Different uses for voting need different types of voting.
Party List PRBecause voters are allowed a choice of parties, they tend to vote for or against each party’s policies. But there is no direct vote to select (and remove) a party’s leaders.
The party leaders can list a team with diverse skills needed on the council. Not all candidates need charisma and campaign skills.
Critics most often attack 3 traits of list PR: 1) it tends to fracture a legislature into splinter groups; 2) it leaves voters uncertain which parties might agree to form a ruling coalition; 3) voters usually cannot throw out a powerful but unpopular pooi
DivisorsThe d’Hondt and Sainte Lague rules are the most common. They use a series of divisors. Sainte Lague favors medium sized parties and is used in some Scandinavian nations. Continental nations are more likely to use the d’Hondt divisors. These and other divisor rules are described in Seats and Votes, the Effects and Determinants of Electoral Systems. by Rein Taagepera, and Mathew Soberg Shugart; 1989. The authors combine the work of many others to build a mathematical model of political systems.
Victor d'Hondt's highest-average rule: the party with the most votes wins one seat, then the party's number of votes divided by its number of reps plus one. Repeat to fill all seats.
QuotasWhen no party has a full quota left and there is still an unfilled seat, which party gets it? It might simply go to the party with the largest number of “leftover” voters. Or it might go to the (small) party whose leftover votes, divided by its number of reps, make each of them represent much more than one quota of voters.
Hare or simple quota: Valid ballots / Seats
Every voter has the power help elect a rep, if he ranks enough candidates. But in practice, most voters save time by ranking only a few. A ballots with few ranks may be passed from 1 loser to another until it runs out of ranked candidates. At that point it is an “exhausted ballot.”
As the number of valid ballots declines, so does the quota. Older rules simply reduce the quota for the remaining seats. More accurate rules reduce the quota even for candidates who have already won (some weight is given back to their supporters to pass to their lower choices) so all winners will represent the same number of votes.
Droop quota:Valid ballots / (Seats +1)
The winners use 5 × 16.67% = 83.35% of the ballots. The remaining voters, almost 1 quota or 16%, do not help elect a rep -- although they could have if their ballots were transferred further.
[ footnote: Loring Ensemble Rule a may resolve the debate about which quota rule is best. It can use Droop's quota for the chairperson and use the remaining voters and seats in Hare's quota for reps. (Both quotas can be adjusted for exhausted ballots.) Droop's quota ensures the majority group gets the majority of seats while Hare's makes every vote count. Thus LERa gets the best of both quota rules.]
STV VariationsThe most complete history of STV development on the web is "The Single Transferable Vote" by T. Nicolaus Tideman in the Journal of Economic Perspectives. Winter 1995, 27-38. Tideman explains the development of STV and its various quota and transfer rules. His CPO-STV improves the selection of diverse reps, although at a cost in complexity. This article is now available in pdf and text formats.