simulation of algorithmic fairness

algo-fairness.R

library(tidyverse)

set.seed(1)
sims <- map(1:200, function(x) {
  
  intercept = -runif(1)/2
  beta_male = runif(1)/4
  beta_smoker = runif(1)/4
  
  dat = 
    data.frame(male = sample(c(0, 1), 1000, replace = T)) %>%  # female: 0, male: 1; makes coding easier
    rowwise() %>% 
    mutate(smoker = as.integer(runif(1) < 0.1 + male * 0.1)) %>% 
    mutate(mortality_logit = intercept + male * beta_male + smoker * beta_smoker) %>% 
    mutate(mortality_prob = boot::inv.logit(mortality_logit)) %>% 
    mutate(observation = as.integer(runif(1) < mortality_prob))
  
  # include gender
  mod_gender = glm(observation ~ 1 + male + smoker, dat, family = "binomial")
  
  # dont include gender
  mod_fair = glm(observation ~ 1 + smoker, dat, family = "binomial")
  
  
  dat_with_pred = dat %>% 
    ungroup %>% 
    mutate(risk_gender = predict(mod_gender, ., type = "response")) %>% 
    mutate(risk_fair = predict(mod_fair, ., type = "response")) 
  
  dat_with_pred %>% 
    group_by(male, smoker) %>% 
    summarize_at(vars(mortality_prob, risk_gender, risk_fair), mean) %>% 
    mutate(error_gender = risk_gender - mortality_prob) %>% 
    mutate(error_fair = risk_fair - mortality_prob) %>% 
    ungroup
}) 


sims %>% 
  reduce(bind_rows) %>% 
  group_by(male, smoker) %>% 
  summarize_all(mean)