The books describe Tyrion thusly:
"grotesque"
"Head too large for his body, squashed-in face beneath a shelf of brow"
"ugly"
And then this is the gorgeous flawless handsome motherfucker they cast:
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And it's even worse in the show! He looks even more handsome, despite the fact that shouldn't be earthly possible:
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I mean, seriously. How is Jaime Lannister supposed to be "the handsome one" with this flawless God walking around the place, being his usual badass self? I don't even get why he's always having to pay for it, because if I was some warrior queen* shooting the shit out of everybody in George RR Martin's fantasy world, you can bet your ass I'd be all over him like white on rice. Or something more medieval-y, like skins on a potato.
And then I'd murder all the Lannisters and all the Starks and just fucking everybody, and rule the realm with him as my King.
Because you know he deserves to be. I've read all of book one and almost all of book two in a fever of reading-crack, and you have to know that Tyrion Lannister only gets even more badass and flawless as the story progresses. Never mind King of Westeros. He deserves to be King of Everything right here and now.
And then inbetween being King of Everything he can be a filthy little lecher all over me. Lech to your heart's content, my love. Lech until the cows come home. Let us lech in our feather bed of deviant iniquity, with all the delights of Medieval Land around us: suckling pig, mead, strange sexual devices the likes of which my own pristine world has never known.
Or failing that, I could just watch you slap the shit out of Joffrey forever and ever and ever:
*Status of self in George RR Martin's fantasy world may have been greatly exaggerated. In fact, it's far more likely that I'd just be some fat peasant wench and Tyrion Lannister wouldn't bother himself to fart in my general direction.