fraction can be up to 70% [e.g., @1970ranp.book.....P]. The more typically observed levels of fractional polarization reach a few tens of percent at maximum , which have been taken as evidence for disordered magnetic fields. The linearly polarized emission is described using the Stokes parameters *I* (for total intensity), and *Q* and *U* (for linear polarization). Using the Stokes parameters, the polarization fraction and the electric vector position angle (EVPA) can be defined as $m=(\sqrt{Q^2+U^2})/I$ and EVPA$=1/2\tan^{-1}(U/Q)$. The polarization fraction and EVPA for S2 0109+22 are shown in Figure \[pollc\].

We estimate the long-term polarization variability of S2 0109+22 by using the methods described in where the optical polarization of a sample of TeV and non-TeV-detected BL Lac objects was studied. We calculate the intrinsic mean polarization fraction and its modulation index (standard deviation of the polarization fraction over the mean), by assuming that the polarization fraction follows a Beta distribution, which is confined to values between 0 and 1, similarly as the polarization fraction. A single polarization observation is assumed to follow a Ricean distribution, so that our probability density function is obtained by convolving the Beta and Ricean distributions as follows,

$${\rm PDF}\left(p;\alpha, \beta\right)=\frac{p^{\alpha -1} \left( 1-p\right)^{\beta -1}}{B\left(\alpha, 