If there are 100 voters with a probability of just 45 percent of voting for your candidate, then you would expect your candidate to lose by 10 votes, assuming everyone voted (45 for vs. 55 against). If you persuaded these 100 voters to have slightly positive feelings towards your candidate—say, a 55 percent probability of voting for him—than he should receive a net gain of 10 votes (55 for vs. 45 against). Overall, then, as your candidate moves from 45 to 55 percent favorability, his campaign experiences a marginal shift of 20 votes—from losing by 10 votes to winning by 10 votes. Now let’s say your 100 voters start out with a 65 percent likelihood voting for your candidate—that’s a margin of +30 if they all vote (65 for vs. 35 against). If you bump up that probability to 75 percent, you now have a margin of +50 (75 for vs. 25 against). The net gain in margin from shifting probability of support from 65 to 75 percent? Twenty votes, just as in the previous example.
Persuadability, then, is not logically restricted to voters in the center; it can potentially be far more broadly distributed. That is what William Mayer found in his analysis of swing voters based on National Election Study data. Swing voters are least likely to be found among strong partisans (12 percent of this group); more likely to be found among independent leaners (27 percent) and weak partisans (28 percent); and most likely to be found among pure independents (40 percent). But since pure independents are such a small group, they wind up being just 13 percent of all swing voters, actually less than the number of strong partisans among swingers (18 percent). Another 28 percent of swing voters are independent leaners, and the largest group, 42 percent, are weak partisans. Thus the overwhelming majority (70 percent) of swing voters are weak or independent leaning partisans—the kind of voters whose probability of support for “their” candidate is more usefully thought of as being movable from 70 to 80 percent than from 45 to 55 percent.