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What does value "_to society_" mean? Can you provide a definition of this term? Arrows Impossibility Theorem generally says that value to a group is meaningles

What does value "_to society_" mean? Can you provide a definition of this term? Arrows Impossibility Theorem generally says that value to a group is meaningless - individuals have preferences, but there is no consistent way to aggregate them into a group preference. You can get around this with things like cardinal preferences (essentially money and prices), but then the value of knowledge _to society_ is by definition what a person would pay for it. So what do you mean when you say "what your society values"? Is it just a code word for "whatever my team can sneak through the political system" or is there something intrinsic there?

Retra 12y ago
What is your definition of 'individual'? A group can have values just as easily as an individual, even if your attempts to quantify that value are necessarily fuzzier. Nothing useful is ever true by definition. Society has values because social contexts promote preferred actions. You start thinking about this by trying to define morality in useful manner: A morality is an algorithm that models counterfactuals and assigns values to them. (I.e., it _evaluates_ possible states of reality and prefers some to others.) Thus group morality is an aggregate of individual moralities, though it isn't necessarily a linear aggregate, nor is it necessarily known or (even knowable) by any individual. Either way, all you need is a hypothetical, because any reliable _reasoning_ you do about group morality is going to try to optimize in terms of flexibility: if there is an ideal outcome for a group, then every action should be taken to ensure such an outcome is not eliminated from potential futures. This implies a lot about group morality. It means information processing is valuable. (And hence, some vague notion of intelligence or creativity is valuable.) Generally speaking, a group is a decision-making entity, and it must value its own ability to make decisions and moral evaluations as a consequence. 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. Social stability, situational responsiveness, rapid dissemination of facts, efficiency, correctness, etc.. Every society values these things, even if they cannot be used to determine specific behavior for individuals. Arrows theorem says that there is no way for a preferred state to be knowable to an individual. It helps to think of a group as a network of brains in the same way that a brain is a network of neurons. It's a different kind of brain, but it still does all the brain stuff as a simple consequence of the fact that it is a strict superset of brains. Naturally, one brain cannot contain the information of 10,000 brains. (Thus, Arrow's Impossibility Theorem.) But one group can. We cannot know it, but we can presume such a state exists and optimize on flexibility, not state.
- yummyfajitas 12y ago
  You could have just said, "no, I can't define value to society". Arrows theorem says that there is no way for a preferred state to be knowable to an individual...Naturally, one brain cannot contain the information of 10,000 brains. (Thus, Arrow's Impossibility Theorem.) You've got Arrow completely wrong. Arrow doesn't assert that a function isn't computable, it asserts that it doesn't exist. https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
  - Retra 12y ago
    There are assumptions in that theorem that do not apply to the situation as I am discussing it. I only brought it up there to point out why it doesn't necessarily work: there is no physical requirement for group morality to be comprehensible to an individual. You can't define societal value in terms of pure state preferences. You _can_ define it in terms of general constraints on optimizations.
    - yummyfajitas 12y ago
      The easiest way to show you can define something is to write down the definition. It's odd that you are unwilling to define a term so central to your original thesis. (Also you clearly don't understand Arrow's theorem at all.)
SamReidHughes 12y ago
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 your definition of 'individual'? A group can have values just as easily as an individual, even if your attempts to quantify that value are necessarily fuzzier. Nothing useful is ever true by definition. Society has values because social contexts promote preferred actions. You start thinking about this by trying to define morality in useful manner: A morality is an algorithm that models counterfactuals and assigns values to them. (I.e., it _evaluates_ possible states of reality and prefers some to others.) Thus group morality is an aggregate of individual moralities, though it isn't necessarily a linear aggregate, nor is it necessarily known or (even knowable) by any individual. Either way, all you need is a hypothetical, because any reliable _reasoning_ you do about group morality is going to try to optimize in terms of flexibility: if there is an ideal outcome for a group, then every action should be taken to ensure such an outcome is not eliminated from potential futures. This implies a lot about group morality. It means information processing is valuable. (And hence, some vague notion of intelligence or creativity is valuable.) Generally speaking, a group is a decision-making entity, and it must value its own ability to make decisions and moral evaluations as a consequence. 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. Social stability, situational responsiveness, rapid dissemination of facts, efficiency, correctness, etc.. Every society values these things, even if they cannot be used to determine specific behavior for individuals. Arrows theorem says that there is no way for a preferred state to be knowable to an individual. It helps to think of a group as a network of brains in the same way that a brain is a network of neurons. It's a different kind of brain, but it still does all the brain stuff as a simple consequence of the fact that it is a strict superset of brains. Naturally, one brain cannot contain the information of 10,000 brains. (Thus, Arrow's Impossibility Theorem.) But one group can. We cannot know it, but we can presume such a state exists and optimize on flexibility, not state.

yummyfajitas 12y ago
You could have just said, "no, I can't define value to society". Arrows theorem says that there is no way for a preferred state to be knowable to an individual...Naturally, one brain cannot contain the information of 10,000 brains. (Thus, Arrow's Impossibility Theorem.) You've got Arrow completely wrong. Arrow doesn't assert that a function isn't computable, it asserts that it doesn't exist. https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
- Retra 12y ago
  There are assumptions in that theorem that do not apply to the situation as I am discussing it. I only brought it up there to point out why it doesn't necessarily work: there is no physical requirement for group morality to be comprehensible to an individual. You can't define societal value in terms of pure state preferences. You _can_ define it in terms of general constraints on optimizations.
  - yummyfajitas 12y ago
    The easiest way to show you can define something is to write down the definition. It's odd that you are unwilling to define a term so central to your original thesis. (Also you clearly don't understand Arrow's theorem at all.)

SamReidHughes 12y ago

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.