The average voter’s prior belief is that the incumbent is better than the challenger. Because without knowing anything more about either candidate, you know that the incumbent defeated a previous opponent. To the extent that the previous electoral outcome was based on the voters’ information about the candidates this is good news about the current incumbent. No such inference can be made about the challenger.

Headline events that occurred during the current incumbent’s term were likely to generate additional information about the incumbent’s fitness for office. The bigger the headline the more correlated that information is going to be among the voters. For example, a significant natural disaster such as Hurricane Katrina or Hurricane Sandy is likely to have a large common effect on how voters’ evaluate the incumbent’s ability to manage a crisis.

For exactly this reason, an event like that is bad for the incumbent on average. Because the incumbent begins with the advantage of the prior.  The upside benefit of a good signal is therefore much smaller than the downside risk of a bad signal.

As I understand it, this is the theory developed in a paper by Ethan Bueno de Mesquita and Scott Ashworth, who use it to explain how events outside of the control of political leaders (like natural disasters) seem, empirically, to be blamed on incumbents. This pattern emerges in their model not because voters are confused about political accountability, but instead through the informational channel outlined above.

It occurs to me that such a model also explains the benefit of saturation advertising. The incumbent unleashes a barrage of ads to drive voters away from their televisions thus cutting them off from information and blunting the associated risks. Note that after the first Obama-Romney debate, Obama’s national poll numbers went south but they held steady in most of the battleground states where voters had already been subjected to weeks of wall-to-wall advertising.