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Infering a majority from a sample: The sawtoothed function phenomenon
Author(s) -
Rodgers Joseph Lee,
Price James M.,
Nicewander W. Alan
Publication year - 1985
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830300303
Subject(s) - phenomenon , sample (material) , probabilistic logic , function (biology) , population , voting , matching (statistics) , econometrics , mathematics , mathematical economics , statistics , demography , political science , sociology , biology , physics , evolutionary biology , politics , law , thermodynamics , quantum mechanics
The probabilistic phenomenon presented in this paper deals with decision making in living systems at the level of the organization, society, or supranational system. Decision‐making bodies often take votes even when some members are not present (given a quorum). But the probability of a sample's decision matching the population's is not an increasing function of sample size. The function is sawtoothed, and even almost complete voting bodies in some circumstances have high probability of making ‘incorrect’ decisions. These circumstances are delineated, and some of the mathematical properties of the sawtoothed function are indicated. It is shown that a quorum is a poor criterion for holding votes.