to society it will be unreasonable. But given his unwillingness so far, I think he's just using "value to society" as a meaningless feel-good phrase to justify whatever policy he likes. The easiest way to prove me wrong would be to actually clearly state your definition of "value to society". Strangely, no one is willing to do that.

Retra 12y ago
"What is valuable to a society is not some specific state, but the ability to rapidly converge to better states as more information is obtained." Right from my other post. It is flexible decision-making capability. You simply get to the "top of the hill" because from there you can move most readily to any other place should you learn it is a better place to be.
- yummyfajitas 12y ago
  I'm asking you how you define "better". All you've told me is that it's good to be able to get there more quickly, which is almost tautological.
  - Retra 12y ago
    No, that is not what you were asking. I'd have been glad to answer that for you, but it really has little to do with my point. Regardless, I don't think your attitude indicates that it would be worth my time to explain. I'm not going to write an academic paper for your convenience. >All you've told me is that it's good to be able to get there more quickly, which is almost tautological. http://en.wikipedia.org/wiki/Recursive_definition http://en.wikipedia.org/wiki/Recursive_definition
SamReidHughes 12y ago
Arrow's Theorem is irrelevant because you don't need to have a way of voting for some group preference that meets its criteria in order to have an approximate notion of what "value to society" means. Formulating a precise definition of "value to society" is irrelevant to the discussion. Gosh, maybe it means there's benefit to people other than the direct recipient of the education! Because, you know, if you look at the way people use that phrase, that's what they use it to mean. > But if you scroll up, you'll see that Retra was arguing against a price-based (i.e. cardinal) construction. Price people are paying is not the same thing as "utility", good job misreading Retra's comment.