I haven’t worked out the mathematical details, but qualitatively it seems to me that we discount the future more than expected because we don’t know what our desires will be like in the future (but nevertheless want to maximize the happiness of our future selves, whatever that may consist in). This means whatever action I take now to benefit my future self has an extra decrement in (present) utility because of my uncertainty in how much the future self will be benefited. And then there’s the higher-order effect that the future self may have turned into someone the present self doesn’t want to benefit (maybe they want to gruesomely murder many people).
For example, I might pay less for tickets to the Bayreuth festival five years from now than I would for this year’s tickets not only because of the loss of interest income, chance that the festival won’t be around in five years, etc., but also because of the chance that I simply won’t like Wagner as well in five years as I do now. (Of course, theater tickets are easily resalable, which should ameliorate the effect somewhat in that case.)
Therefore, since the murder pill is an example where you know exactly what your values will be at a future point, it may not be relevant to many more common instances of akrasia.
There are many different ways in which we could discount the future. The problem with almost all of them—including the “hyperbolic” discounting Ainslie describes—is not (necessarily) the mere fact that they discount, nor that they discount too much, but that they discount inconsistently: given times t1,t2,t3,t4, the relative importance of times t3 and t4 as seen from t1 is not the same as their relative importance as seen from t4. Or, to put it differently: if I apply t2-as-seen-from-t1 discounting together with t3-as-seen-from-t2 discounting, I don’t get the same as if I apply t3-as-seen-from-t1 discounting.
It is possible to discount the future consistently, but there’s basically only one degree of freedom when you choose how to do so. If you give events a time t in the future weight proportional to (constant)^t then that’s consistent. It doesn’t open you up to the bug ciphergoth describes, where your judgement now is that times t1 and t2 are almost equally important, whereas when t1 comes along you regard it as much more important than t2. (If you don’t discount at all, that’s the special case where the constant is 1.)
Ooo, no, actually you have more degrees of freedom than that: the most general scheme is that you choose a function F(t) and weight things according to that function. (Important note: one function, and its argument is absolute time, not time difference.) But the exponential case is the only possibility if you want your discounting function to be invariant if your whole life is shifted in time. (Which you might not—if, e.g., there are external events that make a big difference.)
Anyway, the point is: it’s not discounting “more than expected” that’s the issue, it’s having a pattern of discounting that’s not internally consistent.
Okay, I see how my comment was off-target. To explain the pattern described would require something more along the lines of “People know that the state of things (external or internal) can change quickly, yet over the long term tend to regress to the mean. Therefore they privilege the present over the immediate future, but regard two points in the far future as the same, having no way to distinguish between them.” But that’s both speculative and fairly empty of content.
You mean F(t_1, t_2) where t_1 is the decision time and t_2 is the time of the event whose utility is weighed. Yes, that’s the general form, but we assume that discounting is roughly constant across time (ie depends only on t_2 - t_1).
I guess it would mesh with our instincts if discounting varied with age, but in the simpler special case where we consider only timespans that are short relative to our whole lives the theory works well; there’s room to consider how this extends to a more general theorem.
No, that’s too general; for instance, hyperbolic discounting is F(a,b) = b-a, but hyperbolic discounting is inconsistent in the relevant sense. For consistency we need F(a,b) F(b,c) = F(a,c), or equivalently F(b,c) = F(a,c) / F(a,b) = G(c)/G(b) where G(t) = F(a,t). (Note that the dependence on a has gone away.) This is equivalent to discounting things at time t by a factor G(t), which is the general form I described.
Depending only on time differences is the same thing as being invariant under time-shifting your whole life.
I started getting into this, but there’s not really much point—the important thing is that we agree that if we require that preferences be invariant under time-shifting and not reverse as the choices approach, then only exponential discounting meets these criteria (treating not discounting at all as a special case of exponential discounting)
I haven’t worked out the mathematical details, but qualitatively it seems to me that we discount the future more than expected because we don’t know what our desires will be like in the future (but nevertheless want to maximize the happiness of our future selves, whatever that may consist in). This means whatever action I take now to benefit my future self has an extra decrement in (present) utility because of my uncertainty in how much the future self will be benefited. And then there’s the higher-order effect that the future self may have turned into someone the present self doesn’t want to benefit (maybe they want to gruesomely murder many people).
For example, I might pay less for tickets to the Bayreuth festival five years from now than I would for this year’s tickets not only because of the loss of interest income, chance that the festival won’t be around in five years, etc., but also because of the chance that I simply won’t like Wagner as well in five years as I do now. (Of course, theater tickets are easily resalable, which should ameliorate the effect somewhat in that case.)
Therefore, since the murder pill is an example where you know exactly what your values will be at a future point, it may not be relevant to many more common instances of akrasia.
There are many different ways in which we could discount the future. The problem with almost all of them—including the “hyperbolic” discounting Ainslie describes—is not (necessarily) the mere fact that they discount, nor that they discount too much, but that they discount inconsistently: given times t1,t2,t3,t4, the relative importance of times t3 and t4 as seen from t1 is not the same as their relative importance as seen from t4. Or, to put it differently: if I apply t2-as-seen-from-t1 discounting together with t3-as-seen-from-t2 discounting, I don’t get the same as if I apply t3-as-seen-from-t1 discounting.
It is possible to discount the future consistently, but there’s basically only one degree of freedom when you choose how to do so. If you give events a time t in the future weight proportional to (constant)^t then that’s consistent. It doesn’t open you up to the bug ciphergoth describes, where your judgement now is that times t1 and t2 are almost equally important, whereas when t1 comes along you regard it as much more important than t2. (If you don’t discount at all, that’s the special case where the constant is 1.)
Ooo, no, actually you have more degrees of freedom than that: the most general scheme is that you choose a function F(t) and weight things according to that function. (Important note: one function, and its argument is absolute time, not time difference.) But the exponential case is the only possibility if you want your discounting function to be invariant if your whole life is shifted in time. (Which you might not—if, e.g., there are external events that make a big difference.)
Anyway, the point is: it’s not discounting “more than expected” that’s the issue, it’s having a pattern of discounting that’s not internally consistent.
Okay, I see how my comment was off-target. To explain the pattern described would require something more along the lines of “People know that the state of things (external or internal) can change quickly, yet over the long term tend to regress to the mean. Therefore they privilege the present over the immediate future, but regard two points in the far future as the same, having no way to distinguish between them.” But that’s both speculative and fairly empty of content.
You mean F(t_1, t_2) where t_1 is the decision time and t_2 is the time of the event whose utility is weighed. Yes, that’s the general form, but we assume that discounting is roughly constant across time (ie depends only on t_2 - t_1).
I guess it would mesh with our instincts if discounting varied with age, but in the simpler special case where we consider only timespans that are short relative to our whole lives the theory works well; there’s room to consider how this extends to a more general theorem.
No, that’s too general; for instance, hyperbolic discounting is F(a,b) = b-a, but hyperbolic discounting is inconsistent in the relevant sense. For consistency we need F(a,b) F(b,c) = F(a,c), or equivalently F(b,c) = F(a,c) / F(a,b) = G(c)/G(b) where G(t) = F(a,t). (Note that the dependence on a has gone away.) This is equivalent to discounting things at time t by a factor G(t), which is the general form I described.
Depending only on time differences is the same thing as being invariant under time-shifting your whole life.
I started getting into this, but there’s not really much point—the important thing is that we agree that if we require that preferences be invariant under time-shifting and not reverse as the choices approach, then only exponential discounting meets these criteria (treating not discounting at all as a special case of exponential discounting)
Right.