(Note: This post was going to go up sooner, but with Wikipedia going down to protest SOPA, I put it off for a bit.)
Before disappearing for a third of a year, I was asked a simple question in the comments: Would I support an effort in favor of proportional representation (PR), even if it were for single transferable vote (STV), the PR method on which instant runoff voting (IRV) is based. And yes, I would. I often refer to Duverger's Law, the observation that single-winner plurality elections tend toward two-party dominated government, and PR effectively attacks one of the two legs of that problem.
What is Proportional Representation?
The familiar method for electing a legislature is to divide the region into districts, and elect a single representative from each one, the idea being that someone from where you're from, will want what you want. In practice, this isn't always true. There tend to be factions in each district that split along similar lines, and these ideological splits may be completely independent from the geographic split of the districts. It's possible (by accident or by design) for the narrowest of political majorities to win every single seat in a legislature, or for a group that is a minority in the electorate to have a majority of legislative seats. If the legislature is intended to represent the viewpoints of the whole electorate, only with a smaller number of participants, then these single-winner districts often fail.
The goal of PR is to fix this deficiency. Rather than each district electing a single winner, they elect multiples, and in proportion to the number of votes they have received. In this way, the diversity and popularity of viewpoints among the people will more-closely match the diversity and popularity of viewpoints among the representatives.
Variations and Usage
There are many different variations of PR. The most basic is changing the number of winners elected from each district. This number may be as small as 3 or 5 (usually, but not always, the number is odd) or as large as the 120 used for the Israeli Knesset, which is elected from a single, nation-wide "district". The other major point of variation is whether the system is candidate-based, like our current single-winner elections are, or whether it is explicitly party-based, so that voters do not vote for individual candidates but rather for a party or a list of candidates they have supplied; there are also mixed systems, like the one used in Germany, which provide for both simultaneously. There are also different ways of dividing the votes--basically, which way to round fractions--which can favor having fewer, larger parties or more, smaller parties. Depending on the precise method used, a PR ballot may look just like a plurality ballot, like a pair of plurality ballots (one listing candidates and one listing parties), or it may ask you to rank several choices (candidates or parties), or it may even look like an approval voting or score voting ballot
Most of the worlds democracies use proportional representation, which may come as a surprise to those of us in the United States, but that's because some of the largest exceptions--the United Kingdom and Canada--also happen to be some of the countries we Americans are most familiar with.
Criticisms and Difficulties
Since multiple winners are elected in each district, some critics have said that PR severs the connection between a voter and "their" representative. However, since each district elects multiple representatives, it is more-likely that you'll be in political agreement with at least one of "your" representatives. I also have commonly heard complaints about the party-centric aspects of party-based PR, but usually this is from people who don't realize that there are PR methods that are not party-based. Candidate-based PR tends to become somewhat unwieldy as the number of winners increases, as it becomes more difficult for voters to determine and remember which candidates they prefer. The counting procedures, regardless of the specific form of PR used, are also more complex than plurality voting is. Finally, there are people who legitimately believe that it is best to have as few large political parties as possible, in order to best guarantee the existence of a cohesive majority government, although this is less-significant in the US since we have less expectation of party-line voting, as well as extra veto-points in the President and in one chamber of congress acting more-and-more often under super-majority rules via the filibuster.
Also particular to the US, it is currently federal law that the states elect their representatives from single-winner districts (the law was enacted because some states had chosen to elect all their representatives at-large, guaranteeing that 51% of the voters would choose 100% of the representatives, eliminating representation for minorities) and that law would have to modified in order for any form of PR to be usable for House elections. Furthermore, the constitution requires that House seats be apportioned to the states, so no cross-state proportionality would be possible without a constitutional amendment, making the system rather moot for the 7 states who have a single representative.
This hasn't stopped PR from being used in several US cities, even, at one point, New York City; although most of these later returned to single-winner elections, so that, as of today, Cambridge, Massachusetts has the only governing body in the nation that is still elected via proportional representation.
For those who favor a diversity of opinions, proportional representation can be an effective way to achieve it. It has shortcomings and legal hurdles standing in the way of its use, and obviously can't be used for single-seat offices like a governor or the president. I won't stop pressing for approval or score voting, but there's no reason these advances can't be pursued in parallel. Although, anyone who sought to do so should familiarized themselves with how and why PR elections were rolled-back in recent US history, in order to avoid running into the same mistakes again. But that's a blog for another day...
Now, why would I support STV, but not IRV? It's a known property of STV that, the fewer winners it elects per district, the less proportional it is (and the balancing act becomes ballot complexity versus proportionality.) Since IRV is precisely equivalent to STV with one winner, we know that it loses all proportionality (in other words, IRV is not a PR election method.) This, combined with the other deficiencies of IRV make it an unacceptable alternative to my mind.