*********
Example 5
*********

------
Input:
------

profile with 23 voters and 4 candidates:
 3 x {a, b},
 6 x {a, d},
 4 x {b},
 5 x {c},
 5 x {c, d}

----------------------------------
Proportional Approval Voting (PAV)
----------------------------------


Optimal PAV-score: 19

1 winning committee:
 {a, c}

-------------------------------------------------
Sequential Proportional Approval Voting (seq-PAV)
-------------------------------------------------


starting with the empty committee (score = 0)

adding candidate number 1: d
 score increases by 11 to a total of 11

adding candidate number 2: c
 score increases by 15/2 to a total of 37/2

1 winning committee:
 {c, d}

PAV-score of winning committee(s):
 {c, d}: 37/2


------------------------------------------------------------
Reverse Sequential Proportional Approval Voting (revseq-PAV)
------------------------------------------------------------


full committee (4 candidates) has a total score of 30

removing candidate number 1: a
 score decreases by 9/2 to a total of 51/2

removing candidate number 2: b
 score decreases by 7 to a total of 37/2

1 winning committee:
 {c, d}

PAV-score of winning committee: 37/2



*****************************************************
Example from Janson's survey (Example 13.3) / Thiele:
*****************************************************

------
Input:
------

weighted profile with 10 voters and 4 candidates:
 960 x {a, c, d},
 3000 x {b, c, d},
 520 x {b, c},
 1620 x {a, b},
 1081 x {a, d},
 1240 x {a, c},
 360 x {b, d},
 360 x {d},
 120 x {c},
 60 x {b}
total weight: 9321

----------------------------------
Proportional Approval Voting (PAV)
----------------------------------


Optimal PAV-score: 9651

1 winning committee:
 {a, b}

-------------------------------------------------
Sequential Proportional Approval Voting (seq-PAV)
-------------------------------------------------


starting with the empty committee (score = 0)

adding candidate number 1: c
 score increases by 5840 to a total of 5840

adding candidate number 2: a
 score increases by 3801 to a total of 9641

1 winning committee:
 {a, c}

PAV-score of winning committee(s):
 {a, c}: 9641


------------------------------------------------------------
Reverse Sequential Proportional Approval Voting (revseq-PAV)
------------------------------------------------------------


full committee (4 candidates) has a total score of 30063/2

removing candidate number 1: a
 score decreases by 4581/2 to a total of 12741

removing candidate number 2: c
 score decreases by 3100 to a total of 9641

1 winning committee:
 {b, d}

PAV-score of winning committee: 9641

