/* 

  Multinomial voting in Picat.

  From Mathematica MultinomialDistribution
  """
  There are two candidates in an election where the winner is chosen based on a 
  simple majority. 
  Each of n voters votes for candidate 1 with probability p1 and for candidate 2 
  with probability p2, where p1+p2<1, so that a voter may choose not to vote for either 
  candidate. When n=100, p1=p2=0.4, the probability of one swing vote is: 

    D = MultinomialDistribution(100 - 1, (0.4, 0.4, 1 - 0.4 - 0.4));
    Probability(x == y, (x, y, z) -> D)
    -> 0.0447288


  Probability that a winner won by one vote:

    Probability( Abs(x - y) == 1, (x, y, z) -> D)
    -> 0.0888996

  Probability that candidate 1 wins the election:
    Probability(x > y, (x, y, z) -> D)
    ->  0.477636
  """


  Cf my Gamble model gamble_multinomial_voting2.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.
% import ordset.

main => go.

/*

  var : x
  mean = 39.6598
  HPD intervals:
  HPD interval (0.84): 33.00000000000000..46.00000000000000

  var : y
  mean = 39.5486
  HPD intervals:
  HPD interval (0.84): 33.00000000000000..46.00000000000000

  var : z
  mean = 19.7916
  HPD intervals:
  HPD interval (0.84): 15.00000000000000..25.00000000000000

  var : p swing vote
  mean = 0.0449

  var : p won by one vote
  mean = 0.0842

  var : p candidate 1 wins
  mean = 0.4678


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[mean,
                           show_hpd_intervals,hpd_intervals=[0.84]
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  [X,Y,Z] = multinomial_dist(99,[0.4,0.4,0.2]),

  PSwingVote = check(X == Y),
  PWonByOneVote = check(abs(X-Y) == 1),
  PCandidate1Wins = check(X > Y),
  
  % add("V",[X,Y,Z]),
  add("x",X),
  add("y",Y),
  add("z",Z),
  add("p swing vote",PSwingVote),
  add("p won by one vote",PWonByOneVote),
  add("p candidate 1 wins",PCandidate1Wins).