Crucially, the opponent of participation holds the default political position of passive inaction. This usually ends up having two symmetrical effects. On one hand, it allows him to adopt a posture of cyncism, even if he is making an affirmative, controversial argument; since he can always declare himself unconvinced by criticism, it can seem as if his argument has held, even though it hasn't. On the other hand, it forces the advocate of participation into a defensive posture, even when she is making modest arguments or declining to accept affirmative ones. Anything she says can be doubted, and her failure to persuade can seem to vindicate those doubts.
Simple example: consider the idea that the election of Democratic and Republican candidates will always have effectively identical consequences for society. Basic skepticism demands that we understand this as a claim to be argued for, not a Truth to be accepted. To the extent it's obvious it should be easy to prove; but even in that case, it certainly isn't unquestionable, nor is it somehow self-proving or definitionally true.
As a matter of basic probability, it turns out, the exceedingly particular prospect of absolutely identical outcomes is far less likely than the general prediction that, given an effectively infinite range of possible outcomes, the consequences of two different administrations will probably differ. If only by accident - though more likely, because of predictably different governing practices - one candidate will probably be at least slightly preferential. It would actually be quite difficult to design two policy agendas that are distinct in any way that create, on a national / international level and for all of the foreseeable future, all of the same consequences!
In fact, to believe otherwise, it would seem, demands an incredible degree of credulity. We have to believe that our political system is so finely calibrated that not even the smallest aberration in electoral outcomes is possible. It is unclear why anyone would actually think this; it isn't a tenet or implication of any political philosophy in the known universe. Even if you believe that our system maintains a certain status quo by modulating the two parties, there is no need to suppose that it does so perfectly, or that this status quo cannot encompass a range of preferential outcomes. Faith in such an exact equivalence between parties reminds me of nothing so much as the right's fanatical faith in absolute market equillibrium. These are both extreme and extremely untenable views, for many of the same reasons.
Nevertheless, it's clear that in our political discourse, the person arguing for a difference between parties is understood to occupy the credulous and dogmatic position, while the person arguing for a functional equivalence is somehow the agnostic skeptic. This owes less to the actual merits of their positions than to their respective agendas - one advocating action and judgment, the other advocating passive abstinence. In general, when you examine the leftist case against voting, you find a lot of arguments that on their own are extremely weak and untenable. But by default, they are likely to survive.