Compare acidic strength of crotonic acid (1) and isocrotonic acid (2):
On comparing $\mathrm{p}K_\mathrm{a}$ values, cis-form $(4.44)$ turns out to be more acidic than the trans-form $(4.69)$.
Most of the explanations I found on internet say that cis-form will be more acidic because in trans-form the $\ce{CH3}$ opposite to it, provides electrons by inductive effect directly in its direction (the dipole moment is almost directly in its direction) making the conjugate base unstable.
However, I am not convinced with this explanation as there's also a $\ce{C=C}$ bond between methyl group and $\ce{COOH}$ so same amount of electron density reaches $\ce{COOH}$ group via the double bond in both cases.
What's the flaw in my reasoning? How to compare the acidic strength correctly?