Chris Hanretty

Roberto D’Alimonte has been arguing that the outcome of the elections to Italian senate are a ‘lottery’, product of a fundamentally flawed electoral law, and thus almost impossible to predict.

I agree that the current electoral law is flawed insofar as it makes it extremely difficult to produce any majority. I disagree that it’s impossible to predict.

If we have some function which maps current estimates of parties’ vote shares to distributions of seats, then we can start predicting outcomes. In this case, if we take the parties’ regional strengths in the last election, and multiply them by the swing between the two elections, we can get reasonable estimations. However, the seat projections we get from our formula will be static: the PdL will always win certain regions if we feed in the same number.

Of course, real life is never that deterministic, and our poll estimates come attached with uncertainty estimates. Some have attempted to get round the problem of uncertainty by looking at various scenarios, in which the majority premium in some regions goes to the PdL, sometimes to the PD, and so on.

This is both clumsy and unnecessary. Because we have confidence intervals for our poll estimates, we can simulate the election many times over, drawing a number from a normal distribution centred around our poll estimate, and extending left and right to the margin of error for the poll.

If we do the same for the other parties, we can simulate the election results many times over, and examine the results, thus obviating the need to construct laborious ’scenarios’.

I therefore ran a million simulations of the election (actually, 970,237) [1], using the latest polling trend data (PdL + Lega 44.7%, PD + IdV 37.4%; SA 6.86%; UDc 5.92%) derived from my lowess line, and assuming that this lowess estimate had the same margin of error as an opinion poll with 1,000 respondents. The results were as follows.

• The mean number of seats won by the centre-right across all simulations is 161.7, or almost 2 seats less than a mechanistic prediction based on uniform national swing;
• the modal number of seats is 161, although there’s another peak at 165.
• Berlusconi wins a majority in the Senate in 87% of simulations;
• Razor-thin majorities (158 or 159 seats) occurred in 12.4% of simulations;
• Narrow majorities (160, 161, or 162 seats) occurred in 29% of simulations;
• Slender majorities (163, 164, 165 seats) occurred in 34.65% of simulations;
• Larger majorities occurred in almost 11% of simulations

Bear in mind the ridiculously demanding assumptions here:

• polling companies are on average accurate;
• the only polling errors are sampling errors;
• there’s been no change in public opinion over the past fifteen days;
• there will be a uniform swing across the nation;

If you can stomach these assumptions, then you too should predict a 162 seat majority for Berlusconi in the Senate.

[1] This took a while, not just because my R coding is very sloppy.

Update: Following Roberto’s suggestion, a histogram is now available.