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.

**: 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.**

*A point about majority rule*