(Updated: Nothing substantive, just trying to improve on a rough first draft.)
Why do so many political consultants on our side of the spectrum advise their clients they must appeal to the swing voter with a moderate message? (And why, when that strategy fails, do they keep getting hired again?)
It's like the old IT saw, "Nobody ever got fired for recommending IBM."
It's just the kind the low-risk, "sensible" advice consultants like to give. First of all, the mathematics (though dead wrong) is very easy to explain in a convincing way. The argument goes like this: "The base is going to vote for you no matter what. You just need to capture x many [voters, states, electoral college, etc] to put you over 50%. You do that by moving closer to the center, where those votes are."
Secondly, you have to put yourself in the consultant's shoes. When your client loses the election, do you want to be remembered as the guy who recommended he go with the strong, clear, and decidedly left-leaning message? No, because then it would be your fault. You'd rather have the client blame himself for not finessing his message enough, thereby failing to attract enough of that swing group to eke out victory.
What's wrong with the math? Nothing, in terms of arithmetic.
The fallacy is in applying "math" to the swing voter in the first place. It's not a math problem. It's about attitudes, desires, and fears. It's about convictions -- or more precisely, the lack thereof.
The center isn't a political position - it's the lack of one. The undecided, "swing" voter, by definition, is one who doesn't have strong opinions. He or she doesn't know the answers. She's looking for a candidate who can articulate some convincing solutions - not one who is apparently as unconvicted as she is.
Given a choice between candidate R, with a clear, strong, right-leaning message, and candidate D, who's clinging to the "center" with a moderated, even muddled, positions, is it any wonder if the swing voter tends to be attracted to R? R offers solutions and hope. D offers more muddling along.
Instead of triangulating over to get next to those voters in the center, the candidate should be framing and articulating his strong and clear positions in a way that gets the swing voter to come to him.
In a word: Leadership.