If there’s one idea that crystallizes the magic of computer science, it’s reductions. Classically, in the study of complexity theory, we can demonstrate algorithms which transform a solution for one problem into the solution for another problem. We say that the algorithm reduces the second problem to an instance of the first. Hence if there is a general-purpose solution to the first problem, then we get a general-purpose solution to the second “for free.” Perhaps most famously, this insight is the foundation of the definition of NP-completeness, though it’s useful in many contexts. In more practical contexts, at every level we try to write software that is general-purpose in nature and which lends itself to reuse: that goes for humble functions, APIs looking to prove themselves, and behemoth applications like Excel.

In fact the idea is much older than computer science itself: it’s also a mainstay of organizing and politics. Alas, reductions in politics can be good, bad, and ugly.

The Good

In progressive organizing, we use reductions to demonstrate that a good idea can be applied more broadly than it has been to date. This approach can be incredibly powerful because it creates natural constituencies - if you’ve benefited from the good idea, you may want to see it expanded. If you’ve been left out of it, you almost certainly do. The federalist notion that states are the laboratories for democracy relies on the idea of reductions in policy: if universal health care is a good idea in one state, why shouldn’t it be a good idea in another? Or in the entire country, for that matter?

A classic formulation of civil rights advocacy follows this pattern too. Perhaps most famously, Martin Luther King, Jr claimed that the dream of civil rights is a dream “deeply rooted in the American Dream,” an enormously clever idea. The goal was to restate the then-radical notion of racial equality as a natural consequence of classic American values, as well as to join it to pride in American economic prosperity. Very loosely speaking, King described an algorithm for solving the problem of racial equality using the pre-existing solution for democratic values and prosperity.

Nor was King the first or last to use this ideas to expand civil rights. Sojourner Truth asked “Ain’t I a Woman?” to argue that the feminist moment of her day must be broadly inclusive. Hillary Clinton claimed that “Women’s rights are human rights” to bring the argument to the world stage. There’s also a long tradition in legal circles of reductions that expand rights. In the early 20th century the Supreme Court used the Fourteenth amendment to apply the constraints of the Bill of Rights against state governments in a series of decisions known as the incorporation cases. The movement for marriage equality took off with a Massachusetts supreme court ruling that found that based marriage equality in the state’s sexual non-discrimination statute.

Unfortunately, reductions in organizing are not always so profound.

The Bad

They don’t receive quite as much coverage, but it’s not uncommon for the best-laid plans of policymakers and organizers to go astray. Occasionally we see reductions which simply don’t make sense, or policies which aim to create reductions but fail in doing so.

For example, Obamacare was originally meant to transform the consumer’s relationship to health insurance policy; legislators at the time thought that the law would move more and more people off employee-sponsored health plans onto insurance exchanges, meaning that the exchanges would become relatively broad-based marketplaces in which many insurers would want to compete for an attractive customer base. Reality didn’t quite pan out that way, prompting a wave of hand-wringing articles about the lack of competitiveness of some exchanges.

The history of organizing is full of these kinds of odd tangents as well. For example, temperance was once thought to be the avenue through which women would gain political empowerment. The thinking, approximately, was that a woman’s place of power in guiding her family should extend out to the public sphere. Temperance, which was a public policy that was rooted in many smaller-scale private struggles with alcohol, seemed an ideal vehicle for extending women’s power outside of the home. In other words, this approach suggested that the problem of women’s participation in the political sphere could be reduced to the problem of women’s participation in family life. Today we view this idea with a good deal of skepticism - it carves out far too narrow a role for women in public. But it certainly had its heyday; for a time the Women’s Christian Temperance Union was one of the country’s leading women’s rights organizations. Interestingly, both temperance and women’s rights eventually gained a foothold in the Constitution during the Progressive era constitutional reforms; but of course Prohibition eventually failed as national policy.

More recently, and somewhat more subtly, is the failure of the “individual virtue” framework of environmental activism. Somewhat popular in the 80s and 90s, it’s become quite clear in this century that environmental activism requires national regulatory frameworks and thumb-on-the-scale industrial policy in order to meet the challenge of climate change. The notion that many small acts of individual virtue was one borrowed, in all probability, from contemporaneous social justice movements. It was after all a popular feminist creed in the 70s that the “personal is political,” and indeed, feminism made great strides through a wide range of very personal struggles on the part of individual women throughout that time. Moreover, the theory-of-change which the Sierra Club has called Climate Action 1.0 came to life during the height of neoliberal ideology, when industrial policy and national regulatory frameworks were distinctly out of favor. Thirty or forty years ago, it was both convenient and politically necessary to reduce the problem of environmental reform to the problem of reforming individual lives. The somewhat abstract debate over the environmental movement’s strategy towards climate change is still ongoing, but it’s fairly clear that the individual action framework is very much in question - and still more clear that this framework hasn’t done much to stop climate change.

Misguided reductions like these are certainly problematic, but they come from a good place. There are other reductions which come from somewhere else entirely.

The Ugly

The use of reductions in organizing and policymaking is not limited to progressives; it’s actually a rather devious tool of reactionaries, as well.

One of the most damaging such reductions was the notion of Social Darwinism - an idea that an individual or group’s success in society was a result of natural forces. In short, the poor deserved to be poor, and the rich deserved to be rich; policies to create equity were short-sighted or even harmful. This idea is perhaps one of the most explicit examples of reduction in the name of reactionary policy: it reduced the problem of social welfare to the question of biological welfare. Masquerading as a scientific idea, it was actually grounded in a substantial lack of scientific knowledge: it carried the most sway in the late 19th century, when knowledge of the social sciences was a good deal more rudimentary, and a macroeconomic understanding of the forces undergirding inequality was virtually unknown.

But that is not to say that reactionary reductions are the exclusive province of long-ago eras. One of the most troublesome reductions of our day is the notion that corporations are people and deserve the same rights that people do. This reduction, which has been around for a long time and actually has some common-sense usefulness in incorporation law, has gone too far. Most infamously, ten years ago it engendered the ruling in Citizens United that wreaked havoc on campaign finance laws, and has arguably made elections far less representative ever since.

Closely related to this reduction is a more complex and disturbing one still, the notion that economic liberty is at least as important, if not more so, as political or social liberty. At heart, the modern conservative movement is entirely wrapped around this concept, which reduces the problem of economic policymaking to the question of political and social rights. Just as liberals view curtailment of expression or privacy as a violation of political and social rights, conservatives describe economic regulation as a violation of economic rights. This deceiving conceptual framework has been the veneer behind which one common-sense governmental protection after another has been attacked, and the fig leaf for increasingly regressive tax policies.

The Useful

As a tool of organizing and policymaking, it’s clear that reductions are something of a mixed bag, across a wide variety of contexts. They are to some degree perfectly natural: they arise from the basic insight that two different problems are in fact somewhat similar and can be approached the same way. We’ve seen that this insight can be both profound and world-changing; but it can also be misguided or malevolent. The goal for activists should be to seem more of the first kind, less of the second, and none of the last. My hope is that the experience of software developers can bring some rigor towards that goal.

It’s not an easy bridge to gap, for numerous reasons. But I like to think there are some lessons to be shared. To start I think it’s worth listing some of the qualities which make a reduction useful:

  • Efficiency: The reduction itself is efficient. If we wish to transform one problem into another in order to take advantage of an algorithm which solves the latter problem - then the transformation should not take dramatically longer than the algorithm itself. Reductions which violate this rule can be very interesting but not very practical.
  • Simplicity: The reduction should be simple to understand. Fundamentally, the genius of a reduction is to share expertise from one problem domain into another. The challenge is that expertise does not translate easily and that the transformation in question must be rather intuitive. This quality is admittedly very subjective, but it’s fair to say that transformations which are very complex will fail this test.
  • Effectiveness: The reduction is effective. This quality is arguably the most important, but it’s surprisingly easy to miss. Given a reduction from one problem to another - does the solution for the latter problem actually solve the first one? The reason this question can be so difficult to answer is that we tend to determine effectiveness of a solution for one problem in terms dictated by that problem, which may not be relevant to the second. In the end we may be assessing a solution using the wrong lens.

Allow me to illustrate these qualities using a problem domain which is very much on my mind these days: epidemiology, and specifically contact tracing for infectious disease spread. In many ways this problem has some similarities to graph theory, and indeed contact tracing amounts to a kind of breadth-first search on the social graph of an infected individual. So let’s evaluate this (admittedly rather vaguely-defined) reduction by the qualities above:

  • Efficiency: The transformation from a person’s social graph to a mathematical graph is straightforward, provided we can readily determine the list of people any one individual has contacted in a period of time. To translate from a social graph into a mathematical graph, we say that each individual is a node, and any significant contact between individuals is an edge in a graph. Given a list of an individual’s daily contacts, it’s trivial to create such a graph. So this transformation is quite efficient.
  • Simplicity: Particularly these days, the notion of a social graph akin to a mathematical one is relatively easy to grasp. I’d venture to say that even before the advent of social media, it was not terribly difficult to convey the concept of mathemtical graphs to epidemiologists. The fact that the transformation is so trivial suggests strongly that it is also conceptually simple.
  • Effectiveness: Here is where things get difficult. Put simply, is contact tracing really sufficient to track down the source of contagion? Is the disease in question one which lends itself to this approach? For example, if the disease is flu-like and can be spread from casual surface contact, then one individual can be infected by a stranger not listed on the social graph. It seems like a rather obvious point, but I find that often the excitement of a novel approach can overshadow such seemingly obvious nuances.

Naturally, the above rather superficial analysis is one which is (I’m nearly certain) very well-worn in the world of epidemiology. It’s meant to be illustrative of the kinds of problems that arise in reducing a public policy problem to a mathematical one.

Even so, I think it’s possible to use this rubric to evaluate some of the “bad” reductions we’ve seen. For example, why did Obamacare wind up not creating broad-based health care exchanges that involved lots of middle class consumers? Why was the reduction from health insurance competition to auto insurance competition not very effective? I think the problem was in the implictly-assumed transformation. The notion that a lot of middle class consumers would be participating in health care exchanges presupposed that those people would have lost their employer-sponsored health care coverage, or would have somehow opted out of it intentionally. Such a transformation would itself require a sea change in a huge swath of the job market, and would require at minimum a major public relations effort that never materialized. In other words, the implied transformation in this public policy was not very efficient.

The problem with “ugly” transformations is that they meet all three of these criteria, unusually well in some cases. Social darwinism, for example, relies on a transformation between natural biology and public policy which is easy to understand, easy to apply, and very effective. The problem is that it’s effective in all the wrong ways, justifying regressive and cruel policies. In other words, like many other tools, reductions are a double-edged swords in the world of activism. The hope is that progressive activists can use them more effectively than reactionaries.

The learning goes both ways, incidentally. Activists may be able to learn a thing or two from software developers, but software developers have a lot to learn from activists. I use the term “reduction” because it’s a term familiar to me from computer science, but the notion of repurposing an idea from one domain into another, and solving two problems at once, is a very old one in progressive circles. Take the “Ain’t I a woman” speech, for example. Among other things it suggests that the original sin in the Garden of Eden - which at the time was thought to be conclusive proof that women can’t be trusted in the public sphere - is actually a demonstration of the power and forcefulness of women’s action. It’s an enormousy clever tranformation, and I struggle to think of any kind of software reuse or abstract mathematical reduction that’s nearly as clever. No less stunning - it was delivered, extemporaneously, by someone with no formal schooling and years and years of suffering in her biography!

On the whole, I think the concept of reductions, and its applications in software, is one which merits considerable study and analysis. Economically it’s tremendously significant, sitting at the heart of an industry worth north of $500 billion. To capture even a small sliver of that expertise and turn it towards progressive goals would be absolutely transformative.

Image courtesy of Anna Auza