Thursday, August 22, 2013

The Game of Life

The Game of Life

By Bobby Neal Winters
They do therefore not deny that every man may follow his own interest; but they endeavor to prove it is in the interest of every man to be be virtuous.
--Alexis de Toqueville, Democracy in America
Do you want to win?
You might think that’s a silly question.  Of course you want to win.  Winners are where its at.  Losers are, well, losers.
But even in sports there have been contests in which those involved glory in the level of play to the point of either forgetting who the final winner was or saying that it didn’t matter because the reward was being able to participate in something that was that good.
Sports provides a metaphor for American society.  There is achievement; there is teamwork; there is competition.  But, as Americans, we also believe we should vote on everything.  In addition, we have a self-image of valuing fairness, with “fairness” not necessarily being well-defined.
I would like to explore these notions using Arrow’s Theorem (a mathematical result in economics) and Sid Meier’s computer game Civilization.

Fair Elections

Suppose that you’ve formed a club of eleven people and are holding elections for president and vice president of that club.  If Andrew and Barbara are nominated to run, then the process is straightforward.  Ballots are distributed, each voter marks a preference, and the votes are tallied. The one who gets the most votes wins and the one who comes in second gets to be vice president. (I made the club have eleven people so as to avoid the question of ties which is not germane to my point.)  
Suppose, however, that Charlie (or Charline) enters the race.  Here the situation becomes more complicated.  There are many schemes that can be proposed regarding how to handle this.  I suspect each reader has a way and many of them are different.  The question that arises is: Is the scheme fair?  
One interpretation of fairness is that the voting scheme must have two properties:
(U)  The result of the election must respect the unanimous will of the electorate.  This is to say that if everyone prefers Andrew to Charlie/Charline, then Andrew must be preferred in the election.
(IIA) The relative preference of a third party to two alternatives should not affect how they are ordered with respect to each other in the final ordering.  This is to say whether Barbara beats Andrew should not be affected by how either of them compare in the ratings of the voters to Charlie/Charline.
It is here with introduce Arrow’s Theorem.  Arrow’s Theorem states that when these two conditions are in place in a system with N voters, there are exactly N votings schemes that work.  This sounds promising, but wait, there’s a problem.  In each of these schemes exactly one voter is getting his way in everything and no other vote matters.  While fairness might be slippery to define, it would seem safe to say having one arbitrary individual override the will of all others is not within its parameters.
This becomes somewhat more disturbing when one moves from choosing officers to run a club to the right ordering of principles to run a society.  How to the issues of education, the right to life, and the right to own a gun rate with respect to each other? I have an opinion and so do millions of other voters.  And forget about how complex it is to deal with even one of these.  Arrow’s Theorem gives us little hope of coming to a common consensus on which we should even talk about first.


I have whiled away many hours playing Sid Meier’s game Civilization. In the beginning of a game, various civilizations are seeded on an earthlike planet.  They then begin gathering knowledge, creating farms, making mines, putting  together military units, and trading with each other.  In playing the game, you the player assume the role of dictator in determining your civilization’s values. Those of the other civilizations are determined by other players or by the computer.
The game provides several venues to victory: domination, building a spaceship, culture, etc with the appropriate measures for each of these.  It is not simply a shoot-em-up video game, but while the game is not about war per se, war is certainly a part of it and cannot be ignored. A civilization that values culture, religion, and science will be a tempting target for a militaristic society if it makes no provision for its own protection. This comes at a cost and acts as a drag on other areas.
The game is structured quite nicely to illustrate the interplay of competition and cooperation.  This is done most visibly through the exchange of knowledge.  In the game, knowledge once obtained can be traded as a commodity.  It is an interesting commodity in that one can trade it, but still possess it afterwards. Once everyone has it, it is no longer tradable.
Each civilization has certain innate strengths which encourage developments in particular directions.  Each civilization can, within certain limits, choose to pursue knowledge of a particular type.  The greater variety of knowledge produced gives more opportunity for exchange.  More exchange creates a more robust environment for everyone and history progresses quickly. One can have the Apollo Program in the nineteenth century.
By way of contrast, when there is little cooperation in the game, history progresses much more slowly. One might arrive at the 20 century with a level of development more appropriate for the time of Caesar.
In looking at this, one is faced with the question of whether one would rather be ranked first or for the whole milieu to be farther advanced historically.  The answer may well be different depending upon whether you are simply playing a game or whether we are talking about real life.

The Game of Life

We want to win the game of course.  The game is a way to distract and entertain ourselves for a few hours at a time.  It gives us time to think.  There are times, in fact, when it is incredibly therapeutic to drive our electronic enemies into the dirt at the price of virtual apocalypse.
But that is all make-believe.
We would rather, in general, have our material needs taken care of and be living good and fruitful lives in last place in the game of life that living in poverty, death, and disease in first place.  
Consider the arts, for example. Lovers of the arts might initially insist giving arts a priority over all else.  They are an important part of human life.  However, even artists have to eat.  There must be farmers, processors of food, truck drivers to get it to market, etc.  Insisting that the arts take priority over everything else might create an economy in which very little art is produced.
In Paradise Lost, Lucifer famously says that it’s better to reign in Hell than to serve in Heaven.  We can’t agree with this.
The framework for Arrow’s Theorem is wrong-headed.  Being high-ranked does appeal to our very real ego-need for status, and filling ego-needs is very important, the fact is that by the very nature of the things very few can be ranked high enough to gain the ego-benefit of it.  The probability of a given individual being one of the high-ranking winners in the game of life is small.  I am better advised to cede a bit of my rank to raise the level of common good.

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