6 cards of the 114 in the game are polling cards. 4 players get 28 cards to start & 1 in 19 cards is a Polling card. Turn 2+ is 26 cards.
So on average every turn should have a poll (& 36% chance of a 2nd) & a reshuffle with odds going up slightly due to events dropping out. (ours was about 20 (?) at game end.)
3 players will reduce the odds by 1/4.
I have not counted the event cards yet.
Enjoy the chaos!
Actually, with the 3 reaction polling cards that let you initial polling in a different region if the polling card is not already there, that brings the number of polling cards to 9.
So you should get a polling card 1 out of 12.67 cards dealt.
Edited to correct amount of cards and card average