The Huntington-Hill method is a system of apportioning representatives to states, currently in use for the United States House of Representatives. It is a highest averages method, which uses geometric means to allocate seats to states.
While originally intended for apportionment for the United States House of Representatives, the method can also be used to determine seat allocations for legislative elections determined by proportional representation.
In this post, I will run a fictitious election using this system, to show you the process of electing the Anytown municipal council.
In the Anytown municipal council election, eight parties contested the election. These were Birthday, Surprise, Dinner, Garden, Cocktail, Tea, Block, and Pool. 6,849 people voted, and there are 19 seats up for election. Let's see how each of the parties did:
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In the "Threshold" row, you can see that the Hare quota is in effect. To elect at least one member to the council, you need to get a number of votes, greater than the total number of votes cast, divided by the number of seats available. Block and Pool failed to meet this quota, so they are eliminated. All the other parties qualified, and they will all control at least one seat:
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Six seats out of 19 have already been apportioned, by virtue of the parties that qualified. To apportion the remaining 13, we compute each party's divisor - which is equal to the total votes cast for that party, divided by its geometric mean.
The geometric mean is equal to the square root of the product of the number of seats already allocated to that party, and one more than its current allocation. Thus, we come up with quotients for each qualified party:
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Birthday has the highest quotient, so it is allocated another seat. The algorithm then updates, and new quotients are computed for each party. The party with the highest quotient is then found, which might be another party. Another seat is allocated to that party. This continues, until all the seats have been allocated. Thus, the final balance of power on the Anytown council is this:
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While Block and Pool voters did not receive any representation, due to not having met the threshold, the number of seats controlled by each party approximates its percentage of the votes. Thus, this is a proportional representation method, using a method originally designed for states.
