Everybody loves to read “ways” articles—about “4 ways to make your resume shine”, “3 ways to impress your boss”, “5 ways to better networking” and the like.

As I’ve argued before, in 5 Reasons Why We Like ‘5 Reasons Why…’ Analyses” , there are, in particular, some good reasons why “5 ways…” is especially appealing and common—mostly because of the fact that we have 5 fingers on which to conveniently count and remember them.

So, if starfish wrote HR articles, they would probably display a similar bias for 5 ways, e.g., “5 Killer Ways to Snag an Ideal Catch”.

Mathematical Hamlet

However, most appealing of all has to be making the number of ways as small as possible or at least as small as some symbolically or otherwise psychologically satisfying target number—yet especially 2, because it is the smallest number that suggests freedom of choice and therefore “free will”.

Hence, the freedom and choice-loving human mind being what it is, we’ll probably be interested in having more than one way to reduce the list to two ways, like Hamlet.

Accordingly, an article with the title “4 Ways to Reduce 3 Ways to Impress Your Boss to 2 ways” has got to grab the attention of ways-and-free-choice-minded existentialists who insist on having choice, free will and responsibility for both, but with as few clear-cut choices as possible—if only to avoid “existential clutter” in the form of “over-choice” of options, decisions and responsibilities.

But, in practice, how easy can it be to find 4 ways to reduce 3 ways to 2 ways—or, more generally, to find n ways to reduce p ways of doing X to r ways? 

If that question can be answered, it may be possible to extract from that analysis some general counting principle with terrific applications to ways-list creation or to ways of doing almost anything.

Moreover, the answer may shed additional light on the psychology, strategies and objectives of making lists of ways, in general.

Ways of Reducing Ways

Consider a very simple model involving rolling dice. Suppose we want to get a sum of 4 in a roll of 2 dice. There are, as combinations, 2 ways to do that: Roll a “1” and a “3”, or roll two “2”s.  But imagine that before we do that, we actually have 3 dice to roll, but still want to get a sum of 4.

That’s possible: roll a “1”, another “1” and a “2”. But that’s the only way. If, however, we remove exactly one of the dice from the toss—die #1, #2 or #3—we will have exactly three ways to be left with 2 ways to get the result we want. Hence, in this model, there are, in some sense, 3 ways to get 2 ways of getting the result we want.

To reduce 4 ways of getting 3 ways to get 2 ways of getting a sum of “4”, just add a fourth die and refrain from rolling one of the four. [Yes, I’m equivocating on the concept of “ways”, here—using it to mean mathematical sums on the one hand and dice selection on the other. But, both count as “ways” of doing something.]

Having illustrated even just one way there can be 4 ways of reducing 3 ways of doing something to 2 ways, I think the general principle can be understood: Yes, there can be n ways of reducing p ways of doing X to r ways of getting some result, through a process of “whittling’ of ways—even perhaps all the way down to existentially satisfying 2-ness.

So What?

But apart from that metaphysical consequence, so what? Metaphysical reassurances of our claims and aspirations regarding free will aside, what practical benefit can there be in knowing that this kind of reductive multi-step process is possible?

Consider this very concrete, practical recruiting scenario: You’ve got to prune your candidate list down to 2 “finalists”. Your HR manager has told you that in the time available that’s the manageable number for the final interview. But you sincerely believe you’ve got 10 great candidates. 

Now, you’ve got the challenge of finding a way or ways to reduce that field to the final 2.  You think you’ll be happy to find even one way to do that—until you reflect on it, and wonder whether the first way you find will also be the only or even the best way.

What you’ve realized is that you’ve got a qualitative challenge as well as a quantitative one: to not only reduce the numbers, but also to maximize or at least preserve the quality of those numbers.

You also realize that the first way of pruning the field may not be the wisest—just as the best way to reduce your payroll may not be to lay off essential personnel [instead, eliminating costly overtime pay or reducing general hours, across the board].

So, now you start to enumerate the ways available to you to reduce the candidate field to 2. For example, you identify four ways:

1. Lottery: literally picking the names out a hat

2. Reassigning weights to specific, established selection criteria, e.g., shifting more weight from personnel test scores to prior experience.

3. Adding new criteria, e.g., second-language competencies

4. Reassessing prior assessments, e.g., carefully reviewing notes and comments of your own, of other interviewers, of references and of the candidates themselves

Now you’ve got 4 ways of reducing 10 candidates to 2.

Although each of these 4 ways has its merits, it would be great if these could not only be reduced to a smaller number, but also reduced to the smallest set of optimal ways.

So, revisit the list of 4. The lottery method seems inferior to the others, despite its obvious “fairness”—that is, fairness, assuming that the initial rankings were impartial and otherwise well-grounded. That’s because despite its appearance of being a decision rule, it’s in fact a default option, to be exercised when decisive action is neither possible nor appealing.

Now we are down to three, having found one way to get there, viz., by an analysis of the concept of “real decision making” weighed against an analysis of “fairness”. But that’s not the only way to whittle down the four ways of whittling 10 candidates down to 2.

Consider the second way of accomplishing this: Eliminate #2, above, i.e., eliminate reassigning weights to previous criteria. Way #2 could be effective as a way to end up with only 2 candidates, but only if the reweightings are not arbitrary, are not biased, are not desperate ad hoc juggling, etc. So, pruning away way #2, from our list of 4, is a second way to reduce a field of 10 candidates to 2 finalists.

If you eliminate #1 and #2, for the reasons just given, you are left with 2 ways to reduce a field of 10 candidates to 2, namely, #3 and #4. Which survives the next cut depends on what matters more or seems smarter: adding new criteria or reassessing the assessments.

Either way, from beginning to end, the decision process involves finding n ways to reduce p ways of reducing X things, choices, etc., to r ways of choosing, doing, etc.

Without this concept, understanding and application of this multi-phase, decision-counting process, the likelihood of making the mistake of choosing the first and sub-optimal way to reduce options and ways that pops into one’s head vastly increases.

Exactly how many ways can making this mistake happen? I don’t know. But I do know one thing.

There’s no way you want that to happen.



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