Voting: The Conventional Silliness

Last week, British voters rejected the “Alternative Vote”, much beloved of academic theorists and the Liberal Democratic Party, by a margin resembling one of Saddam Hussein’s elections. Needless to say, the cranks who support it – or one of the other fanciful replacements for “first-past-the-post” – are undeterred. This weekend, the Wall Street Journal’s statistics columnist devoted his inches to them, along with a follow-up on-line post, replaying themes familiar to anybody who pays attention to this controversy.

The pieces are informative, with the particular virtue of paying attention to rivals to the Alternative Vote (dubbed “Instant Runoff” this side of the Pond and actually employed in Oakland, California – doesn’t that tell you all you need to know?), such as “Approval Voting” and “Range Voting”. In the former, you can vote for as many candidates as you want, and the one with the most “approvals” wins. Range voting lets voters give “scores” to candidates, with the highest average winning. There are plenty of other ideas. I even invented my own (see “Addendum”), which was used for Guest of Honor selection by the Chicon 2000 committee.

What the Ivory Tower likes is unsurprising:

Before the recent U.K. referendum, the London School of Economics and Political Science organized a workshop on voting systems where 22 specialists cast a ballot, using approval voting to register their opinion on it, instant runoff and other systems. None chose the plurality system; ten chose instant runoff and 15 chose approval voting.

What’s wrong with the arguments recorded by the “Numbers Guy” is that they pay no attention to what a voting system is for. We vote on a plethora of different matters. In many cases – the Hugo Awards, for instance, or the presidency of the Garden Club – all that we care about is pleasing the largest proportion of the electorate on this particular occasion. No system can guarantee that. (I’m told there’s a rigorous mathematical proof of that proposition, and it certainly seems intuitively obvious.) Still, if that is the only objective, there’s much to be said for first-past-the-post’s competitors.

Governments, however, are more than the method used to select their leadership, and they have to continue year after year. A voting system that gums up the rest of the machinery is a bad idea and will be detrimental to the country’s health, even if every single election results in maximum voter satisfaction.

The reason is that how voting is conducted affects how politics is organized. First-past-the-post tends toward two broad-based, more or less permanent parties. Other systems encourage small parties, extreme parties, party splits and coalition rule. The tendency doesn’t always prevail perfectly. There are non-FPTP countries with coalitions that almost never separate, leading to a close simulacrum of a two-party system (Liberals-Nationals vs. Labor-Greens in Australia, CDU-CSU-FDP vs. SDP-Greens in Germany), while both Britain and Canada, with FPTP, have gone through multi-party periods (albeit that hasn’t been the norm in either and may be coming to an end in both). In general, though, two strong parties result from FPTP, a multitude of weak ones from everything else.

The argument for other ways of voting is, then, an implicit argument against political parties. For the Hugos or the Garden Club, parties (er, political parties) don’t add anything, but the high-minded notion that governments can dispense with them is – even though some of our Founding Fathers believed it – a fine example of nonsense tottering on its stilts.

Addendum: In the Veal Ballot, voters rank the candidates, as in Alternative Voting. Each candidate is then compared against each of the other candidates one-on-one. The one who is ranked higher by more voters wins that matchup. The one who wins every individual contest is the winner of the whole.

There is one case in which this system won’t work. As I said, no conceivable system infallibly picks a candidate whom most voters would prefer to any other. This one falls apart if the voters’ preferences are transitive, that is, if they prefer A to B, B to C and C to A. For an individual voter, that’s an irrational outcome (not that some voters aren’t irrational). It’s easy to demonstrate, though, that a transitive result can be generated by a group of voters with nontransitive preferences (proof left as an exercise for the reader). The possibility isn’t huge – at least, it didn’t happen with any of the Chicon GoH slots – but is definitely greater than zero.

Correction: As Mark Olson points out in his comment, “transitive” should read “intransitive” supra, and vice versa. And I should be heartily embarrassed. Or can I claim that I’m just trying to emulate the President? No, I’d rather be embarrassed.

Comments

[Mark Olson]

When a voter prefers A to B and B to C and C to A, his vote is *intransitive*. It's transitive when A preferred to B and B preferred to C means A is preferred to C. (Transitivity is a property in axiomatic systems in mathematics.)