Boyajian et al. (2015) report that the star KIC 8462852 has undergone a recent series of rapid, significant dips in brightness which Wright et al. (2015) explain by suggesting the star is occluded by an 'alien megastructure'. Schaefer (2016) note the star has been dimming for at least a century; here we use these observations to calculate the time taken to construct a 'Dyson sphere' that will eventually occlude 100% of the star's flux.
We assume our observations cover a typical period in a constant construction rate. Given the current B magnitude of 12.262 and a decrease in flux of 0.165 mag (or 14.099% of total observed flux) per century, an alien civilisation requires at least 7.09 centuries to occlude 100% of the observable surface of its star. Thus, if this time is typical, an alien civilisation capable of constructing such a structure requires a minimum of 1400 Earth years to do so.
On Earth, we observe that it is difficult to gain political support for infrastructure projects lasting longer than one election cycle, and therefore predict elections in this alien civilisation occur less than once a millennium.
The authors acknowledge help from Dr Chris North (via Twitter) in the preparation of this paper.