Braess’ paradox
en.wikipedia.org
en.wikipedia.org
I don't think it's appreciated enough that some forms of regulation actually do make things better for everyone, and that acting only in one's own self-interest can lead to results that are provably worse for your own self-interest.
As someone who is libertarian-ish, I find that a funny thing to say which doesn't jive with reality. Western countries usually have huge governments with huge amounts of regulation, and the default assumption of almost everyone around me seems to be that regulation is the way to deal with almost anything we don't like.
So saying that it's not appreciated that some regulation makes things better for everyone sounds to me like saying "it's not appreciated enough that clothes make us warm".
(Unless, of course, you're referring only to specific circles, e.g. libertarian economists).
this whole article is poorly veiled propaganda by the current communist administration to justify government ownership of roads. After all, who but the government could remove a link to benefit "everyone"? By generating this absurd fake propaganda, it hopes to ply public sympathy toward state involvement and ownership. Naturally the actual proposed "facts" are totally rubbish: it is obvious that you could never decrease traffic congestion in an area by removing already congested roads. The article is an obvious hoax from the first sentence: "Braess's paradox, credited to the mathematician Dietrich Braess" redlinks. I've added a deletion tag. 82.113.121.167 (talk) 01:27, 31 March 2010 (UTC)
Well, in my experience, people are very polarized about this: either they want to go to the gulch, or they want a very protective state that deals with everything. Both population seems comparable, number-wise; YMMV.
Personally I can't help but reading anyone trying to blame underregulation on libertarians as effectively an admission that they have run out of excuses. There just aren't enough libertarians to have that much of an effect on anything. Even "deregulation" is not generally the libertarians running wild, it's non-libertarians trying to implement a "free market", for some definition of said, but they're generally not libertarians and the same people will happily vote for crony capitalism or a ton of other sorts of regulations.
Being a public servant is a thankless job.
Best example is that property rights are such a form of regulation. When it comes to fisheries, wildlife, open public lands, air pollution, and intellectual 'property,' the optimal regulation gets much more complicated.
This paradox would be like if adding more fish to a pond, caused there to be less fish in the pond.
Suppose you have two ponds, one with a large population of low value fish, and one with a limited number of high value fish. The value of fish caught from the big pond is 1/2, and the value of the small pond is 40/n, where n is the number of fisherman using the pond.
Consider 50 fisherman living by both ponds, with a bridge connecting the two. The only equilibrium is 80 fisherman fishing the small pond and 20 fishing the big pond (otherwise at least 1 fisherman's catch rises by moving).
Suppose the government burns down the bridge. Now 50 fisherman fish at each pond, and total catch rises from 50 to 65.
In general, when you have 2 choices, one with higher quality and more sensitivity to increased use, then you get dynamics similar to this paradox. Whether government has the ability and incentive to intervene effectively is a separate question.
You mean a road from one pond to the other one?
</nitpick>
That's analogous because, in a Braess situation, the new route appears more attractive to drivers individually (just as underpriced fish does), but their usage of said route will disproportionately exhaust the network's capacity.
And in both cases, there's a kind of "tragedy of the commons" dynamic.
One individual choosing to simply not catch the one more fish (choosing to not drive the additional road) would make no difference because other people would take the fish/road.
Regulating overfishing (removing the road) leads to more fish for every individual over time (leads to better traffic times for everyone).
It's obviously more complicated in the real world as it misses some economic and biospheric mechanics, but it gives a starting thinking exercise.
> In Seoul, South Korea, a speeding up in traffic around the city was seen when a motorway was removed as part of the Cheonggyecheon restoration project.
It also mentions Stuttgart, New York City, Boston, and London.
For instance, regulations are mostly only effective if they're enforceable. With fishing taking place largely in international waters, and as I understand it, enforcement falling upon the coast-guard-equivalent of whichever country's flag the boat is flying, enforcement would be very difficult.
As far as implementing better regulations, any single nation implementing the good regulations would effectively be putting their own industry at an economic disadvantage (and by extension, their citizens who must pay for the more limited supply) compared to the more lax nations.
We see this with the global climate change debate too; basically every single nation needs to agree at the same time for global progress to be made.
Edit: clarified the first sentence.
To be precise: everyone acting in their own self interest can be worse for everyone's self-interest, than everyone not doing that. For an individual, acting in your own self-interest is still good for your self-interest, tautologically.
Fundamentally, the problem is that people can take resources for themselves, in a way that damages the total resource pool. Each fish you take is one that can't make more fish. Every car on a road slows down all the other cars.
No, the tautology would be "acting in your own self-interest is still acting for your self-interest".
No guarantee that the outcome would be the best for you -- unless you have unlimited information of future possibilities to pick what's best (then it would a tautology again).
For a trivial counter example let's imagine that after your and others actions, a benevolent benefactor gives $10 million dollars to the ones who self-sacrificed the most.
Nature can be such a factor -- only much less benevolent.
The Braess paradox and overfishing are problems even when everyone has perfect information.
My point was more to make a distinction against the argument that regulation against a self-interested sort by definition means a worse outcome for that person. Sometimes a regulation leads to a better personal outcome than you'd get through Nash.
It's been well proven in economics that externalities, if unregulated, will produce sub-optimal outcomes. That the way to restore optimal outcomes is to impose a tax that's proportional to the negative externality imposed on others. In an ideal high-tech world, this can be achieved by having differential prices that each driver has to pay, to use each road/highway. In a low tech world, narrowing/closing a road is akin to imposing a tax on certain routes, which explains why it can counter-intuitively help us get to a more optimal outcome.
In contrast, for heavily congested roads, the primary bottleneck is the congestion itself. Hence, marginally increased traffic will have a proportional impact on travel time.
Edit: the explanation given is that the red spring redistributes forces so that more force is applied to the weak springs and less force to the strong springs, causing an overall greater total extension.
Does this just mean people are making bad decisions based on incomplete information?
For example, would this still be a problem if everyone was using Google Maps routing which changes routes based on congestion patterns?
(Also, is this specified somewhere? It seems like the paradox relies on people making their minds up ahead of time (hence imperfect information) and then not changing their minds halfway.)
The nash equilibrium would be for both prisoners to deflect but this is worse than if they both stayed silent.
Both staying silent is not an equilibrium because if one of them decides to be selfish and cheat, he can do better for himself.
Basically the information you need is agreement/cooperation ahead of time to know that neither side will cheat just to do slightly better for himself at the cost of others.
If you imagine that one of the Start->A->End travellers switches to Start->A->B->End, we now have 1749 cars travelling Start->A->End for 67.5 minutes, 501 cars travelling Start->A->B->End for 45.01 minutes and 1750 cars travelling Start->B->End for 67.51 minutes. The car that switched improved its own travel time from 67.5 minutes to 45.01 minutes, but the total time spent travelling increased to 258750.01 minutes (one driver saved themselves 22.49 minutes, but cost 2250 other drivers 0.01 minutes each).
So yes, if you found yourself in that second state, to improve the global optimum you would have to move to the first state by de-optimising the route of one of those 501 Start->A->B->End drivers.
I've tried to make the case that by closing "key" exits on the highway, we could reduce congestion. But who would be responsible for making that likely unpopular decision?
http://www.gkstill.com/CV/PhD/Chapter3.html
Scroll down to 3.5.3 Flow through a door.
I can't find the original article I read years ago but it showed a large round barrier to be the most effective, and more than one barrier for larger numbers of people
It seems crazy, but interconnecting more nodes to improve efficiency (as measured by travel time, costs, etc.) can paradoxically make the whole network less efficient!
Is there some sort of intuition here that would connect this paradox to the effectiveness of dropout in deep neural networks, or am I drawing connections where there aren't any?
The original dropout paper's handwavy justification for dropout is that it prevents co-adaptation. It prevents individual units (nodes/neurons) in the network from relying on specific units in the previous layer firing as well. This is a bad thing because it's fragile (if one unit is off). I say handwavy because this is just intuition; there is not really any proof that this is actually what is happening.
Another commonly cited motivation is that dropout is like learning an ensemble of multiple networks.
The only paper I've seen that theoretically analyzes dropout is: https://arxiv.org/pdf/1506.02142v6.pdf, which proves it's equivalent to approximating gaussian processes (this is beyond me).
Thank you :)
- Antoine de Saint-Exupery