Monday, July 19, 2010

Which Commute Would You Prefer?

(1) Suppose you have a morning commute that averages 30 minutes. However, the travel time has a high variance. Twenty percent of the time, it takes 15 minutes. Another 20 percent of the time, it takes 45 minutes. The rest of the time, your commute lasts somewhere in between. You have no way of knowing in advance.

What is your optimal behavior? Do you allow 45 minutes, even though you'll be extremely early most of the time (about four days a week)? Do you allow 30 minutes and take your chances that you won't get fired on those days (about once a week) that you'll be 15 minutes late? Or do you do something else?

(2) Suppose instead that your morning commute is usually 30 minutes, but each day there is an X% chance that it will be 45 minutes.

Certainly, you should allow 30 minutes if X is sufficiently small (say, 0.02%); you shouldn't arrive 15 minutes early every day to avoid being late once every 20 years. For larger values of X, though, the risk of being late becomes too high, compelling you to allow 45 minutes. But what is the cutoff point?

(3) Suppose instead that your morning commute is always 45 minutes, without fail.

Each day, you are spending an average of 15 minutes longer commuting (30 minutes, if you count both morning and afternoon commutes) than under the first scenario, yet your schedule is predictable from one day to the next.

Note that you could always allow 45 minutes under all three scenarios and never be late. In the first two scenarios, on those days you arrive early, you could spend some of this time at the coffee shop, or on a park bench, or getting an early start at the office. Your options are wider for that excess time, compared with the third scenario, yet you have a feeling that you're wasting a lot of time by arriving early so often.

I bet many people, myself included, would prefer the third scenario, even though it means a longer expected commute and doesn't allow you the freedom to do other things on the days you are early.

6 comments:

Adam Gurri said...

This is a really interesting thought experiment. At first I thought there's no way I wouldn't choose the first one. But the more I thought about it the more I agreed with you that I'd probably prefer the third one.

It's sort of like the idea that Rule of Law is better than regime uncertainty, even if the law isn't very good, because as long as we know the rules of the game are predictable we can adjust our behavior accordingly.

I can plan the exact number of podcasts I need to fill every last minute of my commute if my commute is relatively stable.

Greg Finley said...

Yes, but the catch is, if you arrived early under scenario one, you could just sit in your car and listen to podcasts until it was time for work. You'd even save gas. Or you could do something else if you thought it was a better use of your time. Scenario one is better on all fronts, except it makes you feel like you're wasting a huge amount of time.

I guess the underlying thought is that people often prefer stable outcomes over unstable outcomes with higher expected values, though this is nothing new.

Adam Gurri said...

Fact of the matter is I basically have scenario 1 (though the time is longer) I usually get to work about 20 minutes early. But I prefer it because I can get to work as soon as I arrive and leave early by the amount of time I arrived early by, so it works out fine.

Greg Finley said...

Good point. I suppose you have to assume a rigid starting work time for the thought experiment to work.

Millsy said...

Hailing from the MD/DC area, I try to explain this problem to people in Ann Arbor where they complain about the 10 minute drive into downtown.

The strategy was always to give the full 45 minutes (or, in my case, 1.5 to 2 hours depending on when I left), as the place I worked had recently fired someone for showing up 3 minutes late two days in a row.

The trick was this: with DC traffic, if I left at 6:30 am, it takes about 40 minutes (give or take 10) when I only need to be there at 8. If I leave at 7 am, it would take 1 to 1.5 hours because everyone else leaves then as well, and I'd be a half hour late.

Luckily there was a Starbucks next door and I always brought a book. But waking up at 4:45 am for no good reason always got to me. Hence, I don't live/work there anymore.

Greg Finley said...

It's weird, right? If instead you had had to leave at 6:30 a.m. and drive 1 1/2 hours on the open highway with no traffic, you probably wouldn't have felt as bad about it.