More noodling with the process of deciding how to vote.
Here's a diagram modeling various schemes for evaluating candidates based on a "focal issue" -- some single issue (or, for that matter, set of issues) which the voter considers of dominant importance. Think abortion, obviously, or life issues generally, or the war on terror, or socialized medicine.
I think interpreting the model is straightforward enough. For those who disagree:
The basic idea is that the voter somehow rates each candidate, from however bad to however good, along two scales or axes. One is the focal issue, the other is an aggregate of all the other issues. Given these two scores, the position of each candidate can be plotted on a graph like the one shown (e.g., points p,q, r, s, and t).
Now, by definition a single-issue voter doesn't care about the other issues; to him all candidates who fall on the same vertical line (e.g., A, B, C, D) are equivalent, and the candidate on the right-most line is his preferred candidate. Given candidates at p, q, r, s, and t, then, a single-issue voter would vote for the s candidate every time.
Some single-issue voters impose a threshold on candidates (e.g., the dashed line T), refusing to vote for any candidate whose score on the focal issue isn't higher than the threshold. If the choice facing such a voter were candidates at points p and q, the voter wouldn't vote. (A single-issue voter without a threshold would, of course, vote for the q candidate.)
One would hope a single-issue voter, given a choice between candidates who have the same focal issue score -- say, candidates at points r and t -- would choose the candidate with the highest score on the other issues (t, in this case), but I suppose if someone were literally a single-issue voter, he might just toss a coin. (This might even be rational, if he knows he knows nothing about any other issue, and so can't tell which candidate is better, although next time he should prepare better.)
Some voters consider a single issue to be a dominant, but not determing, factor. For these voters, a candidate who is a little worse on the focus issue but much better on the other issues -- who is at t, say, rather than s -- will be preferred. A straight line in the graph represents points such voters assign equal worth to, so a particular voter might find candidates at points p, q, r, and s all equally appealing (with one at t clearly better). The steeper the line, the more the voter values the focal issue over all the other issues.