Nov 182016

With the vote mostly counted in the US, PS have posted a useful summary of the Political Science Forecasting Models for that infamous election.

By and large, and in neat contrast to the current fad for self-flagellation, the augurs of the discipline have done well. Eight of the ten predictions that were published in PS got the winner of the popular vote right. Not that it would make a difference. Somewhat ironically, Norpoth’s Primary Model that I had (incorrectly) credited  on that gloomy Wednesday morning with predicting a Trump victory performed worst.  But in fairness to HN, his model has by far the longest lead.

Nov 092016
Ballot - Vote

I’m not a huge fan of predictive Social Science. People are not the weather; they are bound to react to our predictions, which may become self-defeating or self-fulfilling in the process. Either scenario is unpleasant for obvious reasons. Predictive models are often subject to herd behaviour. They rarely rely on first principles, which makes them rather less interesting in terms of understanding the underlying dynamics, and may therefore fail rather spectacularly if the underlying, often implicit assumptions fail. This, in turn, tends to leave us with egg on our collective face.

Having said that, and looking at the rather spectacular result of the US presidential election, it’s difficult not to be impressed by Helmut Norpoth’s “Primary Model”, which predicted a solid Trump victory back in March. The Primary Model relies on very little data, has a relatively long lead (time from prediction to event), and a good track record: It has correctly identified the winner ever since it was introduced in 1996. Whether that makes HN a happy man today is a different matter.

The Primary Model’s rather quaint website is here; the link above points to a more accessible contribution by Norpoth to the PS symposium on forecasting the 2016 election. Which brings us back to the collective egg/face problem.


I wrote  the original post in the early hours of November 9, when it was clear that Trump had a majority in the Electoral College. Since then, it has become clear that Clinton has won the popular vote, probably by a considerable margin. Because (as a couple of people have noted on Twitter) the Primary Model aims at predicting the popular vote, even Political Science’s consolation prize is gone. 

Dec 162012

Following Friday’s events, the attached image went viral. The figures (if correct) are certainly suggestive, but obviously, the population at risk varies widely between countries. What we need is the gun-related homicide rate for a sample of comparable countries. I headed over to the Brady Campaign, which had created the image, but could not easily find comparative data. Next, I tried the very useful Gun Policy Project. Their website features very detailed country profiles, but unfortunately no ready made tables, and so I spent a lazy hour keying in gun-related and total homicide  numbers as well as possession rates (guns per 100 people) for 34 OECD countries.

Looking at the data, I decided to remove Mexico from the sample: The civil war like situation in the North means that relatively few guns are enough to kill about 11,000 people each year in a population of just over 112 million people. Put differently, about one in 10,000 Mexicans is shot dead each year. Thankfully, no other OECD member is in a comparable predicament.

Next, I created boxplots for the distribution of possession rates, gun-related and total homicide rates.

Possession, total homicide and gun-related homicide rates for OECD members

Possession, total homicide and gun-related homicide rates for OECD members

The US of A is clearly an outlier in every respect. I was somewhat surprised by Estonia’s high homicide rate. While the country’s population is small at 1.3 million people so that random fluctuation could have an impact,  a rate that is roughly six times the median seems excessively high.

Next, I specified a Negative-Binomial model of gun homicide counts as a function of the gun possession rate, controlling for the population at risk of being shot dead. Yes, I know this is dodgy with a small, non-random sample:

Negative binomial regression                      Number of obs   =         33
                                                  LR chi2(1)      =       8.17
Dispersion     = mean                             Prob > chi2     =     0.0043
Log likelihood = -162.78208                       Pseudo R2       =     0.0245

gunhomicides |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    possrate |   .0209951   .0083522     2.51   0.012      .004625    .0373652
       _cons |  -12.85624   .2292694   -56.07   0.000    -13.30559   -12.40688
ln(popula~n) |          1  (exposure)
    /lnalpha |  -.1823302    .228441                     -.6300664     .265406
       alpha |   .8333261   .1903659                      .5325565     1.30396
Likelihood-ratio test of alpha=0:  chibar2(01) = 2361.65 Prob>=chibar2 = 0.000

As expected, gun possession raises the risk of being shot dead significantly. According to the model, each additional gun per 100 citizens increases the relative risk by exp(0.021) = two per cent (careful: If the initial risk is very low, that means that you are still quite safe).

These findings are, however, largely driven by the US with their very high possession and homicide rates. If they are excluded from the sample, the effect of gun possession is much less pronounced:

Negative binomial regression                      Number of obs   =         32
                                                  LR chi2(1)      =       0.09
Dispersion     = mean                             Prob > chi2     =     0.7660
Log likelihood = -151.9413                        Pseudo R2       =     0.0003

gunhomicides |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
    possrate |   .0043764   .0148325     0.30   0.768    -.0246948    .0334475
       _cons |  -12.61879    .298236   -42.31   0.000    -13.20332   -12.03426
ln(popula~n) |          1  (exposure)
    /lnalpha |  -.1926419   .2319586                     -.6472725    .2619886
       alpha |   .8247772   .1913142                      .5234716    1.299512
Likelihood-ratio test of alpha=0:  chibar2(01) = 2318.53 Prob>=chibar2 = 0.000

And yet, given the countries the number of gun homicides in the US is massively underestimated 
by the model:
Negative binomial models for gun possession/gun homicides w and w/o US

Negative binomial models for gun possession/gun homicides w and w/o US

Gun possession is easily comparable across countries but a less than perfect measure of the underlying regime. As a ratio, it does not capture the actual distribution/accessibility of guns, nor does it pick up differences in licensing laws or the availability of automatic weapons. As can be seen from the dashed line, outside the US more guns still mean more killings, but there is a lot of noise in that relationship. There are, however, three countries with very low possession rates of less than 1.5. Unsurprisingly, they also have extremely low gun homicide rates. A final, nonparametric plot picks up this relationship:

Nonparametric model for gun possession / gun homicide

Nonparametric model for gun possession / gun homicide

So what’s the implication for the US? If the model was true and the US would bring down its possession ratio to the OECD median of 13.5 per 100 citizens, the model predicts 1071 gun homicides, as opposed to 9,146 actual cases (2009). That would be 8,075 lives saved.

But the model does not fit very well, and we might be better off with a very naive, non-parametric estimate. If the US  became less like the US and more like the rest of the OECD, its gun homicide rate might come down to the OECD median. That would amount to 846 people murdered using a gun, less than 10 per cent of the current figure. Of course, some of those people who would be spared the bullet might be killed by other means, but that is arguably more difficult. And this is just homicides. If you add manslaughter, suicides and accidents, it seems safe to assume that the NRA/Second Amendment culture costs at least 8,000 lives a year.


How many people die each year because of the "Second Amendment"? My estimate is 8000+ 1
Sep 222008

Today, the BBC has a rather amusing piece by Larry Sabato (Virginia) on the “The US election nightmare scenario“: an equal split of the “toss-up” state leads to deadlock in the Electoral College. Enter the unit rule, a constitutional provision which stipulates that the House will select the President in a vote where each state delegation has a single vote. Sounds bizarre? Certainly. Unlikely? Not entirely. And yes, apparently Pelosi could become the next President of the US. Read it yourself.
Technorati-Tags: US, elections, constitution, unit rule, electoral college, Barack Obama,John McCain,Nancy Pelosi, fun

Jul 122008

Library of Electoral Behaviour/Electoral Behavior 2

As a subdiscipline, the study of electoral behavior (or “psephology”) begins with a handful of monographs that were published in the 1940s, 50s and 60s. It’s amazing to see how concepts and ideas that were developed in Downs’ “Economic Theory of Democracy” or in the “American Voter” by Campbell et al. some 50 years ago inform our work to the present day. However, the study of electoral behaviour (or electoral behavior – the publisher keep changing the title just to confuse me) did obviously not end with these holy books. From the 1960s on, the discipline was increasingly defined by a number of ground breaking articles that were published in professional journals.

This collection gave us the opportunity to bring together 66 articles which – in our humble view – define the discipline, represent important new departures, or bring together the knowledge we have on a given subject. As a friend of mine wisely remarked, at $ 950 the collection might be slightly underpriced. Then again, if you teach a course on electoral behaviour or political sociology, or if just want to get an overview of electoral studies, getting much if not most of the important stuff in one four-volume-1640-pages book is really a bargain. Maybe you should invite your librarian for a coffee. Make it a large one.

What the Library of Electoral Behaviour gives you is a full introduction to the study of electoral behaviour plus:

Socio-Political Models

  1. Lipset, S. M. and S. Rokkan (eds.) (1967) [‘Introduction’] in Party Systems and Voter Alignments: Cross-National Perspectives, New York: The Free Press..

  2. Erikson, Robert, John H. Goldthorpe and Lucienne Portocarero (1979), ‘Intergenerational Class Mobility in Three Western European Societies. England, France and Sweden’, British Journal of Sociology 30: 415-441

  3. Alford, Robert R. (1962): A Suggested Index of the Association of Social Class and Voting, in: Public Opinion Quarterly 26, S. 417–425

  4. Lijphart, Arend: Religious vs. Linguistic vs. Class Voting: The “Crucial Experiment” of Comparing Belgium, Canada, South Africa, and Switzerland, The American Political Science Review, Vol. 73, No. 2. (Jun., 1979), pp. 442-458.

  5. Class Mobility and Political Preferences: Individual and Contextual Effects Nan Dirk De Graaf; Paul Nieuwbeerta; Anthony Heath The American Journal of Sociology, Vol. 100, No. 4. (Jan., 1995), pp. 997-1027.

  6. The Developmental Theory of the Gender Gap: Women’s and Men’s Voting Behavior in Global Perspective Ronald Inglehart; Pippa Norris ‎. (Oct., 2000), pp. 441-463.

  7. Alan Zuckerman (1975) ‘Political Cleavage: a conceptual and theoretical analysis’, British Journal of Political Science, 5: 231-248.

  8. Key, V. O. “A Theory of Critical Elections.” The Journal of Politics 17, no. 1 (1955): 3-18

  9. Belknap, G., and A. Campbell. “Political Party Identification and Attitudes toward Foreign Policy.” The Public Opinion Quarterly 15, no. 4 (1951): 601-23.

  10. Converse, P. (1966) ‘The concept of a normal vote’ in A. Campbell et al (eds.) Elections and the Political Order, New York, John Wiley.

  11. Jennings, M.K. and R. Niemi (1968) ‘The transmission of political values from parent to child’, American Political Science Review, 62: 169-84.

  12. Converse, Philip E. (1964), ‘The Nature of Belief Systems in Mass Publics’, in: David E. Apter (ed). Ideology and Discontent, pp. 206-261, New York: Free Press

  13. Jackson, J. (1983). “The systematic beliefs of the mass public: estimating policy preferences with survey data” in Journal of Politics, vol. 45: 840-58.

  14. Markus, Gregory B., and Philip E. Converse. “A Dynamic Simultaneous Equation Model of Electoral Choice.” The American Political Science Review 73, no. 4 (1979): 1055-70.

  15. Fiorina, Morris P. “An Outline for a Model of Party Choice.” American Journal of Political Science 21, no. 3 (1977): 601-25.

  16. Bartels, Larry M. “Partisanship and Voting Behavior, 1952-1996.” American Journal of Political Science 44 (2000): 35-50.

Cognition and the Voter Calculus

  1. Hotelling, Harold (1929), ‘Stability in Competition’, The Economic Journal 39(153): 41-57.

  2. Riker, William H., and Peter C. Ordeshook. “A Theory of the Calculus of Voting.” American Political Science Review 62 (1968): 25-42.

  3. Continue reading »