/* 

  Probability of winning an election - Trump vs Harris in Picat.

  What is the probability of Trump or Harris (or other) winning given forecasts,
  i.e. that they get more votes than the two other?

  From Nate Silver
  (as of writing 2024-11-03 @09:34, CEST)
  https://www.natesilver.net/p/nate-silver-2024-president-election-polls-model

  Probability of national winning;
  - Trump: 0.476
  - Harris: 0.485
  

  Cf
  - ppl_voting_probabilities.pi 
  - my Gamble model gamble_voting_trump_harris.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.

/*

  As can be noted, as the votes increases, the probability of Trump
  winning decreases.

[trump_prob = 0.476,harris_prob = 0.485,num_votes = 10]
var : trump
Probabilities (truncated):
5: 0.2458000000000000
4: 0.2261000000000000
6: 0.1732000000000000
3: 0.1452000000000000
.........
1: 0.0133000000000000
9: 0.0074000000000000
0: 0.0019000000000000
10: 0.0012000000000000
mean = 4.742

var : harris
Probabilities (truncated):
5: 0.2473000000000000
4: 0.2119000000000000
6: 0.1950000000000000
3: 0.1280000000000000
.........
1: 0.0129000000000000
9: 0.0070000000000000
0: 0.0017000000000000
10: 0.0009000000000000
mean = 4.866

var : other
Probabilities:
0: 0.6707000000000000
1: 0.2731000000000000
2: 0.0503000000000000
3: 0.0054000000000000
4: 0.0004000000000000
5: 0.0001000000000000
mean = 0.392

var : trump wins
Probabilities:
false: 0.6098000000000000
true: 0.3902000000000000
mean = 0.3902

var : harris wins
Probabilities:
false: 0.5721000000000001
true: 0.4279000000000000
mean = 0.4279

var : other wins
Probabilities:
false: 0.9999000000000000
true: 0.0001000000000000
mean = 0.0001

var : no win
Probabilities:
false: 0.8182000000000000
true: 0.1818000000000000
mean = 0.1818


[trump_prob = 0.476,harris_prob = 0.485,num_votes = 20]
var : trump
mean = 9.4554

var : harris
mean = 9.7577

var : other
mean = 0.7869

var : trump wins
mean = 0.4168

var : harris wins
mean = 0.473

var : other wins
mean = 0.0

var : no win
mean = 0.1102


[trump_prob = 0.476,harris_prob = 0.485,num_votes = 100]
var : trump
mean = 47.5925

var : harris
mean = 48.5407

var : other
mean = 3.8668

var : trump wins
mean = 0.4387

var : harris wins
mean = 0.5187

var : other wins
mean = 0.0

var : no win
mean = 0.0426


[trump_prob = 0.476,harris_prob = 0.485,num_votes = 1000]
var : trump
mean = 475.822

var : harris
mean = 485.102

var : other
mean = 39.0758

var : trump wins
mean = 0.3629

var : harris wins
mean = 0.6243

var : other wins
mean = 0.0

var : no win
mean = 0.0128

[trump_prob = 0.476,harris_prob = 0.485,num_votes = 10000]
var : trump
mean = 4759.72

var : harris
mean = 4850.24

var : other
mean = 390.043

var : trump wins
mean = 0.18

var : harris wins
mean = 0.818

var : other wins
mean = 0.0

var : no win
mean = 0.002

[trump_prob = 0.476,harris_prob = 0.485,num_votes = 100000]
garbage_collect_when = 10
var : trump
mean = 47597.3

var : harris
mean = 48501.2

var : other
mean = 3901.5

var : trump wins
mean = 0.004

var : harris wins
mean = 0.996

var : other wins
mean = 0.0

var : no win
mean = 0.0

*/
go ?=>
  TrumpProb  = 0.476,
  HarrisProb = 0.485,
  member(NumVotes, [10,20,100,1000,10_000,100_000]),
  println([trump_prob=TrumpProb,harris_prob=HarrisProb,num_votes=NumVotes]),
  reset_store,
  Parameters = cond(NumVotes==10,[show_probs_trunc,mean],[mean,garbage_collect_when=10]),
  run_model(1000,$model(TrumpProb,HarrisProb,NumVotes),Parameters),
  nl,
  % show_store_lengths,nl,
  fail,
  nl.
go => true.
  
  
model(TrumpProb,HarrisProb,NumVotes) =>
  OtherProb = 1 - TrumpProb - HarrisProb,
  [Trump,Harris,Other] = multinomial_dist(NumVotes,[TrumpProb,HarrisProb,OtherProb]),

  TrumpWins = check1((Trump > Harris, Trump > Other)),
  HarrisWins = check1((Harris > Trump, Harris > Other)),
  OtherWins = check1((Other > Trump, Other > Harris)),
  NoWin = check1((TrumpWins == 0,HarrisWins == 0,OtherWins == 0)),

  add("trump",Trump),
  add("harris",Harris),
  add("other",Other),
  add("trump wins",TrumpWins),
  add("harris wins",HarrisWins),
  add("other wins",OtherWins),
  add("no win",NoWin).