Single transferable vote with Borda elimination: proportional representation, moderation, quasi-chaos and stability

Modifying single transferable vote (STV) by removing candidates according to their Borda scores creates a new vote counting system (STV-B) that is not quasi-chaotic, results in proportional representation, and promotes the election of moderate candidates. Dummett, M.A.E. [1997. Principles of Electoral Reform. Oxford University, New York] noted quasi-chaos in STV and proposed the “Quota/Borda system” (QBS) as a solution. STV-B and QBS retain proportional representation from STV, permit some influence on candidate selection to occur between voting blocks thereby promoting moderate results, and are much more stable than STV when subjected to small changes in voter preferences. Under STV-B, and not QBS, a minority that shares some preferences may elect a candidate even if the minority is not a solid coalition.

Single transferable vote with Borda elimination : a new vote counting system

Dummett (1997) notes particular difficulties with single transferable vote (STV) and proposes an alternative vote counting system called "Quota/Borda system" (QBS) to remedy specific difficulties. I propose an alternative system, structurally related to QBS, which accomplishes similar solutions but has some significant differences. This alternative system is identical to STV in all aspects except one. It eliminates candidates in reverse order of their Borda scores rather than by their current ranking of first-place votes. I designate this system STV with Borda elimination (STV-B). STV-B and QBS share general features. They retain proportional representation from STV. However, they differ from STV is two critical manners. First, both permit some influence on candidate selection to occur between voting blocks. Second, they are much more stable than STV when subjected to small changes in voter preferences. Outcomes from STV-B differ from QBS outcomes in two ways. Under STV-B, a minority that shares some preferences may elect a candidate even if the minority is not a solid coalition, as is required for minorities under QBS. Further, QBS always selects Borda winners, either for a minority or overall. STV-B may reject a Borda winner through emphasis on each voter's most preferred candidates.