/* 

  Fairness Hiring model 1 in Picat.

  Port of SPPL model
  https://github.com/probcomp/sppl/blob/master/examples/fairness-hiring-model-1.ipynb

  The SPPL model gives the following exact probabilities:
    p_hire_given_minority:0.007131626828051439
    p_hire_given_majority:0.01945024229170891
    min/maj: 0.3666600508668959

  Cf my Gamble model gamble_fairness_hiring_model1.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.

main => go.

/*

  var : ethnicity
  Probabilities:
  majority: 0.8454144973968762
  minority: 0.1545855026031238
  mean = [majority = 0.845414,minority = 0.154586]
  variance = data is not numeric

  var : years experience
  Probabilities (truncated):
  7: 0.1981377653183821
  8: 0.1925310372446936
  9: 0.1558870644773729
  6: 0.1537845414497397
  .........
  2: 0.0029034841810172
  1: 0.0007008410092111
  14: 0.0005006007208650
  0: 0.0001001201441730
  mean = 7.49449
  variance = 3.74997

  var : college rank
  Probabilities (truncated):
  49.589704274016711: 0.0001001201441730
  49.538496951104001: 0.0001001201441730
  49.228464184050551: 0.0001001201441730
  49.195901413091832: 0.0001001201441730
  .........
  -17.95497845657637: 0.0001001201441730
  -18.22337127077008: 0.0001001201441730
  -19.110980446795047: 0.0001001201441730
  -21.951826220603145: 0.0001001201441730
  mean = 20.7039
  variance = 51.118

  var : hire
  Probabilities:
  0: 0.9775730877052463
  1: 0.0224269122947537
  mean = 0.0224269
  variance = 0.0219239

  var : hire ethnicity
  Probabilities:
  [0,majority]: 0.8249899879855827
  [0,minority]: 0.1525830997196636
  [1,majority]: 0.0204245094112936
  [1,minority]: 0.0020024028834602
  mean = [[0,majority] = 0.82499,[0,minority] = 0.152583,[1,majority] = 0.0204245,[1,minority] = 0.0020024]
  variance = data is not numeric

  var : hire given minority
  Probabilities:
  0: 0.9979975971165399
  1: 0.0020024028834602
  mean = 0.0020024
  variance = 0.00199839

  var : hire given majority
  Probabilities:
  0: 0.9795754905887064
  1: 0.0204245094112936
  mean = 0.0204245
  variance = 0.0200073

  [min = 0.0020024,maj = 0.0204245,min/maj = 0.0980392]


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,variance]),
  nl,
  Store = get_store(),
  HireGivenMinority = Store.get("hire given minority").mean,
  HireGivenMajority = Store.get("hire given majority").mean,

  println([min=HireGivenMinority,maj=HireGivenMajority,"min/maj"=(HireGivenMinority/HireGivenMajority)]),
  % show_store_lengths,
  % fail,
  nl.
go => true.
  
  
model() =>
  Ethnicity = categorical([0.15,0.85],[minority,majority]),
  YearsExperience = binomial_dist(15,0.5),
  CollegeRank = cond(Ethnicity == minority, laplace_dist(25, 5), laplace_dist(20,5)),
  
  % Top 50 colleges and at most 20 years of experience.
  observe(CollegeRank <= 50),
  observe(YearsExperience <= 20),

  % Hiring decision (from the underlying decision tree)
  Hire =  cond(CollegeRank <= 5,
               1,
               cond( (YearsExperience-5) > CollegeRank,
                     1,
                     0)),
  HireGivenMinority = cond((Hire == 1,Ethnicity == minority),1,0),
  HireGivenMajority = cond((Hire == 1,Ethnicity == majority),1,0),

  % observe(Ethnicity == minority),
  % observe(Ethnicity == majority),

  if observed_ok then
    add_all([ ["ethnicity",Ethnicity],
              ["years experience",YearsExperience],
              ["college rank",CollegeRank],
              ["hire",Hire],
              ["hire ethnicity",[Hire,Ethnicity]],
              ["hire given minority",HireGivenMinority],
              ["hire given majority",HireGivenMajority]
              ])
  end.