Where does expectancy collide?

In mathematics, the probability-weighted average of the values a random quantity can take, so that every possible outcome contributes its value times its probability. Huygens set out the idea in 1657 in De ratiociniis in ludo aleae, reasoning about the fair value a gambler should assign to an uncertain stake and building on the 1654 exchange between Pascal and Fermat; the concept was later placed on axiomatic footing in Kolmogorov's 1933 Grundbegriffe der Wahrscheinlichkeitsrechnung. Here the referent is a single number computed from a distribution, the long-run average of many repeated draws, not the number of years a person is likely to live and not a belief that effort will pay off.[1]

Unit

A number in the units of the random variable, its distribution-weighted mean

Recovery means

Not applicable

Measured by

Computed as the sum or integral of each value weighted by its probability, or estimated by the average of repeated observations

In demography, the average number of additional years a person of a given age can expect to live, read off a life table that records how a population thins out with age. John Graunt began the statistical study of death in 1662 with Natural and Political Observations ... upon the Bills of Mortality, and Edmond Halley built the first true life table in 1693 from the birth and burial records of the city of Breslau, from which such expected durations are calculated. Here the referent is a summary of a whole population's death rates expressed in years of remaining life, not the mean of a random variable and not a worker's belief about effort and reward.[2][3]

Unit

Years of remaining life, averaged over people alive at a given age

Recovery means

Not applicable

Measured by

Derived from age-specific death rates in a period or cohort life table, often reported as life expectancy at birth

In psychology, a person's belief about how likely an action is to bring about a given result, and in work motivation the belief that effort will lead to successful performance. Edward Tolman introduced expectancy as a cognitive construct in 1932 in Purposive Behavior in Animals and Men, arguing that behaviour is guided by learned expectations rather than blind habit, and Victor Vroom placed it at the centre of work motivation in 1964 in Work and Motivation, where motivation depends on the expectancy that effort yields performance and that performance yields valued outcomes; Van Eerde and Thierry's 1996 meta-analysis weighed the supporting evidence. Here the referent is a subjective probability held in one person's mind and measured by self-report, not a mathematical average and not a population count of years.[4][5][6]

Unit

A subjective probability, typically rated from zero to one or on a survey scale

Recovery means

Not applicable

Measured by

Assessed by self-report survey items about the perceived link between effort, performance, and outcomes