Condorcet and compromise

American election expert Ned Foley, a professor at Ohio state university, is currently spending time as a visiting fellow at Melbourne University, and last night he delivered the Miegunyah distinguished visiting fellow lecture at the university’s law school. His focus was on the work of Edward Nanson, a mathematician who pioneered the study of voting systems in Australia and was influential in debates over electoral law in the decades before and after federation.

Nanson’s work makes an interesting story, but this wasn’t just a history lecture. Foley (who has been mentioned here a couple of times before) has a moral to draw about our modern condition, and especially about America’s. He argues, as he has for some years, that his country’s woes are due in large part to a bad voting system, and that electoral reform – in directions that Nanson would have approved of – offers an opportunity to help right things.

Far be it from me to discount the importance of bad electoral systems; it’s one of the main themes of this blog. And the United States certainly has one of the worst (in common with many other former British possessions). But its problems have a lot of other causes as well, ranging from cultural factors through to the entrenched two-party system and the presidential system itself; I’m a bit sceptical about the capacity of electoral reform alone to effect much change.

Nonetheless, it’s worth a try: the question is just what to do. Many American reformers have put their faith in preferential voting, on the Australian model, which they call “instant-runoff” or “ranked choice” voting. That’s what Nanson ended up advocating here, although his advice wasn’t adopted at first. But Foley argues that it’s not enough, and says that what America really needs is Condorcet voting, known for its promotion of compromise candidates.

To understand the difference, let’s look at his leading example, the Alaska congressional by-election, or “special election”, of 2022. (We covered it here at the time.) There were three serious candidates: Democrat Mary Peltola, mainstream Republican Nick Begich and Trumpist Republican Sarah Palin. Alaska is a strongly Republican state, so in a traditional first-past-the-post election Palin would have won the Republican primary and then gone on to beat Peltola.

But Alaska has adopted preferential voting, so all three competed in the same ballot. Peltola led with 39.7% of the primary vote, ahead of Palin on 30.9% and Begich 27.8%. Begich was eliminated; his preferences favored Palin, but not strongly enough for her to overtake Peltola, who won with 51.5% two-candidate-preferred.

Foley argues that this was the wrong result, because a majority of voters would have preferred Begich to each of Peltola and Palin: in other words, he would be the “Condorcet winner” (named for Nicolas de Condorcet, who studied the problem in the eighteenth century). And although the Trumpist was defeated on this occasion, he maintains that preferential voting will not be enough to stop Trumpist candidates winning Republican seats, and that a system that effectively favors moderate Republicans would do a better job of safeguarding American democracy.

Nanson had acknowledged that Condorcet voting was mathematically superior, but evidently thought that its adoption in Australia was politically impossible. It probably still is. One problem is that not every election produces a Condorcet winner; voters may prefer A to B and B to C but C to A. There are various ways of getting around that (including one developed by Nanson), but none that are intuitively compelling.

More significant, especially in the conditions of the early 1900s, is that once there are more than three or four candidates, Condorcet voting is fearsomely difficult to count. That’s less of a problem now that these things can be computerised – and in the US voting machines are the norm anyway – but it still means a loss of transparency; if a count can’t be done manually, it’s a lot harder for the lay person to work out what’s going on.*

The most important problem, as I see it, is theoretical as much as practical. In a case like the Alaska by-election, where the Condorcet winner has a reasonably healthy primary vote, it makes some sense to say they should win the seat. But not all cases will be like this. There will be others where two candidates have almost all the vote between them, say about 45% each, and a minor centrist candidate has the remaining 10% or so. And in conditions of polarisation, it’s quite likely that supporters of each side will prefer the minor candidate to the other side with enough unanimity to make them the Condorcet winner.

Is that really what we want? We know that our system discriminates against small parties with widely diffused support, like, for example, the Australian Democrats in the 1970s and ’80s. Condorcet voting would perhaps take us to the opposite extreme, producing a parliament or congress in which such parties were greatly over-represented. No doubt that would be an improvement on the current state of the US, but that may be too low a bar when considering electoral reform.

I suggest that the lesson we should draw is that there is no ideal answer in the context of a system that insists on choosing people for single positions, whether a president as in the US or a constituency representative here. This, by contrast, is one of the advantages of parliamentary government, where an assembly can be chosen by a proportional system, in which the different political preferences are represented according to their support in the electorate.

Nanson also supported proportional representation, although he did not live to see it introduced for our Senate. But if the Americans are going to start learning some lessons from international experience, that would probably be the best place to look.

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* In discussion, Foley suggested that one option would be to hold voting over two rounds, using the first to whittle the field down to three and then having people vote on the three pairwise comparisons in the second. But of course that’s more expensive, and the process used for the whittling down may not be uncontroversial.