Addition by subtraction

Why we're predisposed to favor solutions that "add" rather than "remove", and how to overcome that tendency

When I first sent this article to Patrick, his immediate* response was to the point:

I’ve known Pat for nearly 15 years and I still wasn’t sure if it was meant to be a compliment or a dig. Being the resident skeptical introvert of our company can take its toll, though, and I thought back to an experiment I once conducted on myself.

For about a year, I made a point to respond to the generic greeting, “How’s it going?” by saying, “Best day of my life.” Part cheerful optimism, part willful attempt to create my own reality, that response begat some interesting conversations and often served to aid in my daily struggle not to be Larry David. So I chose to take his kurt response as an endorsement of the topic.

Having said all that, if you don’t like this edition of the newsletter, it’s 100% on Patrick for not being clear enough to deter me from writing about it.

* Actually, this response came immediately after the second time I sent him the article, which was 11 days after the first time I sent it. But who’s counting…


A study recently published in Nature starts with a photo of something that has very little to do with nature, per se:

As a general rule, if you want to hook me into reading something, including a Lego reference in the lede is a solid start. But enough about my childhood nostalgia notwithstanding, because the article introduces about a study with interesting implications for problem solving.

Participants in a study were shown this image, which depicts a Lego structure with precariously unstable roof. They were told to make any changes to the structure they wished so that the roof would support additional bricks being placed on top. Any brick they added cost them $0.10, and they had up to $1 to play with.

Nearly 2/3 of the participants solved this puzzle by placing additional bricks under the roof. Just over 1/3 opted for the quick (and free) option of removing the superfluous 2x2 block who presence was the cause of the instability.

The report outlines seven other studies all testing a similar hypothesis. In some cases, participants were asked to either improve or make worse a putt-putt golf hole; in others, they were asked to make 3 quadrants in a 2x2 grid look the same as the 4th by toggling the color of squares. In all cases, participants tended to focus on “additive” strategies to solve the problems rather than “subtractive” strategies.

The authors described “additive” strategies as one that ended with more components than the original, while “subtractive” strategies as one that ended with fewer components than the original.


Think back to the last time you were involved in some problem-solving exercise at work. Did you reach for a subtractive solution? Were they actively encouraged during brainstorming sessions?

As I think back on my time in city government, not too many stick out. The one big example that kind-of-maybe-not fits came toward the tail end of the design process for a bridge and intersection remodel project. Early on in the project (as in, 7-8 years before this point, since TxDOT was involved), estimates for utility relocations were prepared. The City had included in its initial debt issuance funds for these relocations based on those estimates, but when it came time to let the project and get those gas pipes lowered, things changed. The cost estimates from the gas company, which had changed ownership during the intervening years, was now nearly 3 times as high, and at a level that we simply were unable to bear. Certainly not on such short notice.

Panic ensued, as tends to happen in such situations. In meeting after meeting, we struggled to find a solution to the problem. Each one inevitably seemed geared toward what the study authors would have called additive, and none of them solved in the problem in a timely or cost-efficient manner.

I’ll pause to note that in this case, our struggles could fairly be blamed on a couple of things: tunnel vision due to the length of the design phase, and an engineering bias which tends to disincentivize what we would otherwise call “outside the box” ideas.

Fortunately, the project managers at the city weren’t engineers, so we didn’t have any problem throwing out suggestions that might otherwise be kind of stupid. At one point, we asked:

- At how many locations do we have an actual conflict? One.

- How much more room do we need between pavement and pipe? A couple of inches.

- Is there any way we can just raise the road a couple of inches? [crickets.gif]

It took some arm-twisting, but it turns out there was a way to do it. If we rerouted drainage at one corner of the intersection, we could afford to raise the road enough to eliminate the conflict altogether with no delay, few (if any) quantity changes, and the cash we had originally planned to use available for something else.

Instead of trying to “fix” the problem, we worked our way out of the pickle by just removing the problem altogether.


In the world of city government, though, we tend to be biased toward additive solutions. We get awards for building parks, not removing them. We get better ISO ratings for adding fire stations, not for finding ways to provide similar service levels with fewer stations. We get re-elected for increasing library hours, not scaling them back.

And even doing an objectively great job, such that you win the accolades of your peers, may not be enough to hang on to your city manager chair.

Of course, subtractive solutions don’t necessarily require reducing services, lowering the standard of living, or making life more difficult. It simply means not predisposing oneself to thinking that a solution to a problem necessarily requires something new.

The authors of the editorial accompanying the study offer some thoughts on why we tend to favor additive rather than subtractive solutions. First, they suggest that we might tend to expect that subtractive solutions will be less appreciated than additive ones; that they won’t be viewed as creative or as helpful.

I think there’s some truth to this. “What if we just don't do X” doesn’t necessarily scream Innovative, especially during a brainstorming session where colleagues are throwing new ideas onto the whiteboard.

Second, subtractive solutions might be less attractive, particularly in a workplace setting, because they are more likely to involve downsizing, eliminating functions, or otherwise impact people’s livelihoods.

Finally, they offer the idea that concerns over sunk-costs might bias us toward adding rather than subtracting. While it’s certainly possible, my hunch is that this would have a greater impact in the decision-making phase rather than the ideation phase. However, if you know that the decision makers might be biased toward sunk-cost thinking, that could certainly impact the types of solutions that are offered.


The good news from the study is that our general tendency toward additive solutions can be mitigated by ensuring that subtractive solutions are welcomed. Several of the experiments showed that by including verbal and written clues that subtractive solutions were acceptable, the number of participants who opted for such solutions increased in a statistically significant way.

Repetition also helped. In one experiment, participants were shown a digital grid pattern consisting of 4 quadrants, each with a 5x5 grid. One quadrant had extra boxes shaded, and the participants were asked to make all 4 quadrants look the same.

On subsequent attempts, more and more participants realized that it was more efficient to remove shading from the anomalous quadrant, rather than to add shading to the other three.

Knowing that we can increase our likelihood of receiving additive and subtractive solutions by reiterating that both are acceptable is important. Be sure to use language that lets your employees know subtractive solutions are OK, and they’ll be more likely to consider or suggest them.

It’s especially important for managers to remember this when stress levels are high. Participants that were placed under higher cognitive loads were less likely to find subtractive solutions, even when those cues were provided. At times when they needed the more efficient option the most, the added environmental stress made them less likely to reach for them.


Where are some places that we can add by subtracting in our day-to-day as public managers?

  • Removing restrictions on Accessory Commercial Units might be an opportunity for supporting local small business growth, improving the environment, and creating more dense, walkable neighborhoods.

  • We might be able to encourage alternative transportation and more diverse development while strengthening our tax base by removing parking minimums.

  • Smaller pocket parks or neighborhood green spaces that can be walked to in favor of large, beautifully landscaped flagship parks that you have to drive to.

  • As we continue to struggle with the role of policing in America, one thing to consider is the shear volume of criminal laws on the books. @CrimeADay’s Twitter feed is a shrine to the absurdity of federal criminal law, but the fact that it would take more than 800 years to tweet one federal crime per day raises serious questions. Each law brings the potential for deadly encounters, and we might want to rethink whether we should have laws on the books that we aren’t willing to endanger the lives of our officers or the public to enforce.

  • Federal transportation planning is notorious for adding time and cost to any project with federal funds. And while there isn’t a lot that locals can do about that in the short term, shunning the “free money” that comes in the form of grants and matching funds in favor of locally-controlled projects with fewer strings might be a better long-term option for you.

At the end of the day, each community is different. Your mileage may vary (or, as the kids say, YMMV). The important thing is to encourage open dialogue where additive and subtractive solutions are freely welcomed. Subtractive solutions aren’t always the right way to go, but sometimes they are. If your organizational culture or management style is artificially limiting the world of possible solutions under consideration, it might be worth reflecting on how you can solicit a wider range of ideas.

Although this study showed that we have a tendency to focus on new and more, it also showed that with repetition and explicit reminders, we’re pretty good at adding by subtracting when the circumstances warrant it.


Around the web

Voters would have to approve police budget cuts under bill approved by Texas Senate (Texas Tribune)

While not as Draconian as some of the bills making their way through the Texas House, SB 23 would require an election be held before reductions in police spending could occur in years when the overall budget has not decreased, or if cuts to police spending were proportionally larger than overall budget cuts.

Cities need housing. Parking requirements make it harder (CityLab)

A bill introduced into the California legislature would eliminate parking requirements for new buildings built near public transit or in walkable neighborhoods, arguing that the move will help reduce housing costs.

Elon Musk is donating $30m to Brownsville schools and downtown revitalization (Business Insider)

The move caught the city by surprise, and it will be interesting to watch how SpaceX’s presence will impact Cameron County.


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