Dilemma 18: The Tragedy of the Commons

The Tragedy of the Commons

Dilemmas need not involve only two people; some dilemmas can involve an entire society at once. Unfortunately, mass dilemmas have a worse outlook than pairwise dilemmas. Garrett Hardin tells this tragic tale:

Once upon a time there was a village with a green commons. All the villagers grazed their cattle there; so long as everyone grazed only one cow there, then the common can support all. However, if enough villagers graze a second cow on the commons, then the commons will fail, and all will suffer.

The dilemma is: everyone is tempted to “free ride” by getting a second cow; after all, they reason, one single extra cow won’t ruin the commons. True enough; but enough second cows will. At first only a few free-rode; but as time went by, more and more did. Eventually the commons failed. That is the tragedy.

Alas, strategies like TFT no longer work for these many-player dilemmas; for it is often difficult to identify whom to retaliate against. Group truces are in general far more vulnerable than individual truces; the more players, the easier it is to “free-ride” with relative impunity, until all are punished. Experiment shows that people allowed to communicate in experimental group dilemmas show more fear and greed statements than they do in individual dilemma encounters.

Even if we were to institute a social sanction method to punish free-riders, still that very mechanism is vulnerable to free-riding; and corruption from the top can go very far. (The mayor of the above-mentioned village can have as many cows as he wants!)

This dilemma of social cooperation (also known as the “Volunteer’s Paradox”) is a political problem, with at least three political semi-resolutions:

Privatization.

This is a Market-based solution. Here, the community decentralizes and localizes social dilemmas, preferably down to the level of personal Parley exchanges. The Silver rule (mixed with a little bit of Gold) corresponds to reciprocity, the “natural” justice of  the marketplace. This method’s flaws include: externalities; when one player can make every other player pay his real costs: coordination of masses of agents to work in synch: and monopolization of key elements of the economy by the power-seeking few.

Sanctions.

This is a State-based solution. Here, the community empowers a “legal system”; i.e. institutions designed to dispense artificial justice. The local powers dispense rewards and punishments according to agreed-on rules. This method’s flaws include: corruption; when the influence of money undermines the legitimacy of the law: tyranny; when the power of the State is used by the few to rob and oppress the many: and bureaucracy; when competing political interests promote inefficiency, waste and gridlock in public service.

Memetics.

This is a Church-based solution. Here, the community seeks consensus; its citizens try to set a “good example” for others, and invite others to do as they do. This method’s flaws include: vulnerability to challenge by marginal elements: false consensus arising from social error: and hypocrisy arising from the subversion of principle by privilege.

Theory and experiment confirm what history demonstrates; that the human is a semi-social animal. We are social as individuals, yet anti-social as groups! This is the paradox of social perversity; most individuals have higher social ethics than most societies. Anarchism is not a naive prescription of what should be; if only it were! In fact, anarchism is a cynical description of what is, like it or not.

The human species is only locally socialized. We’re just civilized enough to be aware of our collective barbarism. The problem is not “man’s inhumanity to man”; if only it were that simple! The problem is men’s inhumanity to men.

We, in our collective folly, have given ourselves the name “Homo Sapiens”: Wise Man. When we are inspected individually, such a name might perhaps be justified; but when we are inspected collectively, the misnomer is obvious. Mankind’s social state resembles the fluid state of matter; locally ordered, globally formless. This compares to the gaseous social state of solitary species, and the solid social state of the social insects. (Yet even the social insects limit their loyalties to the nest; beyond the nest, it is nest versus nest.)

Individual dilemmas prosper; thus societies rise. Collective dilemmas deteriorate; thus societies fall. Social dilemmas create freedom within chaos; the Middle Way.

So accept people one by one, but not all in all.

Trust each I; suspect each We.

Little Brother and the Boston Video Militia

Once again I interrupt my blogging of "Dilemma Games" to report on the Boston bombing.


**************

Little Brother and the Boston Video Militia

         My daughter Hannah and I have a nickname for the camera-phone: ‘Little Brother’. The portable camera-phone implies mass ‘sousveillance’; surveillance from beneath. We have seen, in Egypt and with Occupy, that Little Brother can be Big Brother’s revolutionary foe.

         But Little Brother is not all rebel; in fact Little Brother can be a patriot, helping the authorities defend the nation. We have seen this in Boston, in the crowd-sourced identification of the Tsarnaev brothers. For details, see:

         http://www.wired.com/dangerroom/2013/04/boston-data-manhunt/

         Tamerlan the would-be conquerer, and Dzhokhar the joker, thought themselves invisible in that crowd, but Little Brother was there, and Little Brother is the Eyes of the Web, which never forgets. The Tsarnaev naifs thought their target was unarmed; but they were fatally wrong; for the crowd had hundreds of camera-phones, each one a weapon against their cowardice. 

         The camera-phone is a kind of weapon; and those hundreds of videographers were a kind of militia. With the Boston Video Militia’s help, the cops got their men before the week was done. Justice is best when swift and sure.

 

Dilemma 17: Milo’s Trick

Milo’s Trick

... “With your permission,” said Tock, changing the subject, “we’d like to rescue Rhyme and Reason.”

“Has Azaz agreed to it?” the Mathemagician inquired.

“Yes, sir,” the dog assured him.

“THEN I DON’T,” he thundered again, “for since they’ve been banished, we’ve never agreed on anything - and we never will.”

He emphasized his last remark with a dark and ominous look.

“Never?” asked Milo, with the slighest touch of disbelief in his voice.

“NEVER!” he repeated. “And if you can prove otherwise, then you have my permission to go.”

“Well,” said Milo, who had thought about this problem very carefully ever since leaving Dictionopolis. “Then with whatever Azaz agrees, you disagree.”

“Correct,” said the Mathemagician with a tolerant smile.

“And with whatever Azaz disagrees, you agree.”

“Also correct,” yawned the Mathemagician, nonchalantly cleaning his fingernail with the point of his staff.

“Then each of you agrees that he will disagree with whatever each of you agrees with,” said Milo triumphantly; “and if you both disagree with the same thing, then aren’t you really in agreement?”

“I’VE BEEN TRICKED!” cried the Mathemagician helplessly, for no matter how he figured, it still came out just that way ...

- from The Phantom Tollbooth, by Norton Juster

I have long admired the reasoning of this passage, and have sought ways to turn it into mathematics. One way is by dilemma game theory.

Let A and M argue as before; only this time we let them place values upon the outcome of the argument. This Quarrel game is scored thus:

Win   =  I’m right, and you’re wrong.

Truce =  We’re both right.

Draw  =  We’re both wrong.

Lose  =  I’m wrong, and you’re right.

where Lose < Draw < Truce < Win. In this Opinion parley, truce and win are the “upper” outcomes, or “prosperity”; draw and lose are the “lower” outcomes, or “poverty”. Each brother prospers if and only if he is right; and he always gains if the other brother is wrong. One day Milo asked the brothers if they agree. Each brother can say yes or no; so there are four outcomes:

A   =   “A=M”   =   true

M   =   “A=M”   =   true

A   =   “A not= M”   =   true

M   =   “A=M”   =   false

A   =   “A=M”   =   false

M   =   “A not= M”   =   true

A   =   “A not= M”   =   false

M   =   “A not=M”   =   false

Inspection of the table shows that each brother controls the other brother’s prosperity. This yields a dilemma game:

                                            M

            (A,M) outcome                  

                               says A=M     |    says Anot=M

            ______________|________________|_______________|

                          |                 |                |

            says A=M      |      Truce      |   Lose, Win   |

    A       ______________|________________|_______________|

                          |                 |                |

            says Anot=M   |    Win, Lose    |     Draw      |

            ______________|________________|_______________|

Here, saying A=M is the “nice” move, and saying A not= M is the “mean” move. The players both prosper only if they agree to agree; but this truce is vulnerable to exploitation.

One-time play favors draw (“agreeing to disagree”); but in a long tournament, truce can be attained if the players use this strategy:

Do Unto Others As They Have Done Unto You.

That is the “Silver Rule” of reciprocity. Milo’s Trick guides the brothers to social harmony, in the long run.

Dilemma 16: The Shadow Of The Future

The Shadow Of The Future

I have above described many dilemma strategies; AD (Iron rule), AC (Gold rule), TFT (Silver rule), R, RTFT, and Pavlov.

R is an attempt to combine AC with AD; however, it shares an important characteristic with them; it is “unresponsive” (i.e. it does not reward the other’s nice behavior with nice behavior of its own) and it is “unirritable” (i.e. it does not punish the other’s mean behavior with mean behavior of its own).

Responsiveness and irritability are part of the definition of life; thus AD, AC, and R are all “dead” strategies, unlike TFT, which is “live”. There is no point in being nice to a dead strategy; you cannot reform it if it is bad, or anger it if it is good. Conversely there is no point in being mean to a live strategy, for your misbehavior will only backfire on you. Therefore: be nice to the living and mean to the dead!

TFT is a live strategy (i.e. irritable and responsive), a nice strategy (i.e. it never defects first), and a simple strategy (thus easily identified as such by other strategies); these qualities combine to give TFT unique advantages in dilemma play. Robert Axelrod, in his book The Evolution Of Cooperation, reports that in two open-invitation computer tournaments, TFT came out ahead twice.

In Appendix B of that book, Axelrod was able to prove that TFT is a dominant stable strategy, if the “shadow of the future” is large enough. This is the “Axelrod equilibrium”; reciprocity can and does keep the peace, in the long run, provided that the long run is long enough.

The shadow of the future looms large over everyone’s calculations. Tit-for-tat (which mandates cooperation on the first move and reciprocation thereafter) is optimal if w exceeds both  (W-T)/(W-D) and  (W-T)/(T-L). Above the transition probability, the shadow of the future exceeds both (W-D)/(T-D) and (T-L)/(T-D).

It is probably most interesting to run a tournament at the transition probability; for there the Iron Rule meets the Silver Rule head on. Here are some tables of various dilemma scoring systems, and their correspond transition probabilities, times, and recommended randomizing devices:

   L  D  T  W  t. prob.         t. time          randomizer     

“Army”:  0  1  2  3     1/2            2 rounds                    coin

“Navy”: -3 -1  1  3    1/2            2 rounds                    coin

   0  1  3  4     1/3            3/2 rounds        roll < 2

  -2 -1  1  2   1/3            3/2 rounds        roll < 2

Below the ‘transition probability’, Iron rules; above the transition probability, reason favors Silver sweetened by a bit of Gold. After the ‘transition time’, mutual exploitation gives way to a kinder and gentler society.

A shadow is haunting Earth; the shadow of the future. Will we be or will we not be? That is the question; for justice will prevail, but only in the long run. You should live so long!