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Aleatory contract
exchanging a certain cost in the present for an uncertain gain in the future (lottery ticket, annuity payment, insurance); expectation value
Probability of A and B
P(A ∩ B) = P(A|B) · P(B) where P(A|B) is the probability of A given that B happens (or holds)
Probability of A or B
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Probability of A
P(A) = # of favorable events/# of possible events
Bayes’ Theorem
P(X|E) = (P (E|X)/P (E))*P(X); Used to reevaluate (“update”) probability in light of new evidence
Expectation value
(probability of event) · (value of event)
Fourteenth Amendment
1868 as a part of Reconstruction era: rights of citizens (including former slaves)—no discrimination was allowed on basis of “color” because “equal protection”
Title VII of 1964 Civil Rights Act
Part of 1964 CRA where Equal Employment Opportunity is established; no discrimination of protected groups of race, color, religion, sex, or national origin
Equal Employment Opportunity Commission (EEOC)
Government body that handles employment discrimination cases
Disparate impact
Term in employment discrimination cases to refer to a policy or practice that adversely impacts one protected group; after Griggs v. Duke Power Co, Court determines CRA is about consequences and impact, not intent; other examples include Hazelwood School District v. US Supreme Court, Castaneda v. Partida
80% Rule
Rule for determining disparate impact where the selection rate for the protected group (sex, race, etc.) must be less than 80% of the selection rate of the group with the highest rate
Griggs v. Duke Power Company (Supreme Court, 1971)
Employment discrimination case where Black employees sued due to use of promotion aptitude tests; landmark case where Supreme Court decides in favor of Griggs and thus establishes CRA is about consequences and “disparate impact”, not intent
Clinical prediction
focused on decision maker and getting the person right; requires more money and experts’ discretion, is open to more factors, and contains more nuance
Statistical prediction
focus on rule-maker and getting the rule right; is cheaper, framed around a set of pre-determined rules with limited set of factors
Smith v. Rapid Transit (1945)
Case study of statistical interpretation of evidence in courtroom; woman sues bus company after run off road by blue bus without seeing company name at 1am on 2/6/1941
People v. Collins (1968)
Case study of statistical interpretation of evidence in courtroom; robbery with eye-witness account of partly yellow automobile, man with mustache, woman with ponytail, woman with blond hair, Negro man with beard, interracial couple in car; statistician says 1 in 12,000,000 chance that the defendant is innocent
Sears, Roebuck & Co. v. City of Inglewood (CA Superior Court, 1955)
Case study of statistical evidence in court; Sears overpaid local sales tax because of mistaken town boundary and tries to calculate amount owed through random sampling; court says they cannot use sampling, must go through all 826 days by hand
Castaneda v. Partida (Supreme Court, 1977)
Case study of discrimination case; Rodrigo Partida argues grand jury selection in Hidalgo County, TX (majority Mexican-American) discriminates against Mexican-American; Court decides there is not a large enough statistical disparity and uses “governing majority” argument
Hazelwood School District v. United States (Supreme Court, 1977)
Discrimination case brought against district by Attorney General; 2% of district's students were black in 1972-1973, First black teacher hired in 1969. By 1973, 22 of 1231 or 1.8%. In St. Louis County, 15.4% of all faculty were black whereas in St. Louis County excluding city, 5.7% black; Supreme Court ruled that right comparison was instead with racial composition of the qualified teacher population in the relevant labor market
Use of COMPASS in parole decisions
COMPASS is a Northpointe software used to create risk assessment scores for parole, bond amounts, sentencing and more; discourse about the different scores for white vs. Black defendants and possible discriminatory nature of COMPASS
Williams v. Florida (1970)
Jury size case where court rules 12 jurors has been the historical standard, but no reason other sizes couldn’t work
Ballew v. Georgia (1978)
Jury size case where court rules five person jury is too small, but 6 is okay; positive correlation between size and performance, as size increases, so does minority representation, and under 6 jurors, chances of error in conviction increase
Ramos v. Louisiana (2020)
Guarantees right to unanimous verdict in criminal trials