Via Josep Colomer comes notice of a new finding by Rein Taagepera, co-author with one of this blog’s patrons of Seats & Votes.

Given “simple” electoral rules, the number of effective parties can be predicted from average district magnitude and the number of seats in an assembly. Likewise, magnitude can be predicted from the number of effective parties (say, in a constituent assembly) and number of seats. “Simple” here refers to single-tier systems without thresholds (i.e. all SMD, all PR-STV, et cetera). Moreover:

Since, according to Taagepera, the number of seats of the assembly depends strongly on the country’s population (in a cube root relation), we can deduct from the above formula that, for similar number of parties, P, the larger the country, and hence the larger the assembly, S, the smaller the expected district magnitude, M. Very large countries, precisely because they have large assemblies, should be associated to small (single-member) districts. The institutional designers in India, for example, are likely to choose single-member districts, while the institutional designers in Estonia are likely to choose multimember districts, typically associated to proportional representation rules. Thus we should usually see large assemblies with small districts, and small assemblies with large districts. Which is what we indeed usually see.

And from the above, because assembly size is a function of country population, we should see smaller districts in more populous countries. Colomer goes on:

But now we could have an answer to the very intriguing question of why large countries, including the United States, in spite of the fact that large size is typically associated to high heterogeneity, keep small single-member districts and have not adopted proportional representation. The answer may be that in large countries such as Australia, Canada, France, India, the United Kingdom and the United States, a large assembly can be sufficiently inclusive, even if it is elected in small, single-member districts, due to territorial variety of the representatives.

With the caveat that I’m relying only on Prof. Colomer’s helpful summary, I’d make two comments. (One easily could make more; this is a big argument.)

One, the size of the US House has not approximated the cube root of the US population since 1912. Therefore N-seats no longer proxies very well for population in the American case. Of course, electoral rules are sticky, and there was more or less a settlement on single-member districts by 1912, even if a few states still used MMD.

Two, notwithstanding the above, one takeaway message might be: the nexus of a (more than less) large assembly and (effectively) two-party system satisfies elites who otherwise would agitate for reform. That institutional combo offers the likelihood for both factions to hold power at some point in the not too distant future. As such, it dampens the incentive for an out-party to increase district magnitude the next time it wins a seat majority.

This point is different from Colomer’s about territorial variety leading to inclusiveness, even when effective thresholds are high. I don’t believe that, all else equal, an assembly’s inclusiveness of opinion matters much for reform. In any normal year, the battle is in marginal districts for the favor of mercurial swing voters. As long as there is loose ideological correspondence between a party and its base, the state of affairs can roll along undisturbed.

Taagepera’s finding is interesting because it implies, if my understanding is correct, the probability of a future seat majority may override geographic incentives for proportionality in the now. In other words, we’d predict the Democrats to prefer the status quo over reform that maximizes the seat-winning efficiency of their spatially concentrated (i.e. “packed”) voter distribution.

Moreover, if I’ve done the math correctly, the model predicts PR-STV in three-seat districts - a reform I’ve elsewhere called modest - would result in six effective parties. That is counterintuitive given the landscape as we know it: Republican, Democrat, Green and Libertarian. Imagine how the landscape would look if the model does in fact predict the number of parties. Imagine what would happen to the coalitions we now call “major parties.”

And, assuming a constant number of effective parties (two), we would expect a decrease in the size of the House to present incentives for reform.