How to Make Impossible Decisions


It's not uncommon for a group trying to come to an agreement to instead reach an impasse, where they can't seem to close on a decision that satisfies a majority of the group. The problem may not be that those involved haven't explored the issues deeply enough, they haven't necessarily overlooked different ways of approaching the decision, nor are those involved failing to be rational. Instead, they are possibly trapped in a strange corner of game theory mathematics.

The economist Ken Arrow characterized this situation in his grandiose-sounding 'impossibility theorem'. Imagine the situation where three executives have interviewed three candidates for a director-level job. The president, Lou, favors Sarah Jones for the Chief Marketing Officer job, followed by Arran MacNeil, and last, Marguerite Obayo. The COO, Sue, and the CFO, Stu, have completely different orderings of the candidates than Lou and also don't agree with each other, either.

It may not be obvious at first glance, but these three rows have a surprising property: there is no candidate that has a majority of votes for the job. When Lou proposes Sarah Jones for the job, both Sue and Stu prefer other candidates. If Sue proposes Arran, both Lou and Stu would disagree.

This is a sort of rock-paper-scissors paradox since there is no pure winner. Note that there is no clear loser either.

And if the president decides to make the decision unilaterally he might appear to be doing so over the objections of the others involved in the decision.

It turns out, mathematically, that three participants and three options lead to the smallest-sized table of the impossibility theorem, but the situation arises with larger groups and more options, as well. And Arrow proved that there is no way to tweak the voting -- by, for example, allocating points to alternatives -- so that the problem goes away.

So, how can we manage the impossible?

One technique that can sometimes break an impossible deadlock is to add additional voters. Perhaps the Chief Product Officer and the VP of Sales could be invited to interview the candidate, and that might change the voting. Here's how that could change things:

figure 2 - With more voters

The contest lands on Sarah Jones and Marguerite Obayo, which is a simple choice between the two candidates. With Arran out of the picture, Sue's first choice becomes Marguerite, and she ends up with three first-choice votes.

Similarly, adding a fourth candidate for the job might break the deadlock, but it's not assured.

Bob Frisch, in When Teams Can't Decide, outlines ways to counter the deadlock built into impossible decisions.

Articulate clearly what outcome you are seeking -- The executives considering a new CMO may not be aligned with what the new CMO is supposed to accomplish. Does the company plan to enter new markets, roll out new products to established markets, or double down on the status quo? Deciding on the strategic context could change the voting of the executive team. Imagine that the goal hadn't really been established, but through an active process of exploration, it becomes clear that the strategy should be to roll out new products to established markets, an area in which Marguerite seems to have the best background. Thereafter, she becomes the first choice for all three execs.

Break the decision into smaller pieces -- I once worked with a software company that had three co-founders, and they were deadlocked on a repositioning away from the company's initial name, and it was basically the impossibility theorem at work, with the options being 1/ retain initial brand, 2/ adopt new spin #1, or 3/ adopt new spin #2.

figure 3 - Rebrand or no?

Once a straightforward vote led to a deadlock, the way out was to winnow down the choices.

I led a session looking just at the pros and cons of the two new spins. The founders voted, new spin #1 won over new spin #2, and we were then left with a binary decision: new spin #1 or the initial brand. Two of the founders wanted to rebrand the company, and there we were.

Worth noting that I acted as a devil's advocate for breaking the problem into two problems, which hadn't occurred to the founders. I was unaware of the impossibility theorem at the time, but intuitively found an escape hatch.

And the company is now valued at over $1 billion. Which I take sole credit for (LOL).

Take enough time

Important decisions should be given the time necessary to deliberate on the decision.

The decision to add the additional executives to the CMO decision may have effectively doubled the level of management time invested and extended the time frame of the deliberations. So be it. A better decision — and avoiding the president-as-dictator making a unilateral decision not shared by a majority of the deciders — is worth it.

In the case of trying to attack the deadlock by distilling the strategic intent of the CMO near-term mission, that effort may have led to a similar additional investment of time. But strategic clarity is important in and of itself, and certainly critical in the hiring decision.

In my work with the unnamed software company, what might have been a day or so of discussion became a week, since the hard work of deciding which of the two new spins was best had been postponed, and rolled up with the fundamental alternative of 'do nothing'.

But deciding to take the time needed to make a decision is perhaps the most important decision of all.

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