That list of names is amazing! I realize now how many like-minded people are out there, I’m not as alone as it felt before. Let’s not delete it quickly, it’s great that we’re all able to find each other.

# cousin_it(Vladimir Slepnev)

I don’t know the US situation firsthand, but it seems like it could get worse toward the election. Maybe move to Europe?

Maybe stochastic matrix?

Paper by Chalmers, maybe people will find it a good intro.

Overall I agree with your point and would even go further (not sure if you’ll agree or not). My feelings about colloquial language are kind of environmentalist: I think it should be allowed to grow in the traditional way, through folk poetry and individual choices, without foisting academisms or attacking “old” concepts. Otherwise we’ll just have a poor and ugly language.

Yeah. A steel string acoustic guitar is “a friend for life” as Mark Knopfler said. Another versatile instrument is the electronic keyboard.

I met him once and didn’t feel much charisma, he just sounded overconfident about all things. I’m sure it works on some people though.

Yeah. For me the aha moment came from Drawing the Head and Hands by Loomis, which is like an extended version of the post you linked. It feels great, you draw a sphere and some helper lines and end up with a realistic head from any angle.

It seems to me that making people more mobile won’t make more people exit from cities, but will instead pull people into cities. Recall how cities grow when there’s a high supply of highly mobile people from poorer regions.

That said, even if cities grow a lot, I think it’s possible to make rents lower. But it seems more like an economic and political problem.

Every year there’s a handful of new “flying cars” or other vehicles that promise to make personal flight popular, but nothing ever comes of it.

Yeah. I was more trying to argue that, compared to Bayesian ideas, voting doesn’t win you all that much.

Right, this is where strong Bayesianism is required. You have to assume, for example, that everyone agrees on the set of hypotheses under consideration and the exact models to be used.

But under these assumptions, combining evidence always gives the right answer. Compare with the example in the post: “vote on a, vote on b, vote on a^b” which just seems strange. Shouldn’t we try to use methods that give right answers to simple questions?

The hard problem is choosing between points on the frontier… which is why norm-generation processes like voting are relevant.

I think if you have a set of coefficients for comparing different people’s utilities (maybe derived by looking into their brains and measuring how much fun they feel), then that linear combination of utilities is almost tautologically the right solution. But if your only inputs are each person’s choices in some mechanism like voting, then each person’s utility function is only determined up to affine transform, and that’s not enough information to solve the problem.

For example, imagine two agents with utility functions A and B such that A<0, B<0, AB=1. So the Pareto frontier is one branch of a hyperbola. But if the agents instead had utility functions A’=2A and B’=B/2, the frontier would be the same hyperbola. Basically there’s no affine-invariant way to pick a point on that curve.

You could say that’s because the example uses unbounded utility functions. But they are unbounded only in the negative direction, which maybe isn’t so unrealistic. And anyway, the example suggests that even for bounded utility functions, any method would have to be sensitive to the far negative reaches of utility, which seems strange. Compare to what happens when you do have coefficients for comparing utilities, then the method is nicely local.

Does that make sense?

Aumann agreement isn’t an answer here, unless you assume strong Bayesianism, which I would advise against.

To expand the argument a bit: if many people have evidence-based beliefs about something, you could combine these beliefs by voting, but why bother? You have a superintelligent AI! You can peek into everyone’s heads, gather all the evidence, remove double-counting, and perform a joint update. That’s basically what Aumann agreement does—it doesn’t vote on beliefs, but instead tries to reach an end state that’s updated on all the evidence behind these beliefs. I think methods along these lines (combining evidence instead of beliefs) are more correct and should be used whenever we can afford them.

For more details on this, see the old post Share likelihood ratios, not posterior beliefs. Wei Dai and Hal Finney discuss a nice toy example in the comments: two people observe a private coinflip each, how do they combine their beliefs about the proposition that both coins came up heads? Combining the evidence is simple and gives the right answer, while other clever schemes give wrong answers.

I have to say I don’t know why a linear combination of utility functions could be considered ideal.

Imagine that after doing the joint update, the agents agree to cooperate instead of fighting, and have a set of possible joint policies. Each joint policy leads to a tuple of expected utilities for all agents. The resulting set of points in N-dimensional space has a Pareto frontier. Each point on that Pareto frontier has a tangent hyperplane. So there’s some linear combination of utility functions that’s maximized at that point, modulo some tie-breaking if the frontier is perfectly flat there.

Well, the “ideal” way to aggregate beliefs is by Aumann agreement, and the “ideal” way to aggregate values is by linear combination of utility functions. Neither involve voting. So I’m not sure voting theory will play much of a role. It’s more intended for situations where everyone behaves strategically; a superintelligent AI with visibility into our natures should be able to skip most of it.

I see. In that case does the procedure for defining points stay the same, or do you need to use recursively enumerable sets of opens, giving you only countably many reals?

Wait, but rational-delimited open intervals don’t form a locale, because they aren’t closed under infinite union. (For example, the union of all rational-delimited open intervals contained in (0,√2) is (0,√2) itself, which is not rational-delimited.) Of course you could talk about the locale generated by such intervals, but then it contains all open intervals and is uncountable, defeating your main point about going from countable to uncountable. Or am I missing something?

Yeah, being good with proofs is mostly useful for doing original work in math. You don’t need it for applying known math.

Now I feel a bit silly, because my comment wasn’t a new idea at all, but rather the reason why public utilities exist. So maybe looking at their history and performance is the best way to answer your questions.

I have another idea: if the mere existence of a competitor makes a monopoly drop prices all the way from monopoly price (way above break-even) to below break-even (necessary to crush the competitor), maybe the government should be selling some monopoly-prone goods at break-even. It would be very profitable for consumers and cost almost nothing.

Inconsistency is a good problem to have. I think for most people the creativity problem is at an earlier stage—they just can’t come up with non-boring stuff, consistent or not.

If our children are better than us, I hope they’ll offer us the same forgiveness and gratitude as we did to our parents.