The question 'Who's ahead in the polls?' is a delicious and savoury pun, because a poll is a head. Or it was. Shakespeare used poll to mean a head and it was still going strong in the C19th. But now it's mainly used about horses.
Nonetheless a poll was a head and from this you get:
Tadpoles - which are literally toad-heads. Little heads swimming around waiting to grow their bodies.
Poleaxe - an axe with a specialised and rather brutal looking head. See the illustration.
Poll tax - a tax per person. Think of it like a head-count, or the phrase 'a hundred head of cattle' (try not to think of poleaxes at the same time).
Polling station/booth/going to the polls etc - This gives you the head count of an entire nation.
Opinion poll - a headcount of people's opinions
Straw poll - Nobody's quite sure about this one. It's either a poll that is so weak that it may as well have been made of straw. Or it derives from the practice of throwing some straw in the air to see which way the wind is blowing. As Bob Dylan correctly observed "You don't need a weatherman to know which way the wind blows". You do not. You need straw.
Sometimes the poll was just the top of the head, just the bit that your hair grows out of. From this you got the sense of a poll as a haircut. ("Nice poll." "Oh, do you like it? Thank you."). So, in Hamlet, Ophelia sings:
He never will come again.
His beard was as white as snow,
All flaxen was his poll:
He is gone, he is gone...
This meaning was still around when D.H. Lawrence wrote Sons and Lovers in 1913:
The child—cropped like a sheep, with such an odd round poll.
This is because a poll was usually a short, even haircut. And from that you get poll as a verb, meaning to cut short and evenly. If you do that to a tree, then the tree has been pollarded.
Moreover, the paper on which a legal deed is written can be cut evenly at the bottom, in which case poll becomes a postpositive adjective (like attorney general, or astronomer royal) and the legal deed is a deed poll.
But the two most important variants of poll are doddypoll, which is an old word for an idiot, and poll-sickness, which was helpfully defined in 1899:
Poll-sickness..is a kind of sore or abscess which horses get from knocking their heads against low door-ways and is commonly supposed to be incurable.
I fear it is.
Two doddypolls arguing about the polls with poleaxes
P.S. Something really important will be happening on Thursday evening, and it truly is your civic duty, and the duty of everyone, to tune in to BBC2 at 9pm where I will be making a brief appearance on Inside the Factory, discussing the history of kissing under the mistletoe.
This could change Britain forever. I hope for the worse. I just wanted to sell a few copies of Christmas Cornucopia, which, I happen to notice, is available to buy and would make a wonderful Christmas present.