Zero-Sum vs. Non-Zero-Sum

I love the concepts of zero-sum and non-zero sum.  These ideas come from an extension of game theory (another fun topic) and social philosophy, and they can be applied to pretty much all areas of life and theory that deal with multiple participants.

Zero-Sum:
A strictly competitive arrangement where if you add up the gains and losses of all participants, you arrive at a zero-sum.

1) Adam has 1 apple.
2) Bobby steals 1 apple from Adam.
3) Adam loses 1 apple while Bobby gains 1 apple.
4) [Adam + Bobby] = (-)Apple + (+)Apple = 0

This type of relationship can be applied to an infinite configuration of people and fruits, but this illustrates a closed environment where ultimately nothing is added or taken away from a closed environment.

Non-Zero-Sum:
A cooperative arrangement where if you add up the gains and losses of all participants, you arrive at a sum more or less than zero.

Game of Chicken:
Two cars drive towards each other, and whoever swerves out of the way first is chicken and loses.

So let’s assign points to this game::

Crashing your car: -10 points
Swerving out of the way: -3 points
Other player swerves: +5

Using the loose point assignments for the game of chicken, we can then work out all of the possible outcomes of this game:::

Both players crash: -10 + (-)10 = -20 points
One player is chicken: -3 + (+)5 = +2 points
Both players swerve: -3 + (-)3 = -6 points

So in all possible outcomes we get a zero sum from the aggregate of all participants involved.

So, what’s the point?:

• Zero-sum relationships are simple and make sense.
  
  One person gains, another person loses (where the gains are directly inversely proportional to the loss). It’s always 1:1.
  
  
• Zero-sum relationships are also intuitive.
  
  i.e. Cake Cutting - Two siblings are assigned the task of cutting a cake and dividing the parts amongst themselves.  One is assigned to cut the cake in any way he chooses, while the other sibling is tasked with choosing which piece(s) to distribute.  Self-interest would state that the “cutting sibling” will divide the cake evenly (compensating not just for size, but for desirability) and that the “choosing sibling” will have a fairly even choice to make.
  
• However, only the simplest relationships can be strictly confined to zero-sum relationships. (Even when simple relationships are concerned, they must often be simple relationships with idealized conditions and stipulations.)
  
  In the apple example, we only concern ourselves with the apples as the sole, measurable utility.  We forgo originating property, social function, the “cost” of theft to person and society, etc.
  
  Even in the cake example, we assume that both siblings desire various components of the cake in similar amounts. If one sibling detested frosting while the other sibling strongly desired it, a non-zero-sum relationship would occur from each brother’s negative and positive desires.
  
  
• My conclusion being that: zero-sum relationships are simplistic models for utility and function, and can significantly limit growth and decay (expected or otherwise) of all relationships to merely a 1:1 ratio. If we think outside of the short-sighted boundaries of a 1:1 zero-sum relationship, then we can measure and predict models that multiply outcome of every input.

Zero-sum relationships are just too simple for the real-world.  Not to imply that drag-racing and chicken are to become the yardstick by which we measure the complexity of a societal system; what I am trying to illustrate is that most (if not all) societal relationships are complex enough to remove themselves from sheer zero-sum relationships into non-zero sum relationships.

So, really…what’s the point?

I’ve been wanting to write about zero-sum and non-zero-sum relationships, because I see zero-sum mentality being used in situations that impede the maximization of potential if a non-zero-sum mentality were used.  I know that’s extremely wordy, but simply: People have to stop thinking in  1:1 relationships, and start considering the bigger picture of 1:X relationships.

• In politics: Government money is going to that other group/person, so that means it’s being taken away from me.
• In society: I make someone feel bad about themselves, and this should somehow make me feel good about myself.
• In business: The only way that I can gain is to eliminate the chance of gain from my competitors.

The examples given above show zero-sum mentality, and we can see that this line of reasoning will set up systems of direct competition, with limited supply, and limited possible outcome.  This type of reasoning is akin to Thomas Hobbes’ idealization of man in his natural state, where direct competition of each individual in a societal group will lead to that group becoming like an unruly leviathan.  In The Leviathan, Thomas Hobbes states that the original state of man is the war of all against all (bellum omnium contra omnes), and this original state of man is where we find zero-sum mentality.  Illustrated further in The Leviathan, this original state has no civil order and the outcome of “the life of man [is], solitary, poor, nasty, brutish, and short.” Though Hobbes’ conclusion doesn’t stem directly from the idea of a zero-sum relationship, he does align the conclusion of The Leviathan from the impact of self-interest when applied to society at large, and I think there is a lot give and take between the self-interest which Hobbes outlines, and the self-interest behind mentalities which yield zero-sum relationships.

Franklin Roosevelt and Bill Clinton:

One of the most successful applications of non-zero-sum policy was the Franklin Roosevelt’s New Deal of the 1930s.  Though the New Deal did not solve the problems brought about by the Great Depression, it was a success for creating jobs, improving the infrastructure of the United States, and multiplying its utility per unit of input.  By creating networks and avenues for currency to be exchanged, we can trace that there was not a linear relationship between one benefactor and one recipient, but we see that through the avenues of transaction, we see the creation of economy in a similar relationship to the economic principle of “gains from trade”.

Though NAFTA (North American Free Trade Agreement) was largely considered a failure, President Clinton’s intentions are defensible.  In 2000, he wrote:

“The more complex societies get and the more complex the networks of interdependence within and beyond community and national borders get, the more people are forced in their own interests to find non-zero-sum solutions. That is, win–win solutions instead of win–lose solutions…. Because we find as our interdependence increases that, on the whole, we do better when other people do better as well — so we have to find ways that we can all win, we have to accommodate each other…

Simply put: It’s not always win-loss, let’s look for the win-win.

Pareto Efficiency/Pareto Optimality:

I’ve put forth a reasoned mentality, and I’ll now attempt to put forth a balanced methodology: Applying Pareto principles to a non-zero-sum mentality should yield the maximum possible benefit.

Pareto Efficiency: Re-arranging the allocation of goods by which at least one person benefits without making any other person worse off.

Pareto Efficiency (which will be noted as PE from now on) can be considered as either weak or strong by how much benefit can be made per arrangement.  The larger the benefit past 1:1, the stronger the PE of that arrangement becomes.

Pareto Optimality: An arrangement of the allocation of goods by which no more people can benefit without making any other person worse off.

An arrangement with the strongest PE; achieving maximum efficiency.

From the discussion of the New Deal above, we see that the actual manifestation of the New Deal was done through a bottom-up approach, where often the most impoverished were included in the New Deal, and the strategy of targeting the worse off are often more effective than targeting the best off and allowing a trickle-down effect to occur.  The stated intention of both approaches are to improve the economy-at-large, but the application and reasoning behind the trickle-down theory is questionable at best.  Economist John Kenneth Galbraith described trickle-down economics as akin to a horse-and-sparrow relationship: “If you feed the horse enough oats, some will pass through to the road for the sparrows.” There are many reasons to analyze this train of reasoning, but by providing aid to the upper tiers of the economy, there is no guarantee or timeframe of economic effect due to the fact that for the upper tiers of an economy, there is no “immediate need” (stressed loosely) for aid, and would eliminate the automatic use of aid.  If one targets aid to those most in need, the aid would be used immediately and all direct and indirect participants can benefit from the “gains from trade” as illustrated above.

A combination of non-zero-sum mentality balanced with attention to pareto efficiency are needed to maximize effect.  This idea can be further illustrated in the Maximin and Minimax principles, but to simply summarize: We live in a non-zero-sum world, and applying zero-sum mentalities are definitely limiting and potentially harmful.  By making decisions based on short-sighted, non-constructive thinking rather than a unified, long-term, constructive mentality, we create a situation where the losses are numerous and the gains are hard-fought.  We must actively find ways to reach win-win relationships, and this is often accomplished by reaching pareto optimality or at least attention to pareto efficiency.

Croissant: an Analysis

I was eating a croissant with grape jelly and a small coffee when it dawned on me.  A croissant, composed of the same ingredients as many other simple dough, is possibly the highest form of bread.  A croissant is flour, butter, milk, and yeast amalgamated to its maximum potential.

Oh, woe to all other lowly breads.
Oh, woe to such lost potential.

The labour and toils all dough must go through.
Heavy are the strains of pressure, heat, and time.
Woe to those doughs who endure, yet do not become.
Nay, cannot become.

How ethereal, how divine.
Long live the croissant.

Riverside

I was in Riverside twice in the last week.  Picked up a diploma, ate some food, got nostalgic.  As much as I miss it, I can’t go back.  Guess I gotta move forward.