If only a small number of people have power, then it becomes less likely that the correct moral views are represented among that small group, and therefore less likely that we get to a mostly-great future via trade and compromise.
I believe this is correct, but possibly for the wrong reason. If you just have a smaller group of people and they are drawn randomly from the population, yes there is a higher probability that no-one will have the correct moral view. But there is also a higher probability an unusually high fraction of people will have such a view. So a smaller bottleneck just increases the variance. But this is bad in expectation if you think that the value of the future is a concave function of the fraction of world power wielded by people with the correct values, because of trade and compromise. ie if having 10% of power in good hands is less than 10 times as good as 1%, as I understand you believe, then increasing variance by concentrating power is bad. (And of course, there is the further effect of power-seekers on average having worse values.)
In particular, we could model the process of reflection as a series of independent Brownian motions in R2, all starting at the same point at the same time. Then the expected distance of a view from the starting point, and the expected distance between two given views, both increase with the square root of time. The latter expectation is larger by a factor of sqrt(2)​.
The choice of two dimensions is unmotivated, so I don’t trust the numbers, but the general effect seems right and would hold directionally even if there are e.g. 10 dimensions that people are going on a random walk through.
a smaller bottleneck just increases the variance. But this is bad in expectation if you think that the value of the future is a concave function of the fraction of world power wielded by people with the correct values, because of trade and compromise.
Yes, this was meant to be the argument, thanks for clarifying it!
I believe this is correct, but possibly for the wrong reason.
The reason you give sounds right — for certain concave views, you really care that at least some people are bringing about or acting on the things you care about. One point, though, is that (as we discuss in the previous post) reasonable views which are concave in the good direction are going to be more sensitive (higher magnitude or less concave) in the negative direction. If you have such a view, you might also think that there are particular ways to bring about a lot of disvalue, so the expected quantity of bads could scale similarly to goods with the number of actors.
Another possibility is that you don’t need to have a concave view to value increasing the number of actors trading with one another. If there are very few actors, the amount by which a given actor can multiply the value they can achieve by their own (even linear) lights, compared to the no-trade case, may be lower, because they have more opporunities for trade. But I haven’t thought this through and it could be wrong.
The choice of two dimensions is unmotivated
Yep, totally arbitrary choice to suit the diagram. I’ve made a note to clarify that! Agree it generalises, and indeed people diverge more and more quickly on average in higher dimensions.
(more minor points)
I believe this is correct, but possibly for the wrong reason. If you just have a smaller group of people and they are drawn randomly from the population, yes there is a higher probability that no-one will have the correct moral view. But there is also a higher probability an unusually high fraction of people will have such a view. So a smaller bottleneck just increases the variance. But this is bad in expectation if you think that the value of the future is a concave function of the fraction of world power wielded by people with the correct values, because of trade and compromise. ie if having 10% of power in good hands is less than 10 times as good as 1%, as I understand you believe, then increasing variance by concentrating power is bad. (And of course, there is the further effect of power-seekers on average having worse values.)
The choice of two dimensions is unmotivated, so I don’t trust the numbers, but the general effect seems right and would hold directionally even if there are e.g. 10 dimensions that people are going on a random walk through.
Yes, this was meant to be the argument, thanks for clarifying it!
Thanks Oscar!
The reason you give sounds right — for certain concave views, you really care that at least some people are bringing about or acting on the things you care about. One point, though, is that (as we discuss in the previous post) reasonable views which are concave in the good direction are going to be more sensitive (higher magnitude or less concave) in the negative direction. If you have such a view, you might also think that there are particular ways to bring about a lot of disvalue, so the expected quantity of bads could scale similarly to goods with the number of actors.
Another possibility is that you don’t need to have a concave view to value increasing the number of actors trading with one another. If there are very few actors, the amount by which a given actor can multiply the value they can achieve by their own (even linear) lights, compared to the no-trade case, may be lower, because they have more opporunities for trade. But I haven’t thought this through and it could be wrong.
Yep, totally arbitrary choice to suit the diagram. I’ve made a note to clarify that! Agree it generalises, and indeed people diverge more and more quickly on average in higher dimensions.