Mere Addition Paradox Resolved

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David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

LuckyR wrote: May 9th, 2018, 1:40 am Well, in the examples you cite, if 10 "experts" give 10 identical answers, they know something (or there is something to be known). If you get 10 different answers you are dealing with opinions, not knowledge.
Picture a jar packed with an unknown number of sweets/candies (UK/US English). This can be used in a competition where people pay a small amount of money to take part, and the person who comes closest to guessing the correct number of sweets wins the lot. The guesses vary widely, but experiments have shown that if you average their guesses, they collectively come very close to the right answer. People are generally bad at making some kinds of judgements, but they're still applying methods which aren't entirely wrong, as is revealed by this "wisdom of the crowd" phenomenon.

When we have AGI systems doing the calculations though, we will get straight to the more accurate judgements, and different AGI systems weighing up the same evidence will produce the same answers. The fact that people often produce widely differing answers simply reveals that they are bad at calculating - not that there aren't valid calculations that can be made.
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LuckyR
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Re: Mere Addition Paradox Resolved

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David Cooper wrote: May 9th, 2018, 1:55 pm
LuckyR wrote: May 9th, 2018, 1:40 am Well, in the examples you cite, if 10 "experts" give 10 identical answers, they know something (or there is something to be known). If you get 10 different answers you are dealing with opinions, not knowledge.
Picture a jar packed with an unknown number of sweets/candies (UK/US English). This can be used in a competition where people pay a small amount of money to take part, and the person who comes closest to guessing the correct number of sweets wins the lot. The guesses vary widely, but experiments have shown that if you average their guesses, they collectively come very close to the right answer. People are generally bad at making some kinds of judgements, but they're still applying methods which aren't entirely wrong, as is revealed by this "wisdom of the crowd" phenomenon.

When we have AGI systems doing the calculations though, we will get straight to the more accurate judgements, and different AGI systems weighing up the same evidence will produce the same answers. The fact that people often produce widely differing answers simply reveals that they are bad at calculating - not that there aren't valid calculations that can be made.
There is a huge logic flaw in your analogy, namely the jar guesses have an agreed upon objective answer to be compared to, the actual number of candies. OTOH, the "life value" of an accident victim can have multiple guesses (subjective) as to it's quantity, but there is no objective, or even universally accepted standard to measure the accuracy of the guesses.
"As usual... it depends."
David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

LuckyR wrote: May 10th, 2018, 2:15 am There is a huge logic flaw in your analogy, namely the jar guesses have an agreed upon objective answer to be compared to, the actual number of candies. OTOH, the "life value" of an accident victim can have multiple guesses (subjective) as to it's quantity, but there is no objective, or even universally accepted standard to measure the accuracy of the guesses.
I don't do logic flaws. There are absolute amounts of pleasure and suffering involved, and we can compare them within ourselves and decide how they measure up against each other. We can also see what other people say about how they compare them within themselves. By collecting this kind of information from millions of people, we could get very good statistics on average comparisons. AGi will be able to do this work and build up an accurate database which can be used in moral calculations, and this will take over from the guesses of judges when it comes to the amount of compensation that people should get, and the amount of punishment when dealing with criminals. It's all perfectly doable, and it will happen.
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ThomasHobbes
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Re: Mere Addition Paradox Resolved

Post by ThomasHobbes »

David Cooper wrote: April 30th, 2018, 4:57 pm Diagram:

See https://en.wikipedia.org/wiki/Mere_addition_paradox for the diagram, though in case the key parts of it are edited into a different form in the future, I'll provide a description here (adding appropriate numbers of my own invention, chosen to reflect the height of the bars in the diagram)

Description of diagram:

Population A might have 1000 people in it with a quality of life of 8, which we'll call Q8.

Population A+ is a combination of 1000 people at Q8 (population A) plus another 1000 people at Q4 (population A', though this population is not normally named).

Population B- is a combination of two lots of 1000 people which are both at Q7.

Population B has 2000 people at Q7.

The distinction between group B and B- is that B- keeps the two lots of 1000 people apart, which should reduce their happiness a bit as they have fewer options for friends, but we're supposed to imagine that they're equally happy whether they're kept apart (as in B-) or merged (in B).

Parfit's argument (to illustrate the paradox):

"Parfit observes that i) A+ seems no worse than A. This is because the people in A are no worse-off in A+, while the additional people who exist in A+ are better off in A+ compared to A [where they simply wouldn't exist] (if it is stipulated that their lives are good enough that living them is better than not existing)."

"Next, Parfit suggests that ii) B− seems better than A+. This is because B− has greater total and average happiness than A+."

"Then, he notes that iii) B seems equally as good as B−, as the only difference between B− and B is that the two groups in B− are merged to form one group in B."

"Together, these three comparisons entail that B is better than A. However, Parfit observes that when we directly compare A (a population with high average happiness) and B (a population with lower average happiness, but more total happiness because of its larger population), it may seem that B can be worse than A."

Paradox Lost:

First of all, we need to understand why there should be an optimal population size for a given amount of available resources, and if the population grows too high, total happiness goes down rather than up. This must be the case because the happiness of a population falls to zero long before the resources per person approach zero, and if you drag people out of poverty by giving them a modest increase in resources, their happiness shoots up, so it isn't a linear relationship either. The paradox superficially appears to deny this, but it only does so by introducing a fundamental error.

The error in the argument is hidden in the allocation of resources for A. Initially, A has access only to the resources of A and not to the resources of A'. When A' is added to A to make A+, new resources are brought in at the same time.

We can see now that A with access to all the resources of A+ (but without the population A') is inferior to A+ in terms of happiness because it's failing to use all the resources available to it, whereas A with access only to the resources of A is superior to A+ in terms of happiness per unit of resources. This is the key difference which Parfit missed.

When we look at A+, we see an unfair distribution of resources, and if we fixed that by sharing things evenly for all members of A+, A+ might well end up looking like B- because so many people would be lifted out of poverty and gain greatly in happiness without dragging A down very far.

We can thus see that A+ is inferior to an adjusted A+ with a redistribution of resources to even them out, and we can see that A+ is inferior to B- and B if it lacks that even distribution of resources, or it might be on a level with B- and B if it has redistributed of resources to even them out.

B is superior to A if A has access to the resources of A' while population A'=0, but A is superior to B if it doesn't have access to those extra resources of A' when you compare A and B per unit of available resources (which B has a lot more of).

So, the paradox evaporates: A is better than B if A only has the resources of A; but B is better than A if A has access to the full resources of A+ while it fails to use the component of those resources relating to A'.

(Note: If A was to use the resources of A' as well, it might go up to Q9 and have happier people in it, but the optimum population would then be higher and so it would have to grow to maximise total happiness per unit of resources.)

Since quality of life is a value judgement, and does not properly represent an integer the problem is self generated.
An individual human could never have such a complex idea as quality of life expressed by a single integer. No two humans could ever have the same quality of life. How much more ridiculous is it to attach a single integer to 1000 or 2000 humans?
This is not a paradox, but a simple misunderstanding of reality.
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Re: Mere Addition Paradox Resolved

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ThomasHobbes wrote: May 11th, 2018, 7:18 am Since quality of life is a value judgement, and does not properly represent an integer the problem is self generated.
An individual human could never have such a complex idea as quality of life expressed by a single integer. No two humans could ever have the same quality of life. How much more ridiculous is it to attach a single integer to 1000 or 2000 humans?
This is not a paradox, but a simple misunderstanding of reality.
There's no reason to imagine that there aren't absolute values involved. If science can ever get to the point where it can see the mechanism for sentience, we may even be able to make proper measurements of the strengths of feelings in all species. If the data that our brains generate about feelings is true rather than just being baseless assertions, the brain must have a way of measuring how strong those feelings are, thereby enabling us to weigh up whether we get more pleasure out of eating a cake than a piece of cardboard. The "paradox" assumes that such absolute values for feelings exist, and that's a reasonable assumption given that we can make comparisons of the value differences between different feelings and different amounts of the same feelings. Where it goes wrong is in labelling itself as a paradox when it is cheating by switching the basis on which it is making comparisons.
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LuckyR
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Re: Mere Addition Paradox Resolved

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David Cooper wrote: May 10th, 2018, 4:54 pm
LuckyR wrote: May 10th, 2018, 2:15 am There is a huge logic flaw in your analogy, namely the jar guesses have an agreed upon objective answer to be compared to, the actual number of candies. OTOH, the "life value" of an accident victim can have multiple guesses (subjective) as to it's quantity, but there is no objective, or even universally accepted standard to measure the accuracy of the guesses.
I don't do logic flaws. There are absolute amounts of pleasure and suffering involved, and we can compare them within ourselves and decide how they measure up against each other. We can also see what other people say about how they compare them within themselves. By collecting this kind of information from millions of people, we could get very good statistics on average comparisons. AGi will be able to do this work and build up an accurate database which can be used in moral calculations, and this will take over from the guesses of judges when it comes to the amount of compensation that people should get, and the amount of punishment when dealing with criminals. It's all perfectly doable, and it will happen.
Well, you're right about that. It can happen and it will happen. Unfortunately, it won't be based on any reproducible data. It will just be another "that's the best we can do, oh well..." thing.
"As usual... it depends."
David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

LuckyR wrote: May 12th, 2018, 1:21 am Well, you're right about that. It can happen and it will happen. Unfortunately, it won't be based on any reproducible data. It will just be another "that's the best we can do, oh well..." thing.
The best we can do is better than not trying, and it's less moral not to try. The inability to achieve perfection is never a reason not to get as close to perfection as can reasonably be achieved.
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ThomasHobbes
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Re: Mere Addition Paradox Resolved

Post by ThomasHobbes »

David Cooper wrote: May 11th, 2018, 2:30 pm
ThomasHobbes wrote: May 11th, 2018, 7:18 am Since quality of life is a value judgement, and does not properly represent an integer the problem is self generated.
An individual human could never have such a complex idea as quality of life expressed by a single integer. No two humans could ever have the same quality of life. How much more ridiculous is it to attach a single integer to 1000 or 2000 humans?
This is not a paradox, but a simple misunderstanding of reality.
There's no reason to imagine that there aren't absolute values involved. If science can ever get to the point where it can see the mechanism for sentience, we may even be able to make proper measurements of the strengths of feelings in all species.
No. There is a difference between reductionism and complex ideas.
Prima Facie the example is erroneous.
What if... is very interesting, but we are dealing with the case at hand, not some future scientific wonderland.
David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

ThomasHobbes wrote: May 13th, 2018, 10:58 am
David Cooper wrote: May 11th, 2018, 2:30 pm There's no reason to imagine that there aren't absolute values involved. If science can ever get to the point where it can see the mechanism for sentience, we may even be able to make proper measurements of the strengths of feelings in all species.
No. There is a difference between reductionism and complex ideas.
Prima Facie the example is erroneous.
What if... is very interesting, but we are dealing with the case at hand, not some future scientific wonderland.
Within your head you can already feel the difference as pain goes up or down - the brain is measuring the level of pain, and it isn't doing it by magic, but by some kind of method which science will certainly be able to explore some day. Some kind of algorithm is running which produces values, and science needs to disassemble that to find out how these measurements are performed. Every step of the process involves transfers of energy which can in principle be measured, so why dismiss the idea that reductionism applies here just because there's a complexity barrier in the way to seeing what's going on?
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ThomasHobbes
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Re: Mere Addition Paradox Resolved

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David Cooper wrote: May 13th, 2018, 4:21 pm
ThomasHobbes wrote: May 13th, 2018, 10:58 am

No. There is a difference between reductionism and complex ideas.
Prima Facie the example is erroneous.
What if... is very interesting, but we are dealing with the case at hand, not some future scientific wonderland.
Within your head you can already feel the difference as pain goes up or down - the brain is measuring the level of pain, and it isn't doing it by magic, but by some kind of method which science will certainly be able to explore some day. Some kind of algorithm is running which produces values, and science needs to disassemble that to find out how these measurements are performed. Every step of the process involves transfers of energy which can in principle be measured, so why dismiss the idea that reductionism applies here just because there's a complexity barrier in the way to seeing what's going on?
Indeed not.
You cannot measure a thing without changing it.
Emotional states do not produce 'values'. The problems of mathematics is due to the fact that it is noting more than a means to describe. maths is not fundamental. Reality is analogue, complex, and multifarious. Maths can only approximate.
The example you gave is ridiculously in coherent. I've already told you what the problem is.
David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

ThomasHobbes wrote: May 13th, 2018, 5:42 pm Indeed not.
You cannot measure a thing without changing it.
A weight can sit on scales and be measured continually. There is a continual change in that forces are being exchanged continually, but the measurement is fairly constant.
Emotional states do not produce 'values'.
So how do you tell if pain is increasing as you put more pressure on a splinter in your skin? How can you tell if it's reducing when you remove that pressure? How can you tell if it's stopped? It's all quantity/numbers.
The problems of mathematics is due to the fact that it is noting more than a means to describe. maths is not fundamental.
Maths maps to something fundamental which is equivalent to maths.
Reality is analogue, complex, and multifarious. Maths can only approximate.
Reality is most likely digital, but even if it isn't, how much precision do you need to detect massive differences in the amount of pain or any other sensations that you experience?
The example you gave is ridiculously in coherent.
How so? It's correct and profound.
I've already told you what the problem is.
You appeared to dismiss reductionism in favour of irreducible complexity. That is the avoidance of science.
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ThomasHobbes
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Re: Mere Addition Paradox Resolved

Post by ThomasHobbes »

David Cooper wrote: May 14th, 2018, 12:53 pm
ThomasHobbes wrote: May 13th, 2018, 5:42 pm Indeed not.
You cannot measure a thing without changing it.
A weight can sit on scales and be measured continually. There is a continual change in that forces are being exchanged continually, but the measurement is fairly constant.
Emotional states do not produce 'values'.
So how do you tell if pain is increasing as you put more pressure on a splinter in your skin? How can you tell if it's reducing when you remove that pressure? How can you tell if it's stopped? It's all quantity/numbers.
None of it is numbers. None!
Stick a pin in your leg and give me a number. My number would also be a guess and bear no relationship to yours were I to do the same.
The problems of mathematics is due to the fact that it is noting more than a means to describe. maths is not fundamental.
Maths maps to something fundamental which is equivalent to maths.
Equilavent?? LOL And does that mean '=' or is it some sort of guess?
Reality is analogue, complex, and multifarious. Maths can only approximate.
Reality is most likely digital, but even if it isn't, how much precision do you need to detect massive differences in the amount of pain or any other sensations that you experience?
there is not one indication. scrap of evidence, or rationality that makes that remotely possible
The example you gave is ridiculously incoherent.
How so? It's correct and profound.
I've already told you what the problem is.
You appeared to dismiss reductionism in favour of irreducible complexity. That is the avoidance of science.
No it is the embrace of science, and knowing its limitations. Reductionism is the limit; the approximation. Reality is more complex than human conceit.
David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

ThomasHobbes wrote: May 15th, 2018, 5:21 am None of it is numbers. None!
Stick a pin in your leg and give me a number. My number would also be a guess and bear no relationship to yours were I to do the same.
It's difficult to put specific numbers to it, but it's possible to say that it's approximately doubled, or that it's ten times worse - we don't have direct access to the gauge but merely feel the result. The way the value is felt to change though is 100% compatible with numbers - there are numbers behind the scenes.
Equilavent?? LOL And does that mean '=' or is it some sort of guess?
Yes, equivalent. It isn't the same because reality doesn't do negative numbers (never mind imaginary ones), but maths maps to reality regardless.
there is not one indication. scrap of evidence, or rationality that makes that remotely possible
So the brain determines that one amount of pain is worse than another amount of pain by magic? Surely not.
No it is the embrace of science, and knowing its limitations. Reductionism is the limit; the approximation. Reality is more complex than human conceit.
When you abandon reductionism, you abandon science in favour of magic.
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ThomasHobbes
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Re: Mere Addition Paradox Resolved

Post by ThomasHobbes »

David Cooper wrote: May 15th, 2018, 8:17 pm
ThomasHobbes wrote: May 15th, 2018, 5:21 am None of it is numbers. None!
Stick a pin in your leg and give me a number. My number would also be a guess and bear no relationship to yours were I to do the same.
It's difficult to put specific numbers to it,
You ain't getting it.
David Cooper
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Re: Mere Addition Paradox Resolved

Post by David Cooper »

ThomasHobbes wrote: May 16th, 2018, 5:20 pm
David Cooper wrote: May 15th, 2018, 8:17 pm It's difficult to put specific numbers to it,
You ain't getting it.
How do you put absolute numbers to something where you can't see the grain? It doesn't stop you measuring quantities of water without having to know how many molecules are present. Something in the brain may be able to see absolute values, but it doesn't pass that information on.
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