File 03 — Beliefs
The Highlight Reel
Everyone posts the best of thirty days. You turned up with a Tuesday.
Everybody in this feed has exactly the life you have. Each of them posts the best day out of thirty; you open it on an ordinary one. Set how many days a post is the best of, how many people are posting, and how much better your life actually is than theirs, and watch where you rank: below all of it when you are identical, still below 99% of it when you are better than 84% of people, and only in the middle once you are in the top two percent of everyone alive. A post is an order statistic — the maximum of k draws — and the two-step gap comes out of that arithmetic with nobody lying. Every figure is a closed form, not a simulation. Grounded in Festinger, Gilovich’s spotlight experiment, and Jordan’s misery-has-more-company studies.
Everybody in this feed has exactly the life you have: the same spread of good days and bad. Each of them posts the best day out of a run. You open it on an ordinary one. Set how long the run is, how many people are posting, and — if you like — how much better your life actually is than theirs. Then see where you rank. Nobody is lying. The feed keeps the maximum, and the maximum of thirty ordinary days is a two-sigma day.
filled: the posts — everyone’s best of 30 days. dashed: all of your days, the unposted ones included; the shaded slice is the few that would clear the typical post. ticks: the feed itself, one per post, coloured where it lands above your day.
The feed
Seven hundred accounts, each posting its best day of the month. The typical post is a two-sigma day. To rank in the middle of this feed on an ordinary day you need to be in the top two percent of everyone alive.
the typical post sits at
+2.0
steps above an ordinary day — the median best-of-30, from a life no better than yours
of the feed above you today
all of it
on an ordinary day of yours behind
your days that clear the typical post
2.3%
about one in 44 — those are the ones you post
the best post in the feed
+4.0
the best of 21,000 days: a one in 30,000 day, somebody's, once
the price of feeling average
To rank in the middle of this feed on an ordinary day, your whole life would need to sit +2.0 steps above everyone else’s — the top 2.3% of all lives.
Right now your life is set to identical. Better than nobody, worse than nobody, and all of it of the feed is above you anyway. So is everyone else’s, when they open it — the feed is 700 people feeling behind in a room where nobody is.
Where this comes from. That people rate themselves against others when no objective yardstick exists is Festinger (1954). That the negative half of other people’s lives is kept private, and that people underestimate how common it is, is Jordan et al. (2011). That people overestimate how much anyone is looking at them by about a factor of two — 46% guessed, 23% observed — is Gilovich, Medvec and Savitsky’s spotlight effect (2000). The order-statistics arithmetic that turns those into a two-step gap is this page’s.
The honest catch. Everybody here has the same life, which is false, and days are normally distributed, which is a convenience. Both cut the same way: the gap appears with zero difference between people, so the identical case is the floor of the effect, not an estimate of it, and a fatter right tail on real good days would push every maximum further out, not closer in. What the model does not do is tell you who in the feed is actually doing better — a two-sigma day from an ordinary life and an ordinary day from a two-sigma life are the same photograph.