From what I've seen in the research, people may vote non-rationally on some ballot items: usually issue voters, who go to the polls to vote for a specific candidate or issue and are uninformed about other issues or offices on the ballot. They don't vote randomly per se. People (as a rule) are not good at random action, and instead vote in line with unconscious biases or habits. There is a well-documented effect, for instance, that a candidate can get a 5% boost merely by being listed first on the ballot, because (assumedly) people unconsciously associate 'first' with 'best'.
As far as I can tell there is no significant population of voters who intentionally go to the polls to make arbitrary choices. Nor can I see a point in that: ballots are secret, precluding public demonstration; arbitrary votes will cancel out, statistically speaking, so there's no real harm done. Where's the fun in that?
'Swing voters', as the term is commonly used, are not people who arbitrarily or randomly cast their votes. Swing voters are people who make conscious decisions about who they will vote for on criteria other than party affiliation. A partisan voter will cast his vote for his party's candidate, come hell or high water; a swing voter might cast his vote for either party's candidate, for a variety of reasons. Swing voters might vote for the candidate they think is most competent for the position; for the candidate they think is most dynamic and powerful; for the candidate they think is more attractive, or who is taller. Such people may have a party preference, but they are willing to vote across party lines for the right candidate.
In an ideal democracy, all voters would be conscientious swing voters, putting into power those people they think are most fit for office. Of course, that works against the interests of political parties, so political partisans tend to demonize swing voters as irrational or incompetent. Be wary of the things you hear...
