The Jimmie Lunceford Model of Democracy

I have a conjecture about democracy: The truth-value of the claims a politician makes have at most a very slight effect on his chances of getting elected. A politician can stand up on a podium and tell blatant lies, and these lies can be debunked conclusively, yet he will suffer no negative consequences. What matters is that the politician tell the lies confidently and convincingly.

I think that this works because the median voter is simply not equipped to assess the truth-value of a politician's claims, so his vote comes down to a combination of esthetic factors and social proof (these dominate among the party loyalists), and perception of one politician as more likeable or trustworthy than the other (this dominates among swing voters). For the vast majority of voters, style trumps substance.

I'm not 100% sure of this, but it would explain a lot. Can anyone think of any counterexamples? Has a politician ever been caught in a lie (about policy, not sex), refused to acknowledge it or show contrition, and paid an electoral price for it?

Also for consideration: Can a politician beat a sex scandal by immediately coming out and saying, "Yeah, I slept with her, and her sister, too, and it was good. Any other questions?" That is, is it the display of contrition (and thus weakness) that hurts them more than the actual scandal?

Reference here.

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Counterexample

Nixon - Watergate?