This article is a companion material to the Course COM 25100 Information, Technology, Society which I teach at Purdue University as a University core class. The course teaches trade-off thinking as a fundamental method for understanding technological choice and innovation.
All technologies are shaped by competing choices
Any technology is a matter a choice. No technology succeeds because of its intrinsic technological strengths. All technology creators aspire, of course, to create that which is most desirable: the fastest, most comprehensive, most versatile tool. In reality, cost, usability, security, or plain common sense mitigate desire with practicality.
The fact that choices should be made is a banal statement. What matters is what does and what does not count when choices are made. More important, at what point should we decide that what is desirable is desirable enough given the price in time, resources, exposure to risk, or usability loss?
The answer is simple. Implicit or explicit trade-off analysis shapes the choices. Whenever we choose a feature for a technology, we know that the choice we make might limit other decisions. When you are building a communication system, if you want it to reach far you need to make the transmitter big and powerful. This comes at the cost of mobility. The system might be also hard to use. And so on.
However, to only say that other choices limit some choices is trivial. At what point should we decide that enough is enough? When does a system of communication reach an optimal range? When is the amount of information it can send per unit of time sufficiently high for the limitations in reach that come with increased information load?
Marginal utility as a core concept in defining trade-offs
To answer these questions, we need to come up with a yardstick that can measure the advantages of one feature against those of another. We need to find a way to compare apples and oranges! Fortunately, this problem was solved by economists a very long time ago. Studying how individuals choose between competing goods, they found that individuals use what the economists call “utility” to decide at what point a good would be “sufficient.” Utility in this context is not synonym with “useful” or “good for a specific purpose.” Economic utility is not intrinsic to the object. Utility is defined by the present and most salient needs of the user. In other words, utility means “how badly you want something versus something else in this current situation.” Suppose you have exercised a lot. Your body craves both food and water. However, because you just finished working out and you have sweated a lot, you are really thirsty. Now, suppose that you only have 12 dollars. For this money, you can buy either four bottles of Powerade or six RX energy bars. Although you could very well split it even, two bottles of Powerade and three energy bars, you decide that you will, in fact, have three bottles of Powerade, to begin with, and only one energy bar. The reason? For you, one energy bar plus or minus would not mean as much as one extra bottle of Powerade. Your body is THAT thirsty. (Plus, you save a dollar!)
Two days later, you might have just finished studying for one of my classes. All these readings about marginal utility and indifference curves taxed your neurons so much that they burned all the sugar in your system. You are ravenous. Again, you have 12 dollars. What will you do? You could buy six energy bars to quench your sugar craving. Yet, prudently you buy only three. You eat two, and you tuck the other one in the pocket. You just realized you do not even need it. Instead, although you are not that thirsty, you buy a bottle of your favorite drink, Powerade. After all that sugar, you need something to wash the stickiness of the bars off. That makes you even thirstier, and you get another drink. Plus, you have 2 dollars left!
What happened between the two situations? The relative utility of drinking vs. eating has changed, according to your specific needs. Moreover, although in both cases you could’ve either drank your fill or eaten to satiety, you chose not to do so. An extra drink would’ve been one too many or of no use to you. Same with the bars. Two bars were enough; the third satisfied no real need. The chart above shows how the trade-off between the two goods changes at various levels of Powerade or energy bar consumption. The chart is a simulation, but it gives you the idea that the relationship between the two goods is not constant. At the higher end of each axis, declines in each good lead to a significant drop in the curve. Why and how this drop happens will be explained in detail below. Before that, a few more words about utility.
Utility changes with context of use
This example is meant to illustrate two ideas, which are very well explained in economics textbooks, such as Ayers and Collinge, (2003). Economics: Explore and Apply. First, utility is contextual. It is not intrinsic in a good; it depends on the situation. Second, utility decays with quantity. The more you have something, the less you need it. How many energy bars does a man or woman need to be happy? Not that many… This insight can apply to just about anything you can think of: vacations, movies, popcorn, or romantic partners. All vacations become aggravating after the 10th day. I guess all that drinking and walking gets you after a while. Netflix binging has an upper limit of 3 episodes per night. If you get the bucket of popcorn at the movies, the next time you will for sure go for the candy. And do not tell me that juggling multiple boyfriends or girlfriends is fun!
The official term that we should use for explaining why utility decays with quantity is “marginal value.” Economists discovered that there is a law of diminishing returns when it comes to consuming any good. The first unit of a good gives us a lot of pleasure. It is very valuable. As we consume more units, they are only “marginally” -barely – valuable. Or, we can say that they are valuable at the margin. A final, and a directly intuitive way to say it is that as we consume a good, the amount of utility we derive from it declines so that with each unit we only benefit of a margin or part of the utility we initially enjoyed.
There are many ways in which we can use the insight that utility decays with quantity and that all goods have no unique, constant value, but only marginal value. One of them is to decide at which specific point the utility of a good is “useful”and “valuable” enough. The decision can be made by comparing the utility of our target good with that of another one, which we could get for the same money. The economists proposed that we need to only consume a good until the utility we derive from the last unit is equal to that of the last unit consumed from the other. In other words, until the comparative marginal utility of the two goods is even or indifferent. This is called “utility maximization.” When we came to this conclusion, we found the magic point where a trade-off is optimal.
Indifference curves and feature trade-off
With this idea, we come to another discovery made by economists, the so-called indifference curves. These are basically lines that curve up or down in two-dimensional space that tell us how much an increase in the quantity of one good reduces the availability of another good. Or, turning the statement on its head, how much more available a good becomes if we decrease the consumption of another good.
There are two interesting things about these curves. The first one is that they are… curves. The second is that every point on their trajectory is apparently just as good as any other.
Let us start with their shape. Their curvature illustrates in very vivid terms the idea of marginal utility. When the utility of a good decays with each unit consumed, the value of the other one does not follow suit in the opposite direction and in the same amount, since the relationship is not one-to-one. The relationship is, using a word you probably heard before, exponential. Increases or decreases in one good create larger and larger effects on the evolution of the other good… Take another look at our example of the indifference curve for our example for energy bars and Powerade bottles. Remember that after exercise you had three bottles of Powerade and one energy bar and after studying you had three energy bars and one Powerade… (The line does not quite intersect the numbers because it is quite hard to make whole numbers create nice curves).
The other thing interesting about these curves is that if you follow the logic of marginal utility, any mix of two goods that fall on the curve is equally… good. In other words, you derive the same amount of total utility. The only thing that is different is where do you get the utility. From 1 bottle of Powerade or from three energy bars?
However, if you think about it carefully, you realize that in fact, not all areas on the indifference curve are equally desirable. Because as you move toward either end of the curve, the utility you derive from either increase or decrease in one of the goods becomes smaller and smaller, you want to find a point on the indifference curve that is just right, where you get the biggest bang for the buck. That, naturally, should be in the middle of the curve, or where the curve starts to bend. Keep this in mind when thinking about your own technological choices. You do not want to maximize a feature at the extreme since you get very little from it while preceding some valuable opportunities.
Finally, what happens if you have pairs of values that are under the curve? What if you only consume an energy bar and a Powerade bottle, although you could’ve had multiple units of each good? In this case, your use of both products is suboptimal. You are, in other words, underutilizing your resources. Conversely, how about if you want to eat more than four granola bars and more than four bottles of Powerade at the same time. Now, that is not possible. It is over budget!
Marginal utility, indifference curves, and communication technologies
So far so good, but we started our conversation with a discussion about technology choices. How did we get from that to energy bars? Simple, I invited you to assume that a technology creator is just like any other economic actors, consumer or otherwise. He or she has a limited amount of resources (money, time, materials, etc.) while working under various constraints (demands for safety, reach, usability, etc.). He or she needs to combine his or her resources and constraints in the same way a consumer needs to decide how to mix and match her eating and drinking needs. Just like any consumer, a technology creator needs to decide how much more utility a potential beneficiary of his system would derive from a given feature by decreasing the utility in another feature. Furthermore, he or she will realize that the relationship between the two features is curvilinear, that as you add more and more in one dimension, say, reach, the benefit you get from it decreases (say, information load).
Take a look at this chart. It shows the hypothetical relationship between “information load” (number of signals per minute) and reach for three systems of communication: torches, horseback messengers, and the Chappe telegraph. What do you notice?
Well, several things. First of all, for all communication systems, the information load goes dramatically down after the first ten miles. Second, the messenger system has the best information load for very short distances. Yet, after a few miles, it declines dramatically. So does communicating with a simple torch, which is shown or hidden or lit and unlit to encode various signals. However, after 10 miles, torch communication becomes a bit better, although not by much. The best performance is for the Chappe telegraph. Although its information load declines after ten miles significantly, the line is always above the one for the other two systems of communication.
Why does the Chappe telegraph stay above the other two? That is because we assume that the signal will be quite visible within 10 miles (considering that we use a good telescope and the arms a good 4-6 yards in length). After 10 miles, although the signal decays, becoming harder and harder to see, it will still be quite visible, and the message can be easily read and retransmitted. To send it further, the message should be re-transmitted, which adds time, which lowers the information load, yet not as much as for the other two systems.
While these details are obvious, how do we know this is indeed, true, and that the curves for torches and messengers should drop so abruptly, so soon? Simple, we assumed that for the two the rates of decay, which is the same as the “trade-off” rates, will be higher. We expressed this trade-off rate as a fraction of 1, where 1 is the highest number and 0 the lowest. When the trade-off rate is high, as the case for the messengers, as distance increases, the information load drops dramatically. When the trade-off ratio is low, as is the case for the Chappe telegraph, as the distance increases, the information load decreases, but not as dramatically. Most interesting, if you go to the spreadsheet, that stands behind the chart, and if you enter a decay rate of 0 for Chappe (Cell G6), you will notice that the information load stays constant regardless of distance (you need to save the spreadsheet on your Google drive, first).
Now, one more detail to bring it all together. Do you remember the indifference curves discussed above? The lines in the chart clearly look like such curves. However, in this situation, we have three curves, not one. The question is which one is the optimal one? Which one is “the” indifference curve by which we should judge them all? Obviously, the one that rises above all is the optimal one. Why? Simple: for all distances the information load values are higher. You can have the cake and eat it, too.
Finally, if you look at the formula that controls the decay rate, you notice that it is a simple division of the initial information load over the distance raised to the power of the decay factor.
Thus, for the mathematically minded, the final formula for the tradeoff between two communication technology factors is
where X is a target variable (say information load), X1 the information load when the explanatory variable is 0, and d is the decay factor expressed as a ratio between 0 – 1, which indicates how many units in one variable should be traded off for the other.
However, in the context of this course, the formula is far less important than the bigger picture, which is that using a simple, yet effective method of exponential decay we can decide how the trade-off process will work when choosing features for any communication technology.