That is one point I noticed at the first scenario as well. If there is only B1, Clippy will accept it. But if Clippy knows about both bets before deciding, he will reject B1 and take B2, for an expected utility of 4.19 instead of (2+5.57)/2 = 3.78.
When offered B1, Clippy might try to predict future bets and include that in the utility calculations. I expect (but do not have anything except intuition), that a bit of risk-aversion (for B1 only) is a good strategy for a large range of “expected bet probability density functions”.
Gamblers need some superlinear utility function for money (which is unlikely), have to assign a positive utility for the gained time where they don’t know whether they will win (which is likely) or just act irrational (which is nearly certain).
The money themselves have very low utility. The items you can buy with money can have very high utilities in comparison. When you think in terms of items you want to buy, the utility function becomes not just non linear but jagged, with steps and plateaus. It grows monotonously, that’s the only thing about it (and even then in sufficiently stupid jurisdiction it does not even grow monotonously due to taxation)
The heuristics for dealing with such messy function which you know is messy but can’t calculate, are going to be weird.
Why you’d buy an item you need for survival if money themselves had comparable utility to that item? Why you’d exchange $3 for toothbrush if you need a toothbrush and not otherwise?
The survival has extremely high utility, and costs, I dunno, a few $ a day for absolute bare minimum edit: for healthy individual that’s it, but up to millions for sick.
I’ll call the agent that assigns utility of items that can be bought with money, to the money themselves, the miserly knight . It’s miserly because it is very under-motivated to purchase anything as the purchase, for that agent, doesn’t increase the utility much if at all, even if the item is essential and the agent has enough money to live a great life.
A bottle of water can save my life if I am in desert. However, as long as I am not there (and there is no desert within 1000km from my home), I don’t carry a bottle of water with me every time.
In the desert, a bottle of water can have a very high utility. If you know you will go in one, buy a bottle of water. But standing in front of the shop (knowing you will be in a desert soon), the utility of a bottle of water is just a bit higher than the utility of the money to buy one (because you save the time to do so).
Scenario: Let’s remove the time to buy a bottle, we are right next to a vending machine for water. A bottle costs 2€ there and the machine works perfectly. You know that you will be in a desert soon, the vending machine is you only way to get water and you are highly confident that you need one bottle to survive, and do not need more than one.
Example 1: You bought a bottle of water. Would you sell me this bottle for 5€? I am quite sure it would be the rational thing to do so and to buy a new bottle. This means that at the moment, 5€ have a utility which is a bit higher than a bottle of water.
Example 2: You don’t have money and water. In this situation, 2€ have a really high utility for you—you would give me a lot to get 2€, similar to stuff you would give for one bottle of water.
Note that your utility for both money and water is highly nonlinear here. The second bottle of water could be useful, but it does not save your life. With 2€ (or a bottle of water), you would not accept any (reasonable) gamble with a risk of losing.
If you do not assign equivalent utility to money, you should rush to some shops and sell all your money.
“If you do not assign equivalent utility to money, you should rush to some shops and sell all your money.”
If I knew with certainty what items i would need in the future and if the items were non perishable nor if i could obtain more items at later date.
Meanwhile I should run to the bank to sell all my money and purchase the stocks and the like. Indeed most people do that.
Once again, what is it that makes you exchange the 2€ for the bottle if you go to the desert, but not if you don’t go to the desert? When you aren’t going to the desert you may be very unwilling to spend 2 euro on a bottle, going to desert you may be very willing to spend 2 euro on a bottle. The willingness would not be consistent with a small difference in utilities of 2 euros and a bottle.
Selling the bottle for 5euro, you are only willing to do so because you can then buy bottle again for 2 euro AND because you can use the 3 euro on something else that is actually useful. Take out either part, and you no longer should be interested in the exchange.
To utility driven agent that can exchange items, each item has it’s intrinsic utility, and it’s exchange utility, and those are separate values, and the exchange utility is determined in terms of intrinsic utilities of things it can be ultimately exchanged with (via various exchange chains). If agent doesn’t distinguish between those utilities, the agent is simply not going to work correctly, ending up in a circular loop of utility updates when trying to calculate utility of anything. Agent must keep track where the parts of utilities are coming from to avoid circular loops. The vast majority of the utility of money comes from utilities of some items to be bought with the money.
The willingness would not be consistent with a small difference in utilities of 2 euros and a bottle.
The expectations about the future influence the utility of money. If an oracle tells me “tomorrow you’ll need 1€ more than you currently have to save your life” and I know that it is usually right, this 1€ more has a high utility for me and I will really try to get it. Without that oracle, it is just 1€ more or less.
The vast majority of the utility of money comes from utilities of some items to be bought with the money.
This is the only (interesting) utility. So what? As long as you always have the option to exchange money for something useful (or at least know that you will have the possibility when you need it), you are indifferent between getting the item or money to buy the item. A good utility function should assign the same utility for both in that case.
As long as you always have the option to exchange money for something useful (or at least know that you will have the possibility when you need it), you are indifferent between getting the item or money to buy the item.
I don’t think this works correctly… your agent has money and is standing next to a soda machine, getting progressively more thirsty. How does that trigger the exchange if you tie utility of money to utility of water to drink?
The thing to remember is that utility is what you use to push your utility maximizing agent around, to make the agent do things. The agent has some foresight of how it’s actions are going to affect future utility, and picks the actions that result in larger future utility. For human, the utility may be some integral of quality of life over the possible futures. Drinking water when thirsty, eating food when hungry, living in a better house vs living in a worse house, that sort of stuff. Use, not passive possession. If the agent has descendants, or cares for the mankind, then the integral may include other people.
If you include possession of money over time into this integral, your agent will make trade-offs between possession of the money and the ultimate total comfort of his life (and those he cares about). The agent’s behaviour will be that of a miser.
edit: and yes, as a heuristic, you can assign derived utilities to stuff that can be exchanged for usable stuff. But you can’t include those utilities in the sum over the original ones. The derived utilities are a shortcut, a heuristic, and one needs to be careful not to sum together utilities of different types.
edit: to think about it, though, maybe a great deal of people have the kind of utility that you described here, the utility calculated from possession of items. I, personally, try to act according to the utility as I described above, calculated from the uses and comfort of life.
to think about it, though, maybe a great deal of people have the kind of utility that you described here, the utility calculated from possession of items.
I think this is a key point. Our brains seem prone to a dynamic where we assign some attribute to our representation of a thing in a way that makes sense in the short term (e.g., valuing money), but we then fail to entirely re-initialize that assignment when we’re done doing whatever we were doing, so over time our instrumental goals take on a terminal value of their own. Theories involving clear-cut lines between terminal and instrumental goals consequently don’t describe actual human behavior terribly well.
Yes, absolutely. And I imagine that there’s a great variety in human behaviours. I don’t really assign utility to money, as much as foresee that more money allow for higher quality of life if certain conditions are met (and that involves ultimately exchanging the money for things, and the inclination to exchange is not a result of some very slight difference in ‘utility’ of possessions).
Consider playing chess… the effective chess program may assign some simplistic utilities to pieces and particular patterns, which it evaluates in the best-play-of-opponent near future states that it foresees.
It, however, does not do knight1.utility=(utility of victory); for some knight when that knight is critical for the inevitable checkmate (victory) it foresees. There’s no point in that, it’s going to use this knight correctly without that utility adjustment. If it would do that adjustment, it would have a bug when the checkmate involves sacrifice of that knight (or ‘exchange’ of that knight for a bishop). Some people may have that bug, some may not. I think it is better not to focus on how ‘people’ on average work but on the diversity of human behaviour and efficacy of different strategies.
your agent has money and is standing next to a soda machine, getting progressively more thirsty. How does that trigger the exchange if you tie utility of money to utility of water to drink?
In that case, he knows that at some time he has to buy water and a part of his money is equivalent to the soda. He is indifferent between buying it now and later (again assuming the machine works perfectly). When he begins to become thirsty, the utility of the soda increases and he will buy one.
But maybe there is an additional thing to consider: Time. Money is an option to get stuff in the future. Having money as an intermediate step is useful to have food/house/whatever later.
How can we define a single number for a utility, if we want to have food all the time? Maybe like this: Define a current utility density. Integrate the (expected) utility density over the lifetime. In that case, having money increases the expected utility density in the future, and therefore the total utility.
See, the core of the issue is that assigning some utility to money is just a heuristic. The foresight-oriented agent does not need to do that, for it automatically tries to acquire money (and trades wisely) when maximizing other utility such as e.g. quality of life over the future. Such agent, btw, would need to assign not utility number to the money, but the future utility distribution (at very least mean and standard deviation) that he expects to get from having the money at some point in closer future.
And with regards to assigning utilities from the future to the items in the now, well, chess AI doesn’t need to do that, it doesn’t need to have some floating point value for each piece and update those all the time. (see my chess example in another post).
The problem with assigning same type of utility to money as to the items those money buy, as per
In terms of “Hey, I have this nice-looking coin”, of course. But as you can buy items with money (and you know it), money has a comparable utility.
is that if you do so as you get thirstier, the utility of the coin should also increase.
The big issue here is that people speak very informally of the utilities all the time. We do, internally, distinguish between some derived utility (like that of money) and some primary utility (that of water when thirsty), at least to the extent necessary to avoid getting stuck when getting thirsty. Albeit it IS the case that some people act as misers, which is probably due to some confusion.
There needs to be an exploration of addiction and rationality. Gamblers are addicted; we know some of the brain mechanisms of addiction—some neurotransmitter A is released in brain region B, Causing C to deplete, causing a dependency on the reward that A provides. This particular neuro-chemical circuit derives great utility from the addiction, thus driving the behaviour. By this argument, perhaps one might argue that addicts are “rational”, because they derive a great utility from their addiction. But is this argument faulty?
A mechanistic explanation of addiction says the addict has no control, no free will, no ability to break the cycle. But is it fair to say that a “machine has a utility function”? Or do you need to have free before you can discuss choice?
That is one point I noticed at the first scenario as well. If there is only B1, Clippy will accept it. But if Clippy knows about both bets before deciding, he will reject B1 and take B2, for an expected utility of 4.19 instead of (2+5.57)/2 = 3.78.
When offered B1, Clippy might try to predict future bets and include that in the utility calculations. I expect (but do not have anything except intuition), that a bit of risk-aversion (for B1 only) is a good strategy for a large range of “expected bet probability density functions”.
Gamblers need some superlinear utility function for money (which is unlikely), have to assign a positive utility for the gained time where they don’t know whether they will win (which is likely) or just act irrational (which is nearly certain).
The money themselves have very low utility. The items you can buy with money can have very high utilities in comparison. When you think in terms of items you want to buy, the utility function becomes not just non linear but jagged, with steps and plateaus. It grows monotonously, that’s the only thing about it (and even then in sufficiently stupid jurisdiction it does not even grow monotonously due to taxation)
The heuristics for dealing with such messy function which you know is messy but can’t calculate, are going to be weird.
In terms of “Hey, I have this nice-looking coin”, of course. But as you can buy items with money (and you know it), money has a comparable utility.
Why you’d buy an item you need for survival if money themselves had comparable utility to that item? Why you’d exchange $3 for toothbrush if you need a toothbrush and not otherwise?
The survival has extremely high utility, and costs, I dunno, a few $ a day for absolute bare minimum edit: for healthy individual that’s it, but up to millions for sick.
I’ll call the agent that assigns utility of items that can be bought with money, to the money themselves, the miserly knight . It’s miserly because it is very under-motivated to purchase anything as the purchase, for that agent, doesn’t increase the utility much if at all, even if the item is essential and the agent has enough money to live a great life.
A bottle of water can save my life if I am in desert. However, as long as I am not there (and there is no desert within 1000km from my home), I don’t carry a bottle of water with me every time. In the desert, a bottle of water can have a very high utility. If you know you will go in one, buy a bottle of water. But standing in front of the shop (knowing you will be in a desert soon), the utility of a bottle of water is just a bit higher than the utility of the money to buy one (because you save the time to do so).
Scenario: Let’s remove the time to buy a bottle, we are right next to a vending machine for water. A bottle costs 2€ there and the machine works perfectly. You know that you will be in a desert soon, the vending machine is you only way to get water and you are highly confident that you need one bottle to survive, and do not need more than one.
Example 1: You bought a bottle of water. Would you sell me this bottle for 5€? I am quite sure it would be the rational thing to do so and to buy a new bottle. This means that at the moment, 5€ have a utility which is a bit higher than a bottle of water.
Example 2: You don’t have money and water. In this situation, 2€ have a really high utility for you—you would give me a lot to get 2€, similar to stuff you would give for one bottle of water.
Note that your utility for both money and water is highly nonlinear here. The second bottle of water could be useful, but it does not save your life. With 2€ (or a bottle of water), you would not accept any (reasonable) gamble with a risk of losing.
If you do not assign equivalent utility to money, you should rush to some shops and sell all your money.
“If you do not assign equivalent utility to money, you should rush to some shops and sell all your money.”
If I knew with certainty what items i would need in the future and if the items were non perishable nor if i could obtain more items at later date. Meanwhile I should run to the bank to sell all my money and purchase the stocks and the like. Indeed most people do that.
Once again, what is it that makes you exchange the 2€ for the bottle if you go to the desert, but not if you don’t go to the desert? When you aren’t going to the desert you may be very unwilling to spend 2 euro on a bottle, going to desert you may be very willing to spend 2 euro on a bottle. The willingness would not be consistent with a small difference in utilities of 2 euros and a bottle.
Selling the bottle for 5euro, you are only willing to do so because you can then buy bottle again for 2 euro AND because you can use the 3 euro on something else that is actually useful. Take out either part, and you no longer should be interested in the exchange.
To utility driven agent that can exchange items, each item has it’s intrinsic utility, and it’s exchange utility, and those are separate values, and the exchange utility is determined in terms of intrinsic utilities of things it can be ultimately exchanged with (via various exchange chains). If agent doesn’t distinguish between those utilities, the agent is simply not going to work correctly, ending up in a circular loop of utility updates when trying to calculate utility of anything. Agent must keep track where the parts of utilities are coming from to avoid circular loops. The vast majority of the utility of money comes from utilities of some items to be bought with the money.
The expectations about the future influence the utility of money. If an oracle tells me “tomorrow you’ll need 1€ more than you currently have to save your life” and I know that it is usually right, this 1€ more has a high utility for me and I will really try to get it. Without that oracle, it is just 1€ more or less.
This is the only (interesting) utility. So what? As long as you always have the option to exchange money for something useful (or at least know that you will have the possibility when you need it), you are indifferent between getting the item or money to buy the item. A good utility function should assign the same utility for both in that case.
I don’t think this works correctly… your agent has money and is standing next to a soda machine, getting progressively more thirsty. How does that trigger the exchange if you tie utility of money to utility of water to drink?
The thing to remember is that utility is what you use to push your utility maximizing agent around, to make the agent do things. The agent has some foresight of how it’s actions are going to affect future utility, and picks the actions that result in larger future utility. For human, the utility may be some integral of quality of life over the possible futures. Drinking water when thirsty, eating food when hungry, living in a better house vs living in a worse house, that sort of stuff. Use, not passive possession. If the agent has descendants, or cares for the mankind, then the integral may include other people.
If you include possession of money over time into this integral, your agent will make trade-offs between possession of the money and the ultimate total comfort of his life (and those he cares about). The agent’s behaviour will be that of a miser.
edit: and yes, as a heuristic, you can assign derived utilities to stuff that can be exchanged for usable stuff. But you can’t include those utilities in the sum over the original ones. The derived utilities are a shortcut, a heuristic, and one needs to be careful not to sum together utilities of different types.
edit: to think about it, though, maybe a great deal of people have the kind of utility that you described here, the utility calculated from possession of items. I, personally, try to act according to the utility as I described above, calculated from the uses and comfort of life.
I think this is a key point. Our brains seem prone to a dynamic where we assign some attribute to our representation of a thing in a way that makes sense in the short term (e.g., valuing money), but we then fail to entirely re-initialize that assignment when we’re done doing whatever we were doing, so over time our instrumental goals take on a terminal value of their own. Theories involving clear-cut lines between terminal and instrumental goals consequently don’t describe actual human behavior terribly well.
Yes, absolutely. And I imagine that there’s a great variety in human behaviours. I don’t really assign utility to money, as much as foresee that more money allow for higher quality of life if certain conditions are met (and that involves ultimately exchanging the money for things, and the inclination to exchange is not a result of some very slight difference in ‘utility’ of possessions).
Consider playing chess… the effective chess program may assign some simplistic utilities to pieces and particular patterns, which it evaluates in the best-play-of-opponent near future states that it foresees.
It, however, does not do knight1.utility=(utility of victory); for some knight when that knight is critical for the inevitable checkmate (victory) it foresees. There’s no point in that, it’s going to use this knight correctly without that utility adjustment. If it would do that adjustment, it would have a bug when the checkmate involves sacrifice of that knight (or ‘exchange’ of that knight for a bishop). Some people may have that bug, some may not. I think it is better not to focus on how ‘people’ on average work but on the diversity of human behaviour and efficacy of different strategies.
If you don’t assign utility to money, you have to violate one of the rules given here: http://en.wikipedia.org/wiki/Utility#Additive_von_Neumann.E2.80.93Morgenstern_utility—or you have to take choices which do not maximize your utility.
But maybe there is an additional thing to consider: Time. Money is an option to get stuff in the future. Having money as an intermediate step is useful to have food/house/whatever later.
How can we define a single number for a utility, if we want to have food all the time? Maybe like this: Define a current utility density. Integrate the (expected) utility density over the lifetime. In that case, having money increases the expected utility density in the future, and therefore the total utility.
See, the core of the issue is that assigning some utility to money is just a heuristic. The foresight-oriented agent does not need to do that, for it automatically tries to acquire money (and trades wisely) when maximizing other utility such as e.g. quality of life over the future. Such agent, btw, would need to assign not utility number to the money, but the future utility distribution (at very least mean and standard deviation) that he expects to get from having the money at some point in closer future.
And with regards to assigning utilities from the future to the items in the now, well, chess AI doesn’t need to do that, it doesn’t need to have some floating point value for each piece and update those all the time. (see my chess example in another post).
The problem with assigning same type of utility to money as to the items those money buy, as per
is that if you do so as you get thirstier, the utility of the coin should also increase.
The big issue here is that people speak very informally of the utilities all the time. We do, internally, distinguish between some derived utility (like that of money) and some primary utility (that of water when thirsty), at least to the extent necessary to avoid getting stuck when getting thirsty. Albeit it IS the case that some people act as misers, which is probably due to some confusion.
There needs to be an exploration of addiction and rationality. Gamblers are addicted; we know some of the brain mechanisms of addiction—some neurotransmitter A is released in brain region B, Causing C to deplete, causing a dependency on the reward that A provides. This particular neuro-chemical circuit derives great utility from the addiction, thus driving the behaviour. By this argument, perhaps one might argue that addicts are “rational”, because they derive a great utility from their addiction. But is this argument faulty?
A mechanistic explanation of addiction says the addict has no control, no free will, no ability to break the cycle. But is it fair to say that a “machine has a utility function”? Or do you need to have free before you can discuss choice?