Binstack: Making a maximal multi-dimensional decision
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By Jason Cohen on
July 2, 2022
Reading time: 16 min
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Binstack: Making a maximal multi-dimensional decision
by Jason Cohen on July 2, 2022
Binstack is a technique for selecting the “single most impactful” solution when there are multiple, incomparable dimensions to evaluate.
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Many decisions in life and business are instances of “multi-dimensional maximization,” in which we wish to pick the “single best” among a set of choices, but we’re confounded because each choice is variously better or worse along different dimensions.
Examples:
Which major feature should we spend the next six months building?<br>(P would generate revenue, but Q would reduce cancellations, but R would save us money)
Which candidate should we hire?<br>(P has the best skills, but Q has more experience in our market, but R seems like the best culture-fit)
Which new marketing campaign should we spend thousands of dollars to test?<br>(P is cheaper to try, but Q has a larger reach, but R is targeted at our industry)
Not only do you need the best decision, you also need to be able to explain your decision to others , especially to those who wish the decision had gone a different way. Do not under-value the importance of crisp explanation.
The “rubric” is the typical framework for these decisions; a separate paper on this site explains how to use one effectively for “ROI-style” decisions.1 Unfortunately, while it may feel productive to fill many cells with many numbers, and while it may feel analytically rigorous to convolute those numbers into a final score, this fails to clearly identify the best choice, and fails to create a clear explanation for the choice.
After demonstrating and analyzing the causes of this failure, I present an alternative framework I’ve nicknamed “Binstack.”2
The goal of ROI is to maximize efficiency, i.e. deliver the most amount of value per unit of time. This paper asks a different question: How to decide the single most valuable thing, regardless of cost, with incommensurate and conflicting dimensions
Additional resource:<br>Adam Waselnuk created a<br>Notion Process Template for Binstack.
Why rubrics don’t add up
Consider two players in a game, with attributes:
Attribute<br>Player P<br>Player Q
Health
Strength
Speed
Endurance
Which player is better? If one scored higher than the other in every dimension, the choice would be simple. In this case, each player is better than the other along two dimensions, and worse along two; objectively there’s no clear winner.
So let’s try a rubric. In its simplest form, we add up the scores contributed by each dimension, and the total score decides the winner. Unfortunately, this doesn’t tell us which one is better:
Attribute<br>Player P<br>Player Q
Health
Strength
Speed
Endurance
Total:<br>20<br>20
Games often engineer this result on purpose, to create players that are different but not over-powered. This creates a balanced game, but to make a confident decision about which one is “best,” we need something imbalanced.
Real-life rubrics often look like this example: a pile of options that share a similar score, resulting in no clear winner. Even if we make a decision, we can’t explain the decision to others, because in actual fact it’s a tie, and the tie was broken arbitrarily. That’s no way to make a decision.
To create separation, people often add “weights” to the raw value to create a new kind of “score.” In this case, suppose that with our game-playing style we don’t care much about Speed, but we can really leverage Strength. So we assign weights which we multiply against the scores, to compute a customized metric of “value.”
Attribute<br>Orig P<br>Orig Q<br>Wt<br>Wted P<br>Wted Q
Health<br>1.0
Strength<br>2.0<br>10<br>14
Speed<br>0.5
Endurance<br>1.0
Total:<br>20<br>20
24<br>24
That didn’t help. What if we contrive to force Q to be better, by intentionally using weights that penalize the two attributes where P is superior?
Attribute<br>Orig P<br>Orig Q<br>Wt<br>Wted P<br>Wted Q
Health<br>0.5<br>2.5
Strength<br>2.0<br>10<br>14
Speed<br>0.5
Endurance<br>0.5<br>2.5
Total:<br>20<br>20
17.5<br>20.5
Even with a conspiracy to throw the election for Q, it wins by a mere 2.5 points out of 20—hardly a resounding victory that would give everyone confidence in the decision.
This happens in the real world. Even with weights, a clear winner often does not emerge, and again we’re back to a weak, indefensible decision.
Worse: In the real world we rarely have precise scores. Attributes like “potential new revenue” and “increased customer satisfaction” are not predictable with accuracy. For more qualitative measures we use scales “from 1 to 5” which are even less precise. This imprecision creates inherent error, which is then compounded by multiplying weights. Differences in the final results are more error than signal.
Worse again: The attributes aren’t comparable. Whatever the unit of measure for “Health,” it...