A Case of Decision-Making Under Uncertainty

(Or, how my husband and I spent our vacation developing decision aids)

By Linnea Gandhi (TGG Group)

At 4:30 AM on Sunday, January 24th, my husband and I faced one of the toughest decisions of our married lives:

Should we call United Airlines now and confirm one spot on the upgrade list, or take our chances later trying to persuading the airport representative to get us two spots, risking getting zero in the process?

Roll your eyes all you want; this was a major decision-making-under-uncertainty dilemma—or at least it felt like one on that early morning in January! Let me explain...

~~~

Last summer we booked tickets for a long-overdue trip to Mumbai to visit our extended family. The flight is sixteen hours, so we cashed in my husband’s hard-earned upgrades from his past life as a consultant…but the upgrades didn’t clear. When we called customer service, their answer was to wait a few weeks and call back. Which we did, only to get the same response.

This cycle repeated itself over our several-month wait. The more effort we put in, the more we wanted our upgrades. A brief respite came when we cleared for the outbound flight just hours before the trip. Of course, we still had the return to worry about, and worry we did! Throughout our trip, we checked the upgrade list whenever we could find a wireless connection and called United daily, hoping for good news. It was an out-of-control amalgamation of effort justification and sunk costs, and as we neared the final 24 hours pre-flight, no one was in the mood to think rationally.

So around midnight on the 24th, when we saw a chance to switch to an earlier flight home that landed with enough time to get real sleep before work on Monday, we jumped on it. No one wants to sit by and wait for fate to deal them a bad hand when they can act on it, right? Action bias to the rescue!

Well, sort of. Only hours later, Winter Storm Jonas cancelled that flight. We luckily got back on our original flight, but now off the coveted upgrade list. (To boot, had we not jumped ship early, we both would have been upgraded on that original flight. We doubly kicked ourselves, for our premature switch and unhelpful hindsight bias.)

Which brings me back to 4:30 AM on that same fateful day. It was a classic case of decision-making under uncertainty, worsened by very little sleep.

With only hours between us and our in-flight fate, we faced two risky options: 

  1. We could call now and get my husband – but not me, given my laughably low status – back on the upgrade list. If a seat opened in business, at least he had a shot at getting it.
  2. Or, we could wait to try and persuade an airport representative to put us both on the upgrade list. But we might still end up with only him on the list or, worse, on the list and farther down because we waited.

I won’t lie – the behavioral science geek in me saw at once that I needed a decision aid to deal with all this uncertainty! Could my sleep-deprived brain slap together something to make this process easier and more rational? Maybe.

I started by thinking through the possible outcomes and what my utility – on a made-up scale of 1 through 10 – would be in each. Human as I was, my outcomes included not just whether we got upgraded, but also whether we had missed out on a better opportunity, a.k.a., regret.

The question then became estimating the probability of each outcome. First, how likely was it that zero, one, or two seats opened up? And how likely was it that neither, one, or both of us were high enough on the list to get those seats? I cobbled together a probability matrix of sorts, filling cells with the corresponding outcome’s utility. (E.g., if one seat opens and one of us was at the top of the upgrade list, then my utility would be “8”, but if two opened and neither of us was at the top, then my utility would be a terrible “1”.)

I proudly showed these sketches to my husband. For 4:30 AM, on little sleep, your wife is pretty darn smart, huh?

If you’ve ever met my husband, you can guess his reaction. A rational “Econ” if there ever was one, he took one look at my scribblings and sighed. First of all, what was this “regret factor”? Why should missed opportunities matter? And second, how was all this supposed to help us picking between calling now and negotiating at the airport?

His turn with the pen, he got to scribbling and, like a good economics major, he calculated out the expected value of each option. This essentially meant estimating the utilities of potential outcomes (both, one, or neither of us getting upgraded) and the probabilities of these outcomes under the “call now” and “wait to negotiate” options.

I’ll spare you the math. Turns out we got a 5.43 expected utility (out of 10) from calling now and guaranteeing him a spot on the upgrade list. And if we waited to negotiate at the airport, we got…a 5.46 expected utility.  In other words, it was a complete wash either way.[i]

Don't bother trying to read this--my husband may be more rational, but at least I have better handwriting!

Don't bother trying to read this--my husband may be more rational, but at least I have better handwriting!

So, at 5:00 AM, what did we do? We went back to sleep, waiting to try our luck at the airport. Essentially, we gave in to our Human irrationalities: We didn’t want to wonder whether we had passed up the opportunity for a better outcome negotiating an upgrade for both of us on the list. The small chance that waiting meant neither of us got upgraded felt negligible compared to the (equivalently!) small chance that not waiting made us miss out on that far greater upside. (Perhaps we should have plotted out our loss function...)

~~~

It was 9:00 PM, Sunday January 24th, and we were both in coach, figuring out movies to pass the next sixteen hours together. While we failed to get me onto the upgrade list, my husband was there and surprisingly at the top. Unfortunately, no seat had opened up…

…until, as we were about to taxi to the runway, a flight attendant came to whisk my husband away to a haven of free drinks and fully reclining seats.

Thus, almost happily, ends the story of how we overcame one of the toughest decisions of our thus-far blissfully married lives together. (And it continues to be blissful, because he switched seats with me halfway through the flight. I guess he isn’t a full Econ after all!)


[i] The mathematical equivalence of the two options was mostly driven by the fact that, if we waited for the airport, we still had a 70% chance of being in the same situation as if we had called immediately. Further, the false precision of our utility scale didn’t help, given the close utilities of sitting together in coach (“at least we’re together”) and splitting eight hours each upgraded (“at least we get some time in fancy-land”).