Archive for Polls

Yes, We Could.

Posted in G 1 with tags , , , , on April 11, 2008 by Roberto Gravitazero

With less than two days left to go, this is my last post on statistical analysis and predictions on the Italian elections. In the previous posts I had a look at the possible outcome of the race for the Senate, based on available polls data. I will try today to have a reflection on two issues:

1) Is it conceivable that, contrary to all published polls, PD would eventually end up with more votes that PdL, thus securing the majority in the lower chamber?

2) In such a case, what would be the result, in term of seats, at the Senate?

After the polls blackout (15 days before the election date), results from putative reserved polls can be found on the net, in various flavors and disguises (horse races being a rather popular choice, but not the only one). Since I have no way to check how real and reliable these are, I would ignore them and base myself on available data alone, plus some elementary statistics. Only in the end I will add some more “political” consideration.

Starting with question one, the obvious starting point is a comparison with the 2006 elections, in which the polls predictions disagreed strongly with the final result. I show in the plot below the results of the pre-election polls and of the exit polls in 2006 , compared with the 2008 polls. I report as well the final results of 2006, and a hypothetical break-even point for 2008 (PD equals PdL).

In 2006, all polls gave a substantial margin to the Center-left coalition (average in the last month before the blackout 4.8 %), except from 3 polls from 2 institutes, all commissioned by Berlusconi. Such margin was essentially the same even in the exit polls, but was dramatically contradicted by the final results.

At a first look, a PD close victory in 2008 would be an even bigger surprise than the “almost draw” of 2006. The absolute discrepancy of the final data from the last month polls average (7.7 %) would be higher than the one of 2006 (4.9 %), and even more so in relative terms (since PdL and PD percentages are lower than what Center-left and Center-right obtained in the last elections). However, for several reasons, a PD victory cannot be completely ruled out. First, the data looks more “dynamic” in 2008. Besides that, the spread of the data in 2006 is noticeably less than the one of 2008 (especially if the 3 “anomalous polls” are not considered) – possibly due to the “disturbing” factor of the smaller parties now present in the race. If we consider only the last month before polls blackout in 2006, the final Center-Left and Center-Right results were -3 and +3.8 standard deviations away from the averages, respectively. This compares to the +/- 3.8 standard deviations needed to reach the break-even point in 2008. From a purely statistical point of view the two events would be essentially equivalent (i.e., equally unlikely).

The cause of the 2006 discrepancy had been thoroughly discussed. A systematic bias in the polls looks more likely than a drift of electoral preferences in the last two weeks (as confirmed also by the exit polls result). The bias could then arise from non-representative sampling by the polling institutes, reticent answers by part of the interviewed population, or a biased voting distribution in the undecided who finally participated to the elections. The repetition of such a discrepancy in 2008 (and its magnitude and direction) depends on all the above as yet undecided issues. To add another variable, I ignore if the polling institutes had since 2006 put in place corrective strategies, and which ones.

The only possible conclusion is therefore that, if a similar phenomenon happens again, there would be ample space for a PD victory at the lower chamber (but also, potentially, for a large defeat).

In order to try and answer to question two – Senate outcome if PD overtakes PdL – I have done a simple exercise. I have taken the March 2008 polls average and used my model (derived by the one from Sandro Brusco/noiseFromAmeriKa) to study the dependence of PdL and PD seats in the Senate as a function of the PdL-PD distance (keeping the PD+PdL sum constant). I have then repeated the simulation two more times, first adding, then subtracting 1% to both SA and UDC.

In the following plot I show the results, together with the simulations done using the actual March polls (scattered dots). It is interesting to note that the two +/- 1% bands (thinner lines) describe well the variability of the polls.

At a first glance, the conclusion is that a small advantage of PD over PdL would in general not be enough to obtain the majority in the Senate, or even to obtain just more seats than PdL. PD would need a lead of 5% or more to be likely to get the majority. Which looks like a long shot indeed.

However, the simulation I did follows a strict uniform national swing hypothesis. A re-distribution of the votes between regions different from 2006 (as by the way showed in the few published regional polls) could dramatically alter the results, in a way that is difficult to predict. The number of seats are indeed more sensitive to the distribution of votes among the regions than to their global number. I was surprised to find, for instance, that by shifting around less than 100000 votes, it was easy to “give” the senate majority to PD (158 seats) with only a 1% lead with respect to PdL. Thus, even for the Senate, a small possibility for a PD majority do exist.

I have so far talked about statistical possibilities. One must add a “political” dimension in order to make an educated guess on the outcome. For instance, most commentators (and a few polls) maintain that most of the undecided who will finally vote will favor PD rather than PdL (opposite from 2006). Also, the 2008 polls show a Center-left to Center-right ratio more unbalanced towards the latter than ever before. Since in paste elections the movements between the two block were minimal, this could imply a poll bias in favor of PdL.

For these reasons I would expect a reduced PdL-PD gap in the end. If I had to bet, I would place my money on a PdL victory with a 2-4% margin at the lower chamber, and an essential draw in Senate seats. But nothing is excluded, and Veltroni does well to keep up the pressure.

Yes we can sounds too optimistic to me, since the bar is indeed set very high. But I would’t object to a Yes we could.

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More Statistics…

Posted in G 1 with tags , , , , , , on March 29, 2008 by Roberto Gravitazero
dice.jpg

I continue here the theme of the previous post, i.e., predictions on the Senate election outcome in Italy, based on pre-electoral polls, and statistical analysis of the data. In the last couple of days, a few regional polls had been finally published. I tried to incorporate the more recent ones in my model. As before, I start by giving the results, then add a few comments:

PdL PD SA UDC Others
159 141 9 5 1

The model is now an hybrid, using local polls for 9 regions (Piemonte, Lombardia, Veneto, Liguria, Lazio, Campania, Basilicata, Calabria and Sicilia) and national polls for the others. In spite of having considered only recent polls, spanning the same period, the data are not uniform, in the sense that the 9 regions follow the general trend only approximately. In other words, the uniform national swing is not completely respected. In any case, I guess this is the best I can produce with the present data.

I invite you to have a look for a comparison at www.politiche08.org, a site that uses a very similar procedure, based on regional polls whenever available. Other predictions can be found (apart from noiseFromAmeriKa) also at The Right Nation, a right-wing Italian site and on the blog of Chris Hanretty, an English political scientists.

I repeat again the warning, the Senate electoral system is highly unpredictable, and several region are apparently an extremely close call. In some cases a couple of thousands votes can swing a few seats.

Just for fun, I put below another curiosity. It’s the plot of the correlation, for the model based on nation wide polls, between the PdL-PD vote gap and the projected number of seats in the Senate.

correlation3.jpg

The nice thing is that there is no real correlation below 10%. Therefore, the distance between the two main competitors, in general taken as the main indicator to predict the outcome of the election, is irrelevant for the Senate race.

I’m sorry I never got proper training in chaos theory.

 

UPDATE March 31

In order to facilitate comparisons, I publish below a table with the Senate forecasts for PdL, split by Regions, made by the above mentioned sites during the last days. Please let me know if you spot any discrepancy/error in the Table.

senate_comp.jpg

Note1: I don’t have informations about Hanretty’s predictions split by regions – he predicts a total of 164 seats for PdL, though. I have taken the information directly from the corresponding sites for Right Nation (R. Nat.) and Politiche08 (Pol 08). For noiseFromAmeriKa (nfA) I derived the numbers myself using their published spreadsheet.

Note2: R. Nat. and nFA both use the polls superaverage published by R. NAt., while Pol ’08 uses 2006 results integrated by all regional polls available. I have used an average of all nation wide polls made in March (Grav 1), integrated then by recent regional polls for 9 regions (Grav2).

Note3: R. Nat. attributes one likely seat for Sen. Pallaro from South-America to PdL, on the ground that in the past he declared he would vote for the majority. In the table I took it out from PdL to ease comparison with other sites.

 

An Exercise in Elementary Statistics: Application to Italian Electoral Polls

Posted in G 1 with tags , , , , , , on March 27, 2008 by Roberto Gravitazero

abacus2.jpg

As political elections in Italy are getting close, several blogs and sites are publishing predictions, especially about the outcome at the Senate where, thanks to the peculiar electoral law, it is well possible that no clear majority would emerge.

So, I could not resist to make my own prediction. And I start by giving you the results:

PdL PD SA UDC Others
162 131 17 4 1

Which is indeed a very close call, possibly not enough for PdL in order to rule the country. Berlusconi would have only four seats more than the ones obtained by Prodi in the last elections. Who, however, had initially on his side all of the 7 senators nominated for life by the President, and not counted above. Actually, he got 165 favorable votes when he formed his government in 2006.

I should warn you however that I would be very surprised if this prediction will be exactly fulfilled, and I’m going to tell you why. But, before that, I should explain how I got the prediction in the first place. The method is the one developed by Sandro Brusco from noiseFromAmeriKa. Essentially, one takes the results of 2006 (Senate, divided by Regions), and re-normalize them using the ratio between whatever pre-electoral poll one is trusting and the global results (for the lower chamber) in 2006. Technically, a so-called uniform national swing is assumed. Simple, if not at all granted. But the main complication is how to take into account the different political alliances of 2008. For that I have used a slightly different logic than Brusco (for instance, differently from him, I had allocated UDEUR votes half to UDC and half to PD, while I counted for PD only half of the votes of the former alliance between Radicals – now with PD – and socialists – now independent). There’s more to it, but it does not amount to a large effect in the end. I have checked against Brusco system, using data from the last 7 polls. In 5 cases I obtained the same seats than him for PdL, while in 2 cases I had 2 and 4 seats less, respectively. A result that in my mind reflects well the quasi-chaotic behavior of the system.

In any case, my prediction above is obtained by using an average of all published polls from the beginning of March to the 26th (from Toqueville), a grand total of 41! Now, having taken care of the first order, and being a physicist, I could not refrain to have a look at the whole distribution. Here it is:

pdl_hist.jpg

In the histogram the bars show how many times (out of the 41 samples) PdL had obtained in the simualtion a given number of seats, while the line indicates the cumulative percentage of the total samples below a certain number of seats. For instance, about 50% of the times PdL totalized 162 seats or less. The standard deviation is almost exactly 4. Now, I believe this information adds a lot to the bare prediction. If the polls are correctly done, if the hypothesis of a uniform national swing is correct, and if I have made no additional mistakes, the conclusions are:

1) It will indeed be a close call.

2) No need to discuss about a difference of plus or minus 4 seats in the predictions for PdL – one cannot possibly be more precise than that.

3) It’s quite likely that the situation in the senate will not be better for Berlusconi than it was for Prodi in 2006.

A couple of additional remarks:

noiseFromAmeriKa, like other sites, uses for its prediction an average of the last “few” polls, in order to better reflect the evolution of the public opinion. However, the spread between different polling institutes and individual polls is larger (at least since the last month) that the variation of the average, as one can see in the following picture, showing the simulated number of seats for PdL obtained for the different polls:

pdl_trend.jpg

The line is a second order fit. The evolution of the average is negligible. However, if anything, it looks like the standard deviation is decreasing (especially discounting the 14 March MAKNO poll, really sticking out from the rest and with a low statistical coverage – less than 400 interviews). I have no idea of what this means. It could be a stabilization of the vote towards the smaller parties (there’s no evolution visible it the bare percentage for PdL, as shown below), or, one could mischievously suspect, a tendency of the polling institutes to uniform their results with each other.

pdl_trend_per.jpg

The last plot shows the correlation between simulated number of seats and the percentage of votes in each poll, again for the PdL. As pointed out already by Brusco, the correlation is small compared to the spread, showing the impact of the distribution of the remaining votes among other parties. It shows as well that even exceeding 45% of the votes, the PdL could not be sure to obtain a clear majority.

pdl_corr.jpg

I conclude with a warning: the hypothesis of a uniform national swing is far from being sure. There are reasons to believe that local factors could result in an uneven redistribution at the regional level, and the electoral rules makes the system very much sensitive to this. On top of that, in 2006 the pre-electoral polls had been shown to be not exactly reliable. Therefore, anything can happen. It’s well known it’s not easy to make predictions, especially about the future.

Hat tip to Dorigo, to whom I’ve stolen half of the post title.

Update 30 March – many pre-electoral polls have been published just before the black-out (no polls during the last 15 days before the elections). Using the average of all polls (now there are 50 of them), the prediction does not change. I did also an update of the distribution, which I show below. Note that the lowest (156) and two of the highest (172, 173) predictions are from one month old polls(1,2 and 3 March). The other high one (174) is the Makno one I talked about above. I would tend to exclude them, and I report them here only for completeness.

pdl_histogram_march30.jpg