Strategic preferences

At the heart of the discussion of strategic decision-making is how to value each agent’s strategic position. In the theory of games, this is based on the notion of utility; the assumption is that each agent values the outcome of the decision independently. I carry over that notion of valuation into decision process theory. I assume that each agent or player can measure the utility of any given strategy by assigning a numerical preference. As in game theory, the player can also measure the utility of a mixture of utilities by thinking of the choice as assigning sequence of frequencies to each pure possibility and making choices with those frequencies over a sequence of plays. In either case the preferences are idiosyncratic: they go with the player who owns those choices.

It is clear that preferences defined in this way provide a numerical position that is more than just a number for each strategy, it represents a physical attribute of the decision-making process. It is very much like a global positioning system for keeping track of positions on the earth; a fair amount of coordination is involved to relate one position to another. We get by with our GPS systems because this complexity is hidden inside our devices. Such a global positioning system is also used in theories of which decision process theory is a special case. My initial approach was to adopt the same strategy as used in such theories to define a positioning system. I have adopted what is called in the literature, harmonic coordinates to define the positions. It requires the definition of a scalar field for each strategic direction. This scalar field captures the physical characteristics of preferences associated with that direction. There are constraints on the behaviors of these scalar fields that arise from the theory that can be verified by detailed analysis of real world behaviors. The theory addresses the detailed coordination alluded to above.

Since many detailed examples are given in the white papers on this site, it may be helpful to put those numerical examples into a more general context. I suggested that a very large class of models, called stationary models in the literature of general relativity, is a useful class of models to study for decision-making. In these models, there is always a frame of reference in which the decision flows are stationary and the distance metric is independent of time. In the formal language of differential geometry, time is an isometry. I specialized to the case in which the flows are not only stationary but zero in this special frame, which I called the central co-moving frame. The detailed coordination described above however is absent in this frame.

To get an idea of why, consider an analog of a wave traveling in water. The coordination of interest is the behavior of the wave. In particular, if one generates a wave at a source, we want to know the behavior of all the subsequent ripples. There is nothing however that prevents us from viewing the wave from the perspective of an army of corks uniformly distributed and riding on the surface of the water. Each cork, from his point of view, is at rest (co-moving). The model assumption is that over time, the attributes of the water are constant for each cork (though in principle different for different corks). The cork doesn’t see anything of direct interest to us. Nevertheless, from the behavior of each cork, we gain spatial knowledge about the water. That knowledge can be used to reconstruct the ripple behavior if we add additional equations. The harmonic equations from differential geometry are just such additional equations. They take the spatial information from the co-moving frame and provide wave equations that depend on that spatial information to project the behavior of the ripples that might occur.

Software delivery schedules and standing waves

I worked on a large software development project in which the most interesting thing was why the project was delivered two years late to the customer. Both the customer and we, the vendor, knew from the outset what was required for the project. We both agreed on the work that needed to be accomplished and the time it would take to accomplish that work. About half way through the completion of the project, the customer added new requirements, which we as the vendor agreed could be done maintaining the original schedule, but with a known amount of increased effort.

We both looked at the project from a static perspective: we based our estimate of the initial effort on jobs we had done in the past that were similar. We estimated the increased efforts due to additional requirements on the same historical data. This view looks at the completion date as a random event distributed with a normal distribution having a small error. The shape of the distribution, including the standard deviation, is based on the historical data. Despite the best efforts of the development team, the total effort needed to complete the project as well as the delivery time were vastly underestimated.

I believe that the lessons learned from this project are directly related to the need to view the software delivery process as a dynamic as opposed to a static process. We in fact brought in an outside (Systems Dynamics) consultant on the project and learned the following.

  • Our detailed understanding of the project was fundamentally correct: the number of engineers needed to produce a given amount of code didn’t change after the new requirements were added.
  • Our understanding of the quality of the code produced by the engineers didn’t change based on an assessment of their skill set.
  • It was well understood that new hires would be less skilled than those with training in the areas under development. Despite this understanding, standard practice was to not take into account such details when doing cost and schedule estimates. Normally, such differences would generate small increases in costs associated with training.

Though there were many other factors, these three lessons were already sufficient to gain an understanding of why the costs and schedules were terribly out of whack. Let’s say that skilled developers would develop code that contained at most 10% errors. For argument sake, suppose that the delivery of product to the customer would allow 1% error. Suppose further that a test cycle to determine errors would take 6 months and that this was built into the original schedule. One test cycle after initial completion is sufficient to deliver a product of the requisite quality. Now imagine the situation of adding new requirements with the commensurate hiring of new personnel with less experience on the product. Because of the new hires, the initial delivery would contain many more errors, say as an example, 25% errors. So if we start with 100 units, we have 25 units that have errors after the initial pass. After the planned 6 months, we have 25/4 units with errors assuming the same quality of testing and fixing, which is not sufficient to deliver a quality product. This means an additional 6 months of testing, which gets us down to 25/16. To get below the 1 defect requirement, we now need an additional 6 months of testing, to reach the defect level of 25/64. Thus we get an additional year of development because of the change in quality of the new hires.

The actual quality was worse on the project and there were a few other factors, but the essential aspect of the story is unchanged: a dynamic look at the mechanisms demonstrates that small factors lead to unexpected and huge effects. This example illustrates how decisions propagate and impact outcomes. Decision process theory provides a theoretical foundation for such effects that is illustrated in the various models that we have detailed in our white papers. In this software example, we were misled when we assumed certain effects were static, such as the quality of the engineers. We assumed that the engineers would instantly become experts, ignoring what we equally well knew to be true that a training period was needed to make that happen; such a training period could in fact be a couple of years, well beyond the time we allowed for a development cycle.

There are examples in physics where we also make such assumptions, which don’t usually cause problems, but again can lead to incorrect results. A mechanism that is closely related to decision process theory would be that of gravity. In physics we assume that for most purposes, gravity is static. Under extreme conditions however, this is a bad assumption. If our sun were to explode, we would not feel the gravitational effect for several minutes because of the time it takes for the cause to make its effect felt. Such effects might be labeled gravity waves, despite our incorrectly labeling of gravity as a static scalar field.

In decision process theory, it is also true that causes generate effects that are separated by a finite time. There is always a propagation speed: effects are never instantaneous. In our models, in our model calculations we have focused initially on streamlines, which are paths along which the scalar fields are constants. For a picture, imagine the motion of air with smoke; the smoke provides visual evidence of the behavior of the streamline. One specific model might be of someone speaking, whose voice generates sound waves. We would capture the streamlines as displaying a global wave pattern, one that is not visible on any one streamline. Once sound waves are generated, we would see the streamlines undulate: the path of a velocity peak would propagate with a form we call a harmonic standing wave, analogous to shaking a jump rope whose other end is attached to a wall. This wave velocity is quite distinct from, and often much faster than, the media velocity.

Here is a model calculation using Mathematica of what a harmonic standing wave looks like in decision process theory for an attack-defense model:

[WolframCDF source=”” width=”328″ height=”317″ altimage=””]

The myth of a level playing field

I unconsciously subscribe to the view that each day starts anew with new possibilities; I start fresh with no residue from the past. I call this a level playing field. Whatever happened yesterday is of no consequence to today. Decisions that were made yesterday have no ripple into today. This does not agree with reality and is a new feature captured in the theoretical treatment I give to decisions, see Geometry, Language and Strategy, Thomas, 2006, World Scientific (New York).  Some actions carry through while others die out. There are consequences to our actions that sometimes extend into days, weeks or years.

So why do I subscribe to this short-term view knowing full well that there are significant exceptions? I think it is related to similar ideas in mathematics and physics that it is easier to visualize events as local occurrences. For example, we see the earth as flat and stationary. That is our local frame of reference. The earth’s curvature is not easy to grasp. The effects of its rotation about its axis and around the sun are equally hard to grasp.

We make a similar simplification in business when we focus too closely on local effects. We totally understand the consequences of hiring an experienced person versus an inexperienced person in terms of their quality of work. It is less clear how such differences are expected to show up in terms of project schedules.  It is hard to see how such simple mechanisms work together to create system behaviors. In this case as in physics, it is easy to grasp local effects but hard to grasp global effects.

The idea of a level playing field is analogous to the idea that the earth is flat. This assumption is often useful  even though it may ignore important (global) effects that are not important unless you look at large “behavioral distances” or long “behavioral times”. For example if you deny a portion of the population education, adequate nourishment and shelter, this may contribute to the greatest good for the greatest number of people. We say such behavior is not just either because of our ethical position or because logically, we understand that over a long period of time, you have created an unstable society, one that may reverse the roles of the populations.

The problem in economics and in society is that our current theories are local, not global. They highlight the obvious advantages of a flat earth but fail to take into account its curvature when looking beyond the local. it is hard to translate these differences into our expectations of what should happen. And yet we know that a long-term view is essential to understanding. I conclude that however useful, the concept of a level playing field is a myth.

I have argued for the importance of considering both short-term cycles and long-term cycles. That concept I think is particularly helpful in moving beyond the myth of a level playing field. We can still wake up each day and start fresh as long as we understand that we are missing some of the long-term cycle effects. We must be prepared to predict the consequences of the composite behaviors: there will be some situations in which one or the other dominates, and other situations where both are comparable.

I believe that the goal of a theory in physics or in society should be to help provide a mechanism for discussion. The theory must be able to take into account all relevant and significant mechanisms. I argue here that one of those mechanisms is the degree to which the field is not level.

Sustainability–short and long cycles

In many discussions of sustainability, the assumption is made that the distant past and the distant future have no direct relevance to the immediate present. This assumption is not unreasonable since ripples from the past often do die out by the time they reach the present; similarly events in the present generate ripples that often die out if we wait a sufficiently long time. There must be some basis for our belief that events can be considered unconnected. We capture that belief in the use of probability as a means to predict the future: Bayesian probability.

I argue that this assumption is incorrect. See Geometry, Language and Strategy, Thomas, 2006, World Scientific (New York).  There are longterm cyclic effects that originate in the past, whose effects don’t die out. Some events from the present will continue on into the future without appreciable damping. The justification for this argument is as common sense as the above assumption. We see boom and bust cycles in market behaviors; we see the longterm consequences of global wars. The appeal of the above assumption is its simplicity, not its accuracy. I argue that if we had a theory that took into account such longterm cycles, we would consider that theory superior. We would see choices fluctuate according to both the short-term and long-term cycles (e.g. the following CDF figure based on an attack-defense model, chapter 9 of the dynamics of decision processes illustrates choice behavior with two cycles; the CDF format is not yet supported on smart phones, sorry).

[WolframCDF source=”” width=”328″ height=”334″ altimage=””]

An attribute we would look for in a more complete explanation of events would be that longterm cycles, though hard to see (weakly coupled to our observations), can have very strong effects (payoffs). This would contrast with our experiences of the day-to-day short cycle time events that are easy to see (strongly coupled to our observations), but with relatively weak effects (payoffs).

How would this view change our understanding of sustainability? We might then understand that as human beings we make small changes (weak coupling) to our environment that over a long time cycle time can have strong effects (payoffs). Because we have been successful in the past to accommodate environmental changes is no guarantee that we will be as successful in the future.