Gmail was invitation-only at first. https://en.wikipedia.org/wiki/...

That depends, does wash trading (selling to yourself) count?

People choose google, because they like it , not because of some monopoly influence.

People choose Google because they like it.
They like Google because Google provides good results.
Google provides good results because they have huge datacenters and extreme amounts of data.
The cost of acquiring huge datacenters and extreme amounts of data provides a barrier to entry.
This barrier to entry produces a natural monopoly.

And so it is. Not all monopolies have to be ordained by the State.

Those who rob Peter to pay Paul can always count on the support of Peter....

Why would Peter always support being robbed?

If the computer was infinitely fast, there would be two programming languages.

1. Nonlinear optimization.
2. Teach-by-example, e.g. a neural net of maximum size for the RAM constraints, where all the weights are found by brute force.

The former is for when you know exactly what you want, the latter is for when you don't and use supervised learning instead.
For that matter, an infinitely fast computer is a hypercomputer, so 2. could easily be "the smallest Turing machine that produces the desired outputs given the inputs".

The market has no regret... some agents will, others won't.

That would be regret in the game theoretical sense. The regret of a strategy is the best payoff you could get minus the best you got; the "opportunity cost". There's an example here.

Since the market is based on individual predictors, the best it can do is somehow knowing the best predictor at each instant. That would correspond to zero regret. Any algorithm based on experts advice would have a regret greater than or equal to zero, even though it may not have an "emotional" regret.

Also, play money doesn't work... it''s not money.

Again perhaps surprisingly, play money vs real money doesn't seem to have much of an effect (See also this post).

If you consider the market to be a kind of weighted voting algorithm that exponentially amplifies the predictions of good experts (as you've said), then it doesn't greatly matter what the weights correspond to in the real world. All that matters is that good experts get their weights amplified, bad experts "go broke", that you have enough players to begin with to catch some good experts, and that the players can't do Sybil attacks to get around going broke.

As sites like StackOverflow show -- or MMOs for that matter -- there are plenty of people that are incentivized simply by getting a high score, even if that high score doesn't translate into real money. So while it may seem counterintuitive that play market should work, it's not that weird if you consider it from the point of view of an exponential weighting algorithm.

I was talking about real prediction markets, not as use in training NNs with virtual prediction markets. I can't think of any situation where this would even make sense... but maybe?

I might have been a bit hasty in my informal impossibility argument, as it were, but my line of thought was like this:
- The claim is that a prediction market can act as well as the best participant of that market, i.e. have zero regret.
- This should hold irrelvant of what the inputs are, whether the inputs are predictions by people or by other simpler algorithms.
- If the claim were true, you could dump a lot (and I mean an extreme amount) of comparatively simple algorithms into a virtual prediction market, and by the claim, the market would act just as well as the very best algorithm of the lot, producing a super AI.
- Since we don't have such super AIs in the real world, the claim must be wrong (and it is, because of the log(N) term).

More generally, if prediction markets were to have zero regret compared to the best expert, every kind of ensemble method would be easy. Just dump the individual methods into a prediction market and you'd get at least as good performance as the best individual method. The prediction market algorithm is the same irrespective of whether its inputs are by people or by computer algorithms, after all.

If anything Swarm AI is a prediction market, but with equal waiting for every "expert, and no reward feedback mechanism to promote the accurate and remove the inaccurate players.

Perhaps surprisingly, it's often hard to do better than nonadaptive methods. See for instance the Variance method of An empirical comparison of algorithms for aggregating expert predictions. Then again, I have no idea what particular algorithm Swarm AI uses; it may be a bad nonadaptive method.

If you're in the US, you've probably never had a chance to use a prediction market, because they are generally illegal there. I have no idea why.

I imagine the reason they're illegal is that they can produce perverse incentives. Suppose, for instance, that there's a prediction market on when the next act of terrorism will occur in the US, as defined by some criterion. You predict tomorrow, then go (or get a dupe to go) snipe off some people and send a manifesto to the newspapers. Since the market considered tomorrow to be very unlikely, you get a lot of money doing this, and a strategy like that might seem rather tempting for someone who's poor or desperate enough.

I'd thus expect play money prediction markets to be more easily accepted, since there's no reason to murder for Shiny Points or whatever. But I wouldn't be surprised if the law just refers to prediction markets in general rather than real money prediction markets in particular.

So, because it is a meta-prediction technique that optimally combines the results of all participating prediction techniques, it is always going to be better than any given underlying prediction system, or at worst case be as good as the best underlying prediction method.

No, because you're always going to take some hit determining what the optimal ensemble is (and even moreso if situations change or if there's noise). In exponential reweighting, the regret has an ln(N) term, which is what keeps you from just making an optimal AI by dumping an exponential number of algorithms into a virtual prediction market and getting a result "as good as the best underlying prediction method".

In practice, if you run the prediction market with real people, you're at risk of all the fun stuff that sometimes makes real markets behave poorly, such as bubbles. This happens because there's a feedback loop where people alter their predictions based on everybody else's predictions, as in a Keynesian beauty contest. In contrast, "the best underlying prediction method" would not have such problems because there would be no market for it to be influenced by.

30% of 0 is still 0.

I'm having a hard time picturing any culture that celebrates the "everyman". The "strong leader" is pretty much a universal cultural archetype.

A lot of cultures have social regulations of the form "don't think too much of yourself, or you'll be cut down to size". E.g. Japanese nails that stick up, tall poppies, and Jante. Isn't that a darker version of celebration of the everyman? Such cultures would be more suspicious of people trying to appear to be great leaders, and would encourage humility instead.

Even if you could hack the universe, how could you tell an unintended feature (a hack) from an intended feature (a law of physics) from the inside? Science is descriptive, not prescriptive...

What year would that Nobel Peace Prize have been awarded? I can't seem to find him anywhere on this list nor on this list (in case Wikipedia has been vandalized).

If someone invents an auto-bug-finder, won't every software company run it on their software before releasing it, knowing that if they don't, the malware creators will?