First, let's look at a simple estimate of leader survival for all (effective) political leaders in all regimes in the post WWII era:
The figure shows an estimate of the proportion of leaders who are expected to still be in power after n years. So, for example, after four years in power, less than half of all leaders are expected to still be in power, and after 20 years less than 10% of all leaders are expected to still be in power; the majority of all leaders last less than 4 years in power, and the vast majority less than 5. [Update: of course, some of these leaders come back to power after a shorter or longer period out of power.] This may be easier to see if we draw the plot on a logarithmic scale:
This looks like a classic "long tail" distribution of a kind often produced by "rich get richer" processes: most leaders don't last in power very long, but those who beat the odds can do very well indeed, as power feeds on itself and leaders become increasingly difficult to dislodge. (I won't say anything about power laws for fear of attracting the ire of the statistical gods).
Nevertheless, democratic leaders and non-democratic leaders aren't equally successful at hanging on to power:
While the median democratic leader can expect less than 3 years in power, the median autocrat can expect a bit less than 7. And the gap widens with time: less than 8% of all democratic leaders can expect to hang on to power for more than 10 years, but more than 40% of autocrats do, and no democratic leader in the sample has lasted more than 25 years in power (Lynden Pindling of the Bahamas and Eric Williams of Trinidad and Tobago; your mileage may vary as to how democratic you think they were, but that's how they are coded), whereas nearly 20% of autocrats do. This may seem obvious (after all, autocrats typically impose larger barriers to political competition than democratic leaders, and ordinary people face larger obstacles in trying to get rid of them) but it also presents a bit of a puzzle, for democracies are supposed to be more responsive to popular wishes and more legitimate, and dictators are always at risk of being overthrown by their close associates. (For one influential explanation of the observed pattern of survival by Bueno de Mesquita, Smith, Siverson, and Morrow, see here and here). The greater legitimacy of democratic leaders, and their closer connection to popular opinion (to whatever degree: let's not exaggerate, either), does not seem to translate into a surer hold on power.
Not all autocrats do equally well; absolute monarchs are especially successful at holding on to power:
I was also curious to see whether the survival of leaders differs across regions of the world. And at least for non-democratic leaders, that seems to be the case:
can be found here, including the criteria it uses for categorizing regimes as democratic or non-democratic and a general defense of its methodological approach. (It used to be possible to download it as well from that page, but the form no longer seems to be working. I've animated the dataset here.) These criteria have been criticized for a variety of reasons, but in general DD does not suffer from worse problems than many of the other common datasets of political regimes (like Polity IV or Freedom House). It is possible that some of the coding decisions they make might influence the estimates of survival presented above, e.g. because they err on the side of classifying some regimes as dictatorships that could have been considered democratic (when there has been no alternation in power). This would tend to bias downward the survival estimates of democratic leaders. At any rate, DD includes information about leaders and their tenure, which is missing in other datasets and makes the data-wrangling easier, though this information is not always complete (there is sometimes more than one leader in a year for a given country, a fact that the dataset must omit, given its country-year resolution) and is not quite in the right format for survival analysis. I thus had to reshape it (R code and a general description of the process; rank amateurism on display). I created three data files: one for the plots of survival for all leaders and leaders by democracy/non-democracy (ddsurvival.csv); one for the plots of survival by autocratic regime type (ddsurvival2.csv); and one for the plots of survival during and after the cold war (ddcoldwar.csv). (R code for generating all plots is here). These files treat the leader spell as a case; "right censoring" occurs when the leader dies or if the leader is still in power by 2008 (see the DD codebook; the files use a variable called ecens2). Since DD does not distinguish between deaths by natural causes and political assassinations or death in revolution, this introduces a certain amount of bias; in theory, "political" deaths should not result in"censoring" of the data. I should note that the plot of survival by autocratic regime type does not take into account some cases where "left censoring" occurs (i.e., when a regime starts before 1946), though the number of cases where that is a problem is very small. Finally, there are a small number of repeated cases in ddsurvival.csv and ddcoldwar.csv due to problems guessing the right "entry date" for the leader; these must introduce some small amount of error, though I couldn't possibly say how much or in what direction the bias would work.
[Update, 1/31/2012: Fixed minor typos]
[Update, 1/02/2012: Changed location of code and data files]