
The Price of Anarchy - beefman
https://en.wikipedia.org/wiki/Price_of_anarchy
======
bo1024
I just want to mention that many commenters here are reading much more into
the name politically than do the game theorists/computer scientists who
actually do research on it. The research is focused on the game theory and not
meant to make any sort of political points or value judgement. The main
question asked is how to design systems so that even in a game-theoretic
equilibrium, the total "welfare" is close to the best possible.

~~~
sebastos
Ding ding ding. The Price of Anarchy originally described the surprising
result that internet routing seems to work despite the lack of a central
planner. [1] The "central planner" is a theoretical maximum for the routing
problem - it represents an oracle that automatically knows and applies an
optimal routing solution. It's not some kind of government.

It's kind of hilarious seeing all of these people commenting about how this is
"utopian" thinking, ancap-blah-blah, and "who says the central planner would
be just?" People read what they want to read, I suppose.

If you do want to read something interesting about the price of anarchy, check
out this other paper [2], written by one of the original authors, which shows
that the PoA = 1 (that is, there is no cost) when there are private "owners"
of the edges in a routing network who are allowed to charge a "toll" for
traversing that edge. Makes you wonder if a globally-standard-but-locally-
owned electronic tolling system could replace gas taxes to fund our roads in a
fairer way. This could remove the undue toll burden shouldered by certain
unlucky people who have to commute across a heavily tolled bridge. (Seattlites
should know what I'm talking about).

[1]
[http://www.cs.yale.edu/homes/jf/poa.pdf](http://www.cs.yale.edu/homes/jf/poa.pdf)
[2]
[https://people.eecs.berkeley.edu/~christos/papers/selfishrou...](https://people.eecs.berkeley.edu/~christos/papers/selfishrouters.pdf)
[3]
[http://theory.stanford.edu/~tim/papers/routing.pdf](http://theory.stanford.edu/~tim/papers/routing.pdf)

~~~
throwaway729
_> It's kind of hilarious seeing all of these people commenting about how this
is "utopian" thinking..._

I suppose you're referring to me, since I'm the only one who has used that
word.

To clarify, I was _replying to a comment_ , not making any comment directly
relevant to the paper or PoA.

That said, if someone applied this paper's results directly to a defense of
anarchy, I would call that application Utopian because I don't think game
theory provides a particularly compelling model for all of society. FWIW such
an application certainly wasn't the author's intent, and also is not what was
going on in that thread.

 _> Makes you wonder if a globally-standard-but-locally-owned electronic
tolling system could replace gas taxes to fund our roads in a fairer way. This
could remove the undue toll burden shouldered by certain unlucky people who
have to commute across a heavily tolled bridge. (Seattlites should know what
I'm talking about)._

This is an interesting idea (which I think is the role that mathematical
models applied to social systems _should_ play -- as a stimulant for
interesting ideas and possibly a way of bounding the possible. A basis from
which you rapidly diverge, which is OK. TBF I think this is what is also going
on in the other thread...)

By "standard", do you mean "every mile is taxed equally"? Or "according to
construction/upkeep cost"?

The latter seems hard to calculate and easy to fabricate. I think in a
realistic system you'd just always end up with really high bridge tolls. In
that sense, I think this application of this paper is Utopian in the sense
that, when applied to the toll problem, it makes unwarranted assumptions about
accurate pricing.

If by standard you just mean "equal", why not just use gas taxes and set them
so that tolls aren't necessary? They approximate distance traveled pretty
well, so should be pretty identical to tolling each mile equally. With the
added benefit of also indirectly taxing pollution.

~~~
sebastos
Nothing personal about your comment particularly - I agree with how you're
characterizing it. I was reacting to the instant jump to political thought
people were making when the PoA has plenty of interesting implications in the
merely technological realm :)

> By "standard", do you mean "every mile is taxed equally"? Or "according to
> construction/upkeep cost"?

Perhaps confusing wording on my part - by standard I meant that the system
that actually detects the car and charges the dollars and cents is
standardized. In other words, a frictionless lingua franca for tolling that
exerted negligible inconvenience on the driver as they were driving. Think
"everybody has a Visa", not "every item costs $1".

The tolls themselves would be priced neither uniformly nor "at cost" to offset
construction expenses. Rather, they would simply be set to maximize profit for
the local municipality that owned the tolling machines. Pricing the edges to
maximize profit minimizes congestion, and theoretically does exactly as well
as a super-deity oracle with perfect information that could plan everybody's
route from start to finish. (This perhaps counterintuitive result is described
in ref 2 from the grandparent). Whatever money is made in aggregate is used
for all repairs and maintenance, so the idea is that small back roads would
help to subsidize the cost of bridges, which are disproportionately expensive
to repair compared to their importance in the road network. More importantly,
the price to drive on any road is directly reflective of the externality you
impose while driving on it. Right now, the expense and complication of
exacting the toll is high enough that we only extract tolls at critical points
like bridges, which means we only use tolls to discourage congestion in these
few places. We set the tolls too high there to offset the fact that there
should be tolls on feeder streets and other areas that are getting backed up
and contributing to the overall gridlock.

In practice, you'd have to get around some issues surrounding the
advertisement of road prices to the driver. The system would have to strike a
balance between being fair and fatiguing drivers with too much shopping
choice. In this respect, perhaps you could be right that there is some
idealized thinking going on. But it is just an idea, after all.

~~~
Jarwain
This reminds me of the sunpass/turnpike system in South Florida. A toll is
charged to your account by driving through toll booths located at entrance and
exit ramps (done through an RFID chip or something similar appended to the
windshield). The tolls generated are used towards maintaining that highway. It
tends to be much less congested with more considerate drivers, compared to 95.

------
CaptainSwing
I think that this is a really interesting concept, but dislike the name. All
social anarchists (anarchist-communists, anarchist-syndicalists, even
mutualists etc) would see anarchy as a social process rather than a purely
individualised "every man for himself" system. It disregards the possibility
for non-coercive collective forms of decision making.

but, saying this, a concept that discovers the loss in a system where each
actor is purely self-interested is useful and interesting.

~~~
ue_
I talk with a lot of anarchists and perhaps the only ones of them who are
truly in the spirit of "every man for himself" are an-caps and Stirnerists.

~~~
dunslandsboo
Most anarcho-capitalists that I know and from who I learn are absolutely not
about "every man for himself" at all. Charity and voluntary cooperation are
major parts of the society as they would like it to become. See
[https://wiki.mises.org/wiki/Friendly_society](https://wiki.mises.org/wiki/Friendly_society)
and
[https://en.wikipedia.org/wiki/Dispute_resolution_organizatio...](https://en.wikipedia.org/wiki/Dispute_resolution_organization)

~~~
throwaway729
_> ...as they would like it to become... Friendly society... DRO..._

I think this has always been my primary gripe with ancap -- it's Utopian. And
all Utopian thinking has the same problem -- it's either irrational, or very
rational but starting from very strong axioms. Ancap writers, to their credit,
tend to care a lot about crafting strong, rational arguments.

When I think about ancap (or any political theory that sets off my Utopia
alarms), I reason through the entirety of society. I raise a lot of objections
to myself, and make a note each time I come to the conclusion that I need some
assumption about how people will behave.

Then I take those assumptions, and apply them to various state-based systems.
Usually I end up with an equally Utopian world, or only require a small delta
in the axioms to end up at a Utopian world. To me, that suggests that it's the
axioms that are doing all the heavy lifting. If you can make enough
assumptions, the state is much more than unnecessary -- it's also
_irrelevant_! You get a Utopia either way! The enemy isn't the state, it's
human behavior.

FWIW the same exercise can be used to derive ancap out of a thorough analysis
of communist literature. And it also applies to more centrist policy proposals
that posit Utopian-level returns.

At least, that's my experience with struggling through ancap literature. YMMV.

~~~
nickik
I don't think its all that Utopian. An-Caps take a lot of care to make there
institution prove against human weakness. There is also a lot of study into
historical examples that explain part of how a An-Cap society would work.

I don't one can expect more from any group. An-Capism is as un-utipian as you
can get while still having some vauge definition of an ideal system.

Most AnCaps happily admit that the assumed society would not be near perfect.
In fact, I would actually say that it would probably not be that much better
then what we have now.

I don't think the axioms are that special, its basic rational choice political
science/economics that is applied in most AnCap arguments.

~~~
throwaway729
_> An-Capism is as un-utipian as you can get while still having some vauge
definition of an ideal system... Most AnCaps happily admit that the assumed
society would not be near perfect._

Perhaps. That doesn't make it any less Utopian in my book.

 _> I don't think the axioms are that special, its basic rational choice
political science/economics that is applied in most AnCap arguments._

Depends on the writer. There certainly are writers for whom this is true. IMO
it's _not_ true of Molyneux, to name one.

Of course, rational choice is not special, but it is an enormous assumption
that we're pretty sure is not a realistic description of how people actually
behave...

~~~
nickik
Then I don't understand your definition of Utopian or how it is useful.

Molyneux is no longer an AnCap, he has gone of and is basically something on
its own now.

There are actual economics/poetical science PhD working on this stuff, see for
example Peter Leeson, Bryan Caplan.

> Of course, rational choice is not special, but it is an enormous assumption
> that we're pretty sure is not a realistic description of how people actually
> behave...

Rational choice in this context means not Homo Economicus (as in mathematical
maximisation of expected outcome) but rather rational choice limited by
information and so on. This assumtion is much weaker and applies to enough
people as to make it useful.

Its basically what much micro economics and political science already does. I
don't know what better scientific disciplines we have to make better
evaluation of theoretical system of humans.

------
wyager
Wow, people are really running away with the political analogy used here.

Calm down folks, they're not ragging on decentralized systems. If you read and
comprehend the definitions in the article, you'll see that it's a fully
general solution that allows for emergent organization through market systems
or cooperation. You can bake those things into the strategies and utility
functions of the actors.

It's just a fun and descriptive name for the difference between an idealized
central controller (which can force everyone into a configuration that
maximizes an arbitrary global utility function) and the lack of such a
controller. The outcomes could be the same, they could be different. If you
factor in the negative utility of having the central authority in the first
place, you can game-theoretically justify your particular favored level of
anti-authoritarianism.

------
clydethefrog
Already in the first line it claims that anarchy is a system wherein

>a system degrades due to selfish behavior of its agents

To my point of view, most game theory is just capitalistic ideology disguised
in mathematical models.

~~~
TeMPOraL
If anything, this sounds anti-capitalistic - capitalism is based on an
assumption that selfish behaviour of individuals produces greater good for the
society.

~~~
automatwon
"It is not from the benevolence of the butcher, the brewer, or the baker that
we expect our dinner, but from their regard to their own interest" \- Wealth
of Nations, Adam Smith

I tend to think of self-interest being equivalent to selfishness. Your point
makes me wonder if self-interest is not equivalent to selfishness, at least to
Economists.

~~~
TeMPOraL
Well, what you quote is true, but I think a lot of discussion stems from
focusing on the wrong question, namely "does selfishness lead to better
outcomes" as opposed to _when_ it does, and when it does not.

Too many people seem to approach economy as an ideology rather than a complex
system in which a given approach produces good results here and bad results
there, and everything should be subject to optimization and careful design.

~~~
JumpCrisscross
> _Too many people seem to approach economy as an ideology rather than a
> complex system_

Few of these people have any decision-making authority. This mass ignorance of
economics _does_ occasionally bubble up on the policy side. But it is
generally, at least in the United States, contained by more knowledgeable (and
influential) parties.

~~~
mcguire
...like Alan Greenspan?

------
schoen
That has the most math notation of anything I've seen written about anarchy in
some time!

~~~
quotemstr
Math is important. It tells us the shape of the possible. Game theory tells us
when we're creating an unstable set of incentives. Our intuition for fairness
is only a crude approximation of game theory.

Societies and their moral systems (there's little difference) don't come out
of nowhere.

Sentiments like "game theory is just capitalistic ideology" make me sad. Math,
like all sciences, is true whether you accept it or not.

~~~
CaptainSwing
it may be 'true' within the set of axioms on which it rests, but 'wrong' in
that those axioms (rational self-seeking behaviour, etc) don't hold in
reality. More, those axioms themselves could be reflections of capitalist
ideology.

------
johngalt
Think of it as structured vs unstructured if you can't avoid gettng hung up on
the name.

Basically this is talking about the net difference between what is locally
optimal and globally optimal in a multi agent system.

~~~
hyperbovine
an ("without") + arkhos ("ruler"). Seems like a fine name to me.

------
wodenokoto
Isn't libertarian thinking (put very heavily on the edge) the exact opposite?

That a system will become more efficient if actors are let to do things for
their own sake, and that actors are smart enough to calculate the negative
impact of short term selfish action (that is, actors can help out now, with an
exception of a positive roi)

~~~
SonOfLilit
This assumes a theoretical optimal central planner, a superintelligent BDFL of
sorts.

Libertarian thinking is that in practice humans are so bad at management that
every time we tried central planning it came up even worse than non-optimal
Nash Equilibria (which are the failure mode of non-centrally-managed agent
systems.) Libertarians would say that no dictator or government in history
turned out to know better than The Market. That The Cost of Regulation is
higher than The Cost of Anarchy.

Of course, both costs are high for some problems and low for others, and the
solution to practical problems usually lies at neither this extreme nor that
one.

------
inlineint
This submission seems to be a kind of follow-up to the one about Braess's
paradox
([https://news.ycombinator.com/item?id=13352513](https://news.ycombinator.com/item?id=13352513)).

~~~
cardiffspaceman
I have seen clusters of posts and have not had the time to study: Are they a
dialog between unrelated people who share an interest in a topic, or is one
person pursuing a theme?

------
tehabe
Incomplete models are incomplete. It completely ignores the ways on which the
mentioned transport should take place. It ignores that you usually don't have
one place from which everybody starts but multiple places to other multiple
places.

And if you think about it, individual car mobility is this in practice. The
ways are build by someone else but you can decide how and where to drive. And
it kinda failed in many areas.

~~~
alimw
It's not clear what you are referring to. The section on Selfish Routing
begins with Braess's Paradox but swiftly moves on to a Generalized Routing
Problem which appears to address your concerns.

------
madmaniak
"In the 'centralized' solution, a central authority can tell each agent which
path to take in order to minimize the average travel time"

That's a wishful thinking. Central authority can and usually is selfish and
corrupted but the impact of it is much bigger.

So we can call this piece of math a science but voting for centralized systems
based on that is super naive.

~~~
madmaniak
I see my comment is not well received.

Who will explain me why we assume that a single unit is selfish, but a big one
contained of many selfish units is altruistic?

~~~
grive
You assume the central planner to be the same as a single unit (as in, of the
same kind, the same species).

Who is to say that the central planner must be the ontological equal of a
single unit? Why not a more complex system?

You could have for example a quorum of single-unit who will need to reach a
consensus concerning their diverging self-beneficial impetus. You can also
imagine, if you represent the interest of each single unit as a vector in some
kind of space, that the quorum must navigate a product of those vectors.

You can imagine an AI then, a machine exploring that vector space that could
learn to balance the wants and needs of its single units.

Et cætera. I don't know exactly why you comment was not well received, I am
not able myself to downvote comments here and I did not do that, but my own
opinion about yours was that it was basing itself on some assumptions that
were biased by some real-world considerations that were irrelevant for the
concept presented.

~~~
madmaniak
Thank you for your reply.

"Who is to say that the central planner must be the ontological equal of a
single unit"

My impression is that's what most people here are discussing.

I can see a definition of an anarchy in your quorum example, can't you? But
you say we could have AI which will find a balance. Interesting concept. Does
it imply obeying AI <=> obeying the law?

~~~
grive
Well, the quorum could be organized in any matter of way. Expected a consensus
for a decision would be akin to anarchy indeed, however there could always be
some kind of recursive hierarchy, with another sub-committee of higher
authority that would make other units diverge. (Parties within an assembly,
with deputies having to follow their party lines). This quorum could also be
tied to following the interest of the masses outside or lose substantial
advantages, thus tying their own selfishness to the common good.

It could be anarchy. It could be anything else.

The AI could simply do whatever its specialization is. It could be trying to
direct the single-units or to disorganize them and try to keep some level of
entropy. Maybe its own benefit would be a generalized state of chaos.
Whatever.

The system itself could be considered the legal framework. The relationship
between any supervisor and its units could be the metaphor for any subservient
relationship in the real world, going from managed teams to parenting to
politics to social dynamics between friends. It does not mean anything as long
as the specifics of the system itself are not defined to permit the dynamics
to be correctly mapped on some real-world dynamics.

Obeying the law? Are you obeying the law of gravity? Is it from your own will
that you agree to stay on the ground?

~~~
madmaniak
Well yes, I am obeying the law of gravity :D Is your point, that AI could
replace human will?

~~~
grive
No, sorry it was somewhat tongue in cheek. It's just that within the
simulation, the way a single unit obeys a central planner (not at all,
partially, entirely) is defined by the rules of the simulation, so the rules
of the world.

So asking if that rule, that authority of the AI over the units is similar to
human law, is I think a bit beside the point. It's more akin to the law of
physics. It's simply the fabric of that reality.

Of course, you could then create a simulation that would try to recreate the
same kind of domination as within a human society, but that would be only one
kind of simulation, one kind of system, with specific parameters. It would not
give much about the very essence of the system itself, only of it within
constraints.

