Why the other queue moves faster and your friends have more friends

Observation is a sampling procedure

Every impression you form about how common something is comes from a sample, and that sample was collected by whatever put you where you were standing. Most of the time nobody chose the procedure, which makes it easy to treat the resulting impression as a plain observation about the world. It is not. It is an observation about the world filtered through the way you encountered it.

Survivorship is the famous case, where the filter is the outcome itself. The less famous cases are more common and harder to notice, because the filter is something structural about time, size or position that has no obvious connection to what is being judged.

The queue, worked through honestly

Two things are happening in the adjacent lane, and only one of them is interesting. The dull one is that with several lanes available, the chance that yours is the fastest isn’t high, so most of the time somebody is legitimately doing better than you. Nothing needs explaining there.

The interesting one is about how time is spent. When your lane is moving well you pass quickly and observe little; when it stalls you sit there accumulating observations of everybody overtaking you. Your sample of the experience is therefore weighted towards the periods when you were losing, and the memory of the journey is assembled from that weighted sample. The same logic applies to the crowded carriage, the busy hour and the slow checkout: you spend more of your life inside the congested instances, so congestion is over-represented in everything you remember.

Waiting times and the interval you landed in

A related effect shows up whenever you arrive at random into a sequence of intervals. You are more likely to arrive during a long gap than a short one, simply because long gaps occupy more of the available time, so the wait you experience is systematically longer than the average gap between events.

This means a service can be entirely truthful about its average interval while nearly everybody using it waits longer than that figure. Nobody is misreporting anything. The average is computed over intervals and your experience is sampled over time, and those are two different populations that only coincide when every interval is identical.

The one about friends

On average, your friends have more friends than you do. This sounds like an insult and it’s a mathematical near-certainty in almost any social network, for a reason that has nothing to do with you: people with many connections appear on many lists, and people with few appear on few, so any sample assembled by following connections over-represents the well-connected.

The same structure produces several familiar mismatches. Most people attend classes larger than the average class size, because more people are in the large ones. Most people work in organisations bigger than the average organisation. In each case the institutional average is computed per unit and your experience is sampled per person, and the difference between those two denominators is doing all the work.

Where this stops being a curiosity

It stops being a curiosity as soon as somebody draws a conclusion from an impression. A clinician who sees the cases that come back has a sample selected by not getting better. A manager who hears about the projects that went wrong is sampling on escalation. Anyone judging how common a problem is from the complaints received is sampling on the propensity to complain, which varies enormously and isn’t evenly distributed across the population of the affected.

The characteristic error isn’t believing something false about the cases you saw. Those observations are usually accurate. The error is treating them as a picture of the population when they were drawn by a mechanism correlated with the very thing being estimated.

The question to keep asking

How did this case come to be in front of me? That single question catches most of these, because the answer is usually available and usually reveals the filter. Somebody chose to tell me. It lasted long enough to be noticed. It was large enough to contain me. It failed in a way that produced a record.

Where the filter can be named, the correction is sometimes possible — weight by size, count intervals rather than time, go looking for the cases that would not have reached you. Where it cannot, the honest move is to keep the estimate and attach the filter to it in writing, so that a later reader knows what the number is a sample of. That is a much weaker remedy than fixing the bias, and it is considerably better than presenting the impression as a measurement.