The following started as a further comment to propagate some ideas already planted beneath the post on Palestinian exit polls. It seemed appropriate to give it a new planting of its own. It is specifically in response to the point raised by Kao Hsien Chih (welcome back to the orchard, by the way!) regarding coordination failure. And a tip of the hat to Wilfred for inspiring the idea of plurality as a genus. Why hadn’t I though of that?
[Correction, Jan. 29. The definition below of the limited vote has been fixed. Initially, Word Press took my attempt at defining mathematically “1 is less than w” as an html tag and failed to render a whole block of rather important text!]
On coordination failure, all forms of nominal plurality voting are vulnerable to it one way or another. (When I say ‘nominal’ I mean a vote given to candidates by name, and in this context mean that votes are counted only for candidates, and not pooled onto a party list. In the case of Palestine this is true for 66 district seats. There are also party-list PR seats, but they are allocated completeley separately, or in ‘parallel’ and based on a separate list vote.)
Of all the plurality species, the single nontransferable vote (SNTV) is the most prone to coordination failure, because it is not clear to a party how many candidates to run, optimally, and if it rus more than one, then the party has to find a way to spread its voters out across the candidates to ensure that they don’t pile up a lot of votes on just one. Under multi-seat plurality or block vote* (as in Palestine’s nominal tier), the nomination strategy is clear: run as many as there are seats in a district. The problem then is to ensure that your voters vote the full slate. If they do not, then you have a problem.
The “genus” plurality (which forms its own orchard block here at F&V) includes FPTP, multi-seat plurality (a.k.a. block vote), SNTV (like Taiwan’s nominal tier through 2004, and Japan formerly), and other systems.
What this genus has as its identifying trait is that all its species establish that the winners are the M candidates with the M highest individual vote shares, where M is the district magnitude (the number of seats elected in the district). Where the sepcies vary is in two things: First, of course, M. Secondly, in whether the voter has M nominal votes or less than M. Let w be the number of votes per voter.** Then the systems are:
FPTP, M=1, w=M=1
SNTV, M>1, w=1
Block vote or multi-seat plurality, M>1, w=M
Limited vote, M>1, 1< w < M (SNTV is actually a special case of limited vote, so perhaps we should say that limited vote is the species and SNTV a variety)
If some voters do not use all their votes in multi-seat plurality, then they are treating the system as though it were limited vote. This may have happened to Fatah. It certainly happened to nearly all parties in the Liberian 2-seat-plurality senate races.
If we also allow w>1 and the voter to cast more than one vote per candidate, then we have cumulative vote also as part of the same family. (However, rationally the voter ought to cumulate all on one candidate, in which case it becomes SNTV.) And if we allow w=c, where c is the number of candidates, then approval vote also is part of the family.
All of these systems provide both parties and voters with dilemmas about how to coordinate their support across multiple candidates in ways to ensure that the desired candidates and not some others are elected. In the case of FPTP, of course, the problem is not usually that a party has more than one candidate in a district; it is that multiple parties lead to coordination problems and may result in the candidate of a majority-disapproved party winning.
* Actually, the term, multi-seat plurality, is not precise, and block vote, while well established, is even less so. Consider the typical rule used in US states for the electoral college: the candidate with the plurality of votes wins the full slate of electors. That’s multi-seat plurality, and given that the votes go as a block (i.e. the voter isn’t voting for individual electors and thus cannot partially abstain or split her ticket), it could be called block vote. I prefer to call systems on the order of the US electoral college list plurality, because the list with the plurality is elected as a whole. For the type of system used in Palestine’s district races, I would prefer multiple nontransferable vote (MNTV), because that is far more descriptive of a system in which the voter has more than one vote which need not be cast as a block, and each is strictly nominal and cannot be transferred or pooled to other candidates. MNTV would be identifable as a sub-class of both the broader category of multi-seat plurality (which includes list plurality) and the broader category of nominal plurality (which includes FPTP, SNTV, etc.).
**w rather than v, as we like to use v to refer to the total number of votes cast in an election, rather than the number cast by an individual voter.