Double Jeopardy Law

The double jeopardy law is one of marketing's most durable empirical regularities: smaller brands have far fewer buyers, and those buyers are also slightly less loyal — they buy the brand a little less often and are a little less attached. The 'twice' is the jeopardy. Sociologist William McPhee named the pattern in 1963 (observing it in awareness of Hollywood actors and radio presenters), and Andrew Ehrenberg showed it generalizes to brand purchasing, where it has held across categories, countries, and decades since.

The law's content is the linkage: loyalty metrics — purchase frequency, repeat rates, attitudinal attachment — move with market share, differing far less between brands than buyer counts do, and in the direction that compounds the leader's advantage. Ehrenberg's Dirichlet model of repeat buying supplies the mathematical engine: in markets where buyers have steady propensities and brands compete for the same population, the size-loyalty link falls out of the arithmetic rather than from any brand's virtue. The strategic implications are the Ehrenberg-Bass canon this glossary's CATEGORY BUYERS and BRAND PENETRATION entries carry: brands grow primarily by acquiring more buyers (penetration), not by deepening loyalty, because the loyalty differences available to win are small and themselves size-linked; loyalty programs cannot lift a small brand to big-brand loyalty numbers, since the deficit is a symptom of share, not a cause; and benchmarking loyalty metrics against bigger competitors mostly measures the size gap (a small brand with leader-grade loyalty is the anomaly worth investigating, not the plan). The law also disciplines interpretation: when retention or frequency trails the category leader's, double jeopardy is the null hypothesis to rule out before diagnosing program failure. Exceptions exist at the margins — niche brands with unusual loyalty for their size, the 'natural monopoly' wrinkle where big brands over-attract light buyers — and they are studied precisely because the baseline holds so widely.

Double jeopardy matters whenever loyalty metrics get compared, targeted, or budgeted against — which is every brand tracker and retention review. It matters most as protection against two expensive mistakes: loyalty programs tasked with closing gaps that are share symptoms, and growth plans that prioritize squeezing the base over expanding it. The discipline is to read loyalty metrics share-adjusted, treat penetration as growth's primary lever, and let the law set expectations — a brand's loyalty numbers are mostly its size, measured twice.

William McPhee coined 'double jeopardy' in 1963, finding that lesser-known Hollywood actors were both known by fewer people and liked slightly less by those who knew them; Andrew Ehrenberg showed the same arithmetic governs brand buying, and his Dirichlet model made the size-loyalty link one of marketing science's few laws — the foundation the Ehrenberg-Bass school built on.

Etymology: source.

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