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PROLOGUE
From One to Many
This is a book about how we collectively make decisions and about the tools we use to reach those decisions. The tools we use may be as important as the decisions themselves.
We make joint decisions out of necessity because the choices we make affect each other. Each decision we take has a consequence— sometimes perhaps very little, as in a private decision on what to have for breakfast, or perhaps a bit more, on whether to exercise or not. Some decisions involve jointly planning for dinner or vacation, or entering into a business partnership. Some decisions follow rules, laws, and constitutions. These decisions involve and affect large groups of people and organizations. The consequences are also greater and could last longer.
The problem of converting preferences of individuals into a collective decision has been pursued by a small academic field. The so-called social choice analysis tracks back at least to the 13th century, perhaps much earlier. The topic gained prominence in the late 18th century as the French Academy of Sciences sought reliable methods to elect its new members. Imagine such a debate between
some famous people in science and public affairs: Laplace, Borda, Condorcet, and Napoleon Bonaparte.
Social choice analysis, though, mainly looks at what effects voting rules can have when used properly and manipulatively. This has implications in all sorts of scenarios in life. Consider the following: social clubs and professional groups electing new members; ranking of research proposals to be funded by taxpayer money; choosing space and telescope missions; exploring sites for major science and engineering projects such as the Large Hadron Collider in Europe; homeowners’ associations choosing their directors and setting their annual fees and property rules; publicly traded corporations selecting their boards of directors with annual votes; and flying and sailing clubs voting about their fleet composition. And of course, we hold local, state, and national elections. Similarly, papal elections for the Church of Rome have become international events, as people wait for the telltale white smoke signaling a successful vote at the Vatican. In another context, in places like California, certain water districts give their members voting power in proportion to the acreage of land they own. In concept, one large landowner can control the vote to impose a tax on everybody living in the area to support the water supply. Making the most prudent decision remains a challenge throughout our lives.
Social choice analyses are also very limited in scope. They study how groups can choose among a given set of options. The menu is set. Groups are given a list of options. Groups vote. End of story. The issue of how the menu is set is not addressed.
Setting the menu is the realm of systems analyses, an approach most commonly associated with engineering design. While appreciated in concept and practice throughout the history of civilization, systems analyses came to prominence during the height of the 20th century war efforts when much more seemed to be at
stake, including military superiority, space missions, and Cold War competition. Systems analyses is common in urban planning, waste management, environmental considerations, supply chain, and logistics, and it should ideally be even more common given the consequences of our work and how we are frequently unable—and unwilling—to track them. In simplest terms, systems analyses enable us to deliberately and consciously bring together factors that can and do matter in a situation. It’s about recognizing that any decision has multiple criteria to satisfy—it’s never one thing to vote on, and it’s never one single answer. However, that is exactly how we have designed our commonly used voting systems to be: to come to a single conclusion without any consideration of expression, experience, and enjoyment. Engineers are well versed in certain aspects of design on how to integrate these key dimensions of life into the products and services they are building.
But until now, the task of systems design and the task of choice analysis within a system have been largely separated, particularly in settings where groups need to make decisions. In our decade-long collaboration, we have studied many decision-making processes. We have come to realize, from our perspectives as an economist and an engineer respectively, that the rules influencing how decisions are made seldom receive sufficient attention. But we have also learned in this project that organizational bylaws are imponderably vague—perhaps deliberately opaque—on some key steps in the decision processes. Further, these rules often give certain individuals vast power to control the process through designation of key groups and their own process rules. Thus, we were convinced that much work needs to be done on shaping the rules— or at least in making people aware of them—that guide social decisions. These rules are, in effect, the shadow decisions behind the real decisions.
We hope that this book will reinforce why we need better systems design and analyses given the consequences of our decisions. It is also about carefully thinking about the values of the choices we make, whether they be in a small meeting of individuals in your local association or community or in a national election. It will illuminate the differences between sincere voting and strategic behavior to defeat an opponent in voting, the latter being quite common. The book will also review different voting systems, what their original intents were, and what their deficits are. In trying to bring all these topics together and more, we realized that the book is in essence an outcome of the arranged marriage between social choice and systems engineering. The more one begins to explore the aspects of social choice and systems engineering, the more one realizes how much they have in common, and how much more they can offer if unified.
Chapter 1
Systems of Complexity
Around the world, men and women participate in track and field events. They compete for glory, every year, every summer, every winter. With commercial endorsements for high-profile performers, financial gain remains a motivator to perform well.
The first Olympic decathlon event was held at Stockholm in 1912. The winner was Jim Thorpe, an American and the first Native American to win an Olympic contest. King Gustav V of Sweden told him after his win, “You, sir, are the greatest athlete in the world.”
This tag—the world’s greatest athlete—has stuck on future decathlon winners. Bob Mathias twice won the Olympic decathlon (the first at age 17) and rode that fame to a career in the U.S. House of Representatives for four terms. Bob Richards won two U.S. decathlon championships, becoming the first person to appear on the front of a Wheaties “Breakfast of Champions” box in 1958, followed by Bruce Jenner in 1976 after his victory in the Olympic decathlon.
Combining the performances of multiple events (10 for the men’s decathlon, seven for the women’s heptathlon) is a quintessential situation involving many attributes. The International Association of Athletic Federations (IAAF) uses a complex formula to do this. The alleged goal is to make each event contribute equally to the total score in terms of some standard of “fairness”
Making Better Choices. Charles E. Phelps and Guru Madhavan, Oxford University Press (2021). © Oxford University Press. DOI: 10.1093/oso/9780190871147.003.0001
that remains unspecified. As we’ll see, the IAAF systems do not come close to achieving this goal. Let’s dive into the IAAF scoring formulas for a bit.
For the four running events (where T is time in seconds and “less” is better):
Points =− ( ) ab T c where a, b, and c are specific to each event.
For the six field events (where D is distance in meters and “more” is better), which include three throwing events, two jumps, and pole vaulting:
Points =− ( ) aD b c
The formulas begin with the somewhat arbitrary choices on the b and c parameters. The b values are “minimum acceptable performances.” For the throwing events, these minimum values are 6.5, 5.4, and 6.7 percent of the comparable world records. The leaping events—long jump, high jump, and pole vault—are next lowest (24.5, 30.6, and 16.2 percent of comparable world records). Then come the distance race of 1,500 meters and the 110-meter hurdle (42.9 and 44.9 percent of the world record), and then the 100- and 400-meter races (53.2 and 52.7 percent). These choices have a direct effect on scoring, since smaller minimum values (as in the throwing events) make it harder to gain points, and conversely. They have the effect of biasing the scoring toward sprinters and away from larger, stronger, and perhaps slower participants.
Another powerful effect comes from the c coefficients (power multipliers), which give a direct reading on the apparent importance of the event to the IAAF. The four running events have power multipliers ranging from 1.92 (110-meter hurdles) to 1.81 (100- and 200-meter sprints). The three leaping events have power numbers of 1.42 (high jump) to 1.35 (pole vault). The three “throwing” events have power numbers of 1.10 (discus throw) to 1.05 (shot put). These closely correspond in effect on scoring to the b multipliers, favoring speedy sprinters and disfavoring stronger and larger athletes.
After the IAAF agrees on the b and c values, they pick a scores so that a prespecified strong performance nets 1,000 points. IAAF historical documents say that the intent in the 1912 Stockholm Olympics was to award 1,000 points in each event for the Olympic record (typically less than the world record, which would produce about 1,200 points), but the formula has been modified six times since then.
In the real IAAF process, the scoring system favors the fast over the strong, but it is very hard to decipher how exactly. The three parameters (a, b, and c) interact in a complex way and show what’s important for each event. The decathlon and heptathlon scoring methods may seem arbitrary and capricious and may disfavor some events, such as throwing, over others, such as running. This creates some selection pressure on individuals who can compete effectively in the men’s decathlon or women’s heptathlon. Again, lighter and faster athletes have an advantage over stronger athletes. That is, it’s not a pure competition where each event has an equal effect on the outcomes.
Two issues emerge. First, the ways in which multiple values are combined affects the final results. Second, and perhaps more important, these grading rules can and do change the nature of possible
choices. The rules we create influence what’s considered valuable and affect the choices presented to us.
Our collective decisions usually revolve around three basic factors: (1) how many people are affected by the decision; (2) how many people make the decision; and (3) how important the decision is both to the makers and recipients of the decision.
Some decisions have one decider with one or two people affected, as in deciding what to have for lunch today. This is of hardly any consequence to society. A similar decision can have higher consequences, as in what car to buy, or of greater consequence, as in deciding on surgery versus hospice for cancer care. Another example of a decision that is made by one decider with at least two people affected, and that is of great consequence, is filing for divorce. Couples on the verge of a divorce usually don’t take votes on such matters.
Some types of decisions have—or at least appear to have—one decider but affect many people, as in decisions of a government to go to war, to shut down its operations, or to declare a national emergency. These decisions affect a wide range of people, perhaps an entire country or continent. Arguably, decisions made by a few individuals at the political helm of a few organizations and nations affected the entire world in the COVID-19 pandemic.
Such decisions (set aside totalitarian regimes) are seldom made by one person. The U.S. House of Representatives has sole jurisdiction to initiate tax bills. The U.S. Senate ratifies presidential, judicial, and cabinet appointments. The senators must also ratify U.S. participation in international treaties and in declarations of war. The ultimate decision authority remains with the people, who, through
established procedures, elect the leaders of cities, states, and nations. So even the apparently significant decision-making power of the U.S. president is tempered, at least in concept, by the power of the vote. If people actually employed their full right to vote, elections of the U.S. president would both involve and influence the entire country.
In many types of decisions, the number of deciders and the number of affected people are both small. Elections for mayor, town council, sheriff, and judge are examples. They expand to the level of counties and states as well as many other forms of government, such as those that support water supply, education, and medical care. The same idea applies to the private sector.
Certain decisions involve an intermediate number (several hundred) of decision-makers in situations where millions (sometimes billions) of people are affected. Conversely, some decisions are made by groups of people but affect very few. The Supreme Court of the United States has nine voters, but on certain concerns, their decisions could affect everyone in the country (about 330 million in 2020). The College of Cardinals consists of 222 members, but only those under age 80 are eligible to vote for a new pope, and the number of electors is limited to 120. Their vote affects the estimated 1.2 billion members of the Roman Catholic Church around the world, if not more. The state of California has about 25 million eligible voters out of a total population of about 40 million, and while many of their votes have influence only within California, on policies for auto emissions and minimum wage the effects of their decisions can ripple throughout the United States. The result of the recent elections in the United States and the United Kingdom has had an influence on the entire world. In India, recent elections for national governance involved 900 million registered voters (out of
1.3 billion people), the largest democratic exercise in known space. Each of these scenarios requires agreement by the participants on the decision rules. However, a key point of this book is that people seldom think about the rules behind their decisions, even though these rules can and do have important effects on their own and other people’s lives.
There are many predictable components in decision-making. Sometimes they get rolled into moments that cannot afford time for thinking, as in encountering a grizzly bear on a mountain trail. We have enough experience with fight-or-flight situations; these are instinctive and evolutionary. And paradoxically, we do not have much experiences in situations we ourselves have created: when decision-making needs to involve multiple people, various steps, numerous discussions, arriving at an agreement when possible, and launching the decision.
Many decisions first involve a process to whittle down a larger list of options to a manageable set. This step is ubiquitous and often strongly influences the outcome. Many organizations and corporations do this using committees of individuals. Sometimes these committees are permanent (with a rotating cast of characters who serve)—for example, a committee tasked with having ready a list of candidates at any needed time to fill vacancies on a board.
Sometimes the committee is ad hoc and need based, as in selecting a new leader for an organization. The selection process and the voting rules to choose the final list of candidates are usually well specified and available for public view. In contrast, earlier steps have greater mystery. These rules are often not written down, and when they are written down they are available only to a select group of insiders. From college admissions to competitive awards, the mechanisms and decisions for creating a list of candidates to be voted on are likely to be less obvious and probably even obscure.
A high-profile example makes the point: the process of selecting winners for the Nobel Prize in Economics, formally the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. The point here is not to say that the process is wrong or very secretive but rather that the obscurity of the process overrides its transparency. The members of the prize committee are elected by the Royal Swedish Academy of Sciences for three-year terms, but the details about how those committee members are chosen remain obscure to the public. The committee seeks nominations, typically from about 3,000 people. This pool includes former prize winners, members of the Royal Swedish Academy, and professors from around the world who are chosen by the committee. From the list of nominees, typically 250 to 300 in any year, the committee then determines a preliminary list of candidates in a secret process and seeks specialized evaluations of their work.
Next comes the majority vote. Even this step of the process is obscure. On exactly what attribute do they vote? It cannot be true that they choose the winner from a long list, because (as will be discussed later) majority voting does not always determine a winner if three or more candidates exist. Plus, the committee has never failed to award a prize in any given year. So, they might choose among two or three finalists, except that sometimes the prize is awarded jointly to several individuals, dividing the funds between them. The vote might consist of two proposals from the committee, one of which might involve multiple participants. Or perhaps the vote is a “rubber stamp” vote to approve the committee’s recommendations. Whatever process they use—and this is not just with the Nobel prize selections—we know that (a) it is not publicly described in detail; (b) it apparently always produces a winner; and (c) the winner might be one person, or two, or occasionally three. In the
50 years of awarding this prize, half of the years have had multiple winners; in six years, three winners have shared the prize.
Again, the basic point here is not about the secrecy of the selection process (which is understandable) but more about the mysterious winnowing process that underpins this award and those in many competitive pursuits.
The rules (or lack thereof) surrounding our selection processes can and do affect the diversity and inclusion in society, the very essence and engine of democracy. This is well known and often acknowledged in theory but not in practice.
The importance of the decisions that are created by collective choice is a product of how many people are affected and the impact on well-being. Decisions of high consequence that affect large numbers of people deserve special attention. Decisions are also a function of who can make decisions and if those rights and privileges are clearly specified. The U.S. Constitution specifies those rights. Every country, state, county, and municipality in the world probably has some comparable document. But these statements are often abstract and can easily be interpreted differently, as can be seen in debates concerning the powers of the presidency or legislature in the United States. Constitutions regularly specify judicial systems, for which another set of pivotal decision rights is laid out. In the United States, the ultimate “decider” on consequential matters of law is the Supreme Court. In totalitarian societies, a dictator often holds final decision rights over almost everything, despite the extent to which the nation’s official name tries to otherwise persuade (e.g., “The Democratic People’s Republic of X”).
Next, when decision-makers “decide,” what should they decide? The best choices, we submit, will not necessarily involve choosing among candidates but rather choosing what is valuable—and by how much and to whom—and also finding how well these candidates perform against what we value. Many decision support systems have become very popular and easier to use. The value of these aids has become increasingly apparent as we learn more about the foibles and (sometimes) major defects of intuitive human abilities to make decisions. We struggle with probabilities. We use estimates incorrectly, even inappropriately. Our judgment is affected by how questions are framed. Decision support systems play a good role in helping us recognize and minimize cognitive errors.
Three key issues have emerged. Who gets to decide? What are they deciding? What rules and choice mechanisms do they use? On these topics, many mathematically dense publications on social choice only offer “caution.” These are well intentioned but do not provide useful advice. In Making Better Choices, we’ll address these questions and also consider the human factors of those choice mechanisms. How do they work? How friendly are they? How expressive are they? How meaningful are they across contexts? Throughout this book, our goal is to focus not on the rules of voting but on the rules of discourse—how to design better decision mechanisms in democracy.
Before we launch into more detail, let’s consider a practical insight from systems engineering: We must make tradeoffs, which in turn requires knowing the relative importance of our priorities and what we consider valuable.
In the late 1970s, all high-end bicycles (including those used on the Tour de France) had steel frames. Fine distinctions were drawn between various types of steel tubes that best served the triple goals of competitive bicyclists—low air drag (smaller diameter), low weight (thinner walls), yet stiff as possible to avoid frame wobble. The relevant design parameters were choice of steel alloy, tube diameter, and wall thickness. This frontier of possibilities led bike makers to different choices, sometimes small and irrelevant. Climbing steep mountain passes in the Alps and then racing down the other side at 60 mph created the greatest stiffness challenges: Insufficiently stiff bikes cost a lot of energy on the climb and then wobbled dangerously on the descent.
Then along came engineer Gary Klein, who wondered while a student at Massachusetts Institute of Technology if a way existed to break the paradigm. For a design class, Klein began experimenting with aluminum tubing of substantially greater diameter than existing steel-tubed bikes. The larger-diameter tubes were much lighter and much stiffer but had greater air resistance. A tube’s stiffness relates directly to the fourth power of its diameter. When you double a tube’s diameter, it becomes 16 times stiffer, which greatly improves the bicycle’s performance in competitive races.
Klein revolutionized bicycle construction.1 His design was vastly better than any other bike on the market at the time. Tungsteninert-gas (TIG)-welded aluminum tubing has been replaced by carbon fiber, yet another technology that pushed the performance frontier even farther. Only cost stands in the way of using carbon nanotubes as the next-generation foundational material. This could
1. One of us (Phelps) rode a Klein Stage bike across the United States from Oregon to Maine, averaging 100 miles a day for five weeks. Not only was it faster and more efficient than steelframed bikes, but it was also remarkably more comfortable to ride.
allow thinner tubing, hence less air resistance, but trade-offs would remain. In the long run, Klein’s key idea was not to use aluminum but rather to make fatter-tubed bicycles, which rapidly evolved into oval rather than round tubes, and other materials beyond aluminum to do this. But even with this improvement, trade-offs remain as an essential part of bicycle design.
Automobile design faces the same conundrum. Car design always has competing goals—say, fuel efficiency (miles per gallon), acceleration capability (torque), and emissions reduction. Limited to the technology of combustion engines (gasoline or diesel), you can’t have all three. Some have tried (by deception), but the iron laws of physics—and the practical necessities of engineering design—require tradeoffs. The market recognized this with a onethird drop in the share price of the firm within days of its emissions fraud becoming public. You can’t improve on all of these goals at the same time. Yet (like with Klein’s aluminum tubing) automakers have found a way to improve on all three dimensions at the same time by changing the paradigm from internal combustion to stored electricity—batteries. But this adds three new dimensions to the problem—weight, range, and cost. The concern with electric cars to date has been their limited range. Someday, a new battery technology will alter that equation, or hydrogen-powered fuel cells will come into play. Then a new constraint will emerge, and new tradeoffs will need to be made.
An enduring insight from the practices of systems engineering is that you can’t solve all of your problems at once; tradeoffs are essential. Consider this adage: If quality, speed of completion, and cost are three variables, you get only two of them. The skill, even achievement, becomes how to arrive at good-faith tradeoffs, and this is where the practice of systems engineering tries to ensure reasonable and maximal levels of quality, speed, and cost.
There are many denominations of systems engineering according to the industry and contexts, but variations of the following themes are put into practice: development of a strong conceptual understanding of the problem and solution space, generation of requirements (options) for the desired solutions, periodic verification (as in quality assurance) and validation (as in ensuring safety) through multiple rounds of testing, and iterative improvements in the processes, services, and products. Although simple in description, this kind of engineering has to deal with complexities at every level: business objectives, human psychology, market needs, political forces, and time constraints. Even systems are of different kinds: simple systems with a single path to a single solution; complicated systems with multiple paths to a single solution; and complex systems with multiple paths to multiple solutions. In complex systems, the properties and character of the phenomena change frequently, fundamentally challenging assumptions and established processes that work for well-understood systems. Systems engineering in this case becomes a process of disciplined learning and unlearning. The approaches may not necessarily yield a pinpointed solution per se but can offer an insight on the nature of compromises to be made, which is true of scenarios in making both decisions and policy. But the hard practical fact remains: Life is replete with tradeoffs.
