How to Study Things that Can Go Around in Circles

Two voters plus three voters makes five voters. If a party that used to hold four ministries loses one, it still controls three ministries. For many phenomena that we analyze in political science this linear world view seems appropriate or at least an acceptable simplification. But for many it does not. If terrorists used to attack at around 11pm, but now these attacks tend to happen two hours later, this means that they occur at 1am. If political candidates compete on a circular issue space, then a candidate moving far enough to the left will eventually end up at the extreme right. We measure such phenomena on circular scales: the 24-hour clock, compass direction, or calendar measurement. They do not have an origin, since the endpoints are connected.

Although examples for political events measured on circular scales abound, we still lack appropriate methodological tools to analyse this type of data. In an article recently published in Political Analysis, Jeff Gill and Dominik Hangartner start filling this gap. One of their applications analyzes the direction of party movements. This relates to a post by Romain Lachat (“Which Way from Left to Right“), where he conceptualized political competition in the Zurich municipal elections as taking place on a circle. The figure below shows the direction in which parties moved from 2002 to 2006. Most parties shifted to what many would call the economic right.


Figure: Directions of party movements in Europe from 2002 to 2006. Source: Gill and Hangartner 2010 (working paper version)

Another application contributes to research on violent conflict. Experts estimate the number of civilian fatalities in Iraq since the beginning of the Second Iraq War to exceed 80’000 deaths. An analysis of the time at which these incidents occurred (table 1), measured on the 24-hour clock, suggests that fatalities due to gunfire or mortar rounds happen on average earlier during the day than incidents due to bomb attacks, which form the reference category.

Table: Results for timing of attacks involving civilian fatalities in Iraq


While the signs of the coefficients indicate the direction of the relationships between the predictors and the time of incident, interpreting their size requires some trigonometric computations which the article describes in detail. The results suggest that gunfire casualties happen on average about one hour earlier than bombings. Moreover, their timing has shifted over the years. Directly after U.S. forces had invaded Iraq in 2003, bomb attacks used to occur Saturdays shortly before 8am on average. Such attacks now happen later during the day. The annual shift equals about one hour on average. I look forward to seeing papers that analyze circular data in political science!

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