For Lord Kelvin, “when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind”. More and more political scientists share this conviction, but unfortunately the things  that political scientists find interesting are often resistant to measurement.

For example, it’s hard to measure the political positions of individuals or parties. Sure, ever since the French Revolution we have an idea that positions can be located in some n-dimensional space — the most common example of which being a 1-dimensional space with one axis divided into “left” and “right”.

Going beyond that, however, is tough. You can ask experts to rank parties on one-to-twenty scales; or you can code their manifestos by breaking them down to the sentence level. But both of these are labour-intensive and, in any case, give different answers about parties’ mutability on the left-right dimension.

So, the least-bad alternative is looking at how politicians vote on particular things — that is, roll-call analysis.

Like most technical developments in political science, roll-call analysis to recover ideal points developed in the United States. It made sense there – you’re trying to recover the ideal points of individual voters in the legislature (be they Senators or members of the House), and we all know that American parties are weak; so employing the assumption that all these voting decisions are independent and identically distributed is fairly legitimate – or at least not obviously crazy.

The only problem comes when you try to transfer this methodology to legislatures outside the US where parties are fairly strong, and where party pressures on roll-call votes are enough to violate this i.i.d. assumption. No biggie – you develop a non-parametric method called Optimal Classification (at least, you do this if your name is Keith Poole).

And that would be nice – except that party pressure works in funny ways. Optimal Classification is based on the assumption that members of the legislature vote sincerely: if you offer them half a loaf instead of no bread at all, they’ll vote for it. Except sometimes members of the legislature vote strategically: they’ll vote down half-a-loaf if they think they can get a whole loaf later.

That’s why Spirling and McLean found that optimal classification doesn’t work in the UK. When I say, `it doesn’t work’, I mean, the techniques gives estimates of politiicans’ positions which lack face validity. They argue that left-wing Labour MPs voted strategically with Liberal Democrats and Conservatives in order to push the government left-wards and thereby secure their support. If the government didn’t do that (ran the threat), the rebels would give the government a humiliating defeat.

That’s pretty much what I find when I apply the technique to Italy. Below are two graphs showing the kernel density estimates for legislators’ ideal points in the 14th and 15th legislatures. The median voter in each party is marked with a dotted grey line. (Don’t take the kernel density estimates too seriously, I just think they look cooler than a histogram or rug-plot).

These estimates also lack face validity, particularly in positioning the parties on the extreme left and right-wing of each coalition.

In the 14th legislature, the government was formed by a centre-right coalition made up of Forza Italia, the UDC, Alleanza Nazionale, and the Lega Nord. The Lega Nord can be a difficult coalition partner, but they are almost definitely to the right of the UDC. In this plot, however, they seem to be the most centrist of all the parties in that coalition. That’s probably because they voted insincerely with the opposition parties in order to force the government to move to rightwards.

Conversely, in the fifteenth legislature, the Communisti Italiani (COM-IT) and Rifondazione Comunista (RC-SE in the diagram, don’t know what happened to the kernel density estimate curve, but the median voter in each party is indicated by a grey dotted line) were the awkward squad — but again they appear here to be completely centrist.

So, optimal classification doesn’t work in Italy, probably because parties vote insincerely.

Now, these estimates were generated on all roll-call votes with the defaults in the oc package for R. Maybe if one excluded final votes, or excluded non-final votes, or in some other way tinkered with the data, we’d be able to get something that had greater face validity. But as it is, the options for calculating ideal points are getting more limited. We’ll either have to look at ideal points estimated on the basis of what politicians say, or on some other low-cost low-intensity legislative act, like motions.