Proportional and Cumulative Voting
We have seen that there can be difficulties obtaining minority represention in elections with multiple candiates elected using either voting districts or at-large voting (a single voting district). An alternative is proportional voting, where voters vote for a party, and the parties are assigned representatives in accordance with the number of votes they received. Sometimes the rank order of party members to serve as representatives is established prior to the election, but there is also a variant where the rank order of party members to serve as representatives is established by the election process. Another alternative (or a form of proportional voting) is cumulative voting where voters cast more than one vote, but they may cast all their votes for the same candidate. This is widely used in stockholder elections (for corporate boards), it is supposed to give more power to minorities, but has been alleged to entrench serving boards. Proxy votes allow management to cumulate the votes they cast any way management wants to. There is also a Hare method for multiple candidates elected where voters rank all candidates and the excess vcotes of winners are reaassigned; we shall not discuss this.
Proportional voting requires candidates to identify themselves as members of political parties (individuals can run as parties of one). Cumulative voting forces voters to determine the `parties' and rankings. But once the parties are established, the analyisis for either proportional voting or cumulative voting is the same as for one vote at-large elections. Each party distributes there votes, whether one per voter under proportional voting or N per voter under proportional voting so as to give as many of their candidates as possible the minimum number to assure election (1+n/(N+1) or 1+Vn/(N+1)), there is no ceiling (no one vote per voter constraint) to the number of votes a candidate can receive.
Problems with proportinal representation
a) Forming candidates into parties
b) ranking candidates within parties
c) assigning fractional representatives
d) may be harder to form a majority government
Contrast gerrymandering with how many they would get under proportional representation
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