Why is the victory threshold eight votes?
The victory threshold in choice voting derives from a straightforward
formula that identifies the fewest number of votes that only the winning
number of candidates can obtain. In percentage terms, the victory
threshold equals:100
______________ % + 1 vote
(seats elected) + 1
For instance, if electing ONE candidate (like a mayor), here's how the formula determines the victory threshold
100 100
______ % + 1 vote = ____ + 1 = 50% + 1
(1 + 1) 2
This of course is obviously true. A candidate is sure win once he or she receives an absolute majority of 50% plus one of the votes. Two candidates could each win 50%, but only one can win 50% plus one.
If electing NINE seats, here's how we determine the victory threshold.
100 100
______ % + 1 vote = ____ + 1 = 10% + 1
(9 + 1) 10
Consider that if nine candidates win 10% plus one, that collectively is 90% plus nine. While 10 candidates could earn 10% of the vote, only nine can win 10% plus one vote.
In the video, we are electing THREE seats, the victory threshold is 25% plus one.
100 100
______ % + 1 vote = ____ + 1 = 25% + 1
(3 + 1) 4
In our video, there are 31 voters. 25% of 31 is a fraction more than 7 votes. The next highest whole number is 8 votes. That's our victory threshold. To see why this makes sense, consider our example. If three candidate win 8 votes, they collectively have 24 votes. The most votes that any other candidate could have is 7. Eight votes is the minimum number of votes that only three candidates can win.
A point about majority rule: Note how this victory threshold ensures majority rule. If 51% of voters all support two or more candidates as their top choices in an election for three seats, they will be sure of winning two of three seats. If 51% of voters all support five or more candidates as their top choices in an election for nine seats, they will be sure of winning five of nine seats.