Many anti-voting arguments by radicals are basically consumerist, sometimes dressed up in metaphysical notions of the act of voting "legitimating" the system or "ceding your power."

I think we can afford a more nuanced take on this...
Basing abstention discourse on the ethics of individual ballot activity uses a liberal, individualist lens to examine the issue — hence its similarity to "consumer activism." As socialists we should examine this topic from the perspective of collective action.
So let's start by talking about consumer activism. There are two kinds of "boycotts" we hear ppl talk about.

One is the offhand or personal kind: you object to something about a product and so you choose not to purchase it.
The more profound kind of consumer boycott is one that's seriously organized. These boycotts hold a prominent place in the history of social change: think of the Montgomery Bus Boycott, the UFW's 1960s grape boycott, and of course the first letter of "BDS" stands for "boycott."
The hallmark of a serious, successful boycott is not found in the injustice being opposed but the organization behind it.

*Unorganized* boycotts, regardless of the cause, aren't effective. All they offer is a good feeling when passing over a product in the grocery aisle.
It's useful, then, to think of individuals abstaining from voting as an unorganized boycott. It'll feel good, but it won't accomplish anything.

If that's the case, then what would an *organized boycott* of voting look like?
The CNT is a good example of what *organized* abstention looks like. In the 1930s the CNT had both the abstentionist position and the numbers to actually have an impact. Abstention was so widespread in the '33 election the state had to hold a second one to fill 97 vacant seats.
The '33 election was a victory for right-leaning parties. When the CNT chose not to push an abstentionist position in '36, left parties won a majority. So this was a tactic that, when organized, was big enough to affect electoral outcomes, and had internal organizational impacts.
Indeed, it was the left coalition's promise of freeing political prisoners that induced the CNT to relax its abstentionist position. Those politicians recognized the CNT's power, both economically and politically, and adjusted their positions accordingly.
Of course the '36 victory of the left parties was a proximate cause of Franco's coup in the first place. And unfortunately, despite the prisoners freed in February, by the time of the coup attempt there were roughly the same number of CNT partisans in jail as before the election.
*Organized* abstention should absolutely remain a viable tactic in the revolutionary left's toolkit, subject to the same questions of strategy and appropriateness as any other tactic.

And for those who're pushing abstention only at an individual level so far: step up your game!
Personally, I don't think organized abstention is a viable tactic at this moment. We just don't have the level of organization and militancy needed.

In 1933, CNT's slogan was "Social Revolution, Not the Ballot Box." It was a promise they could plausibly keep.
For our fellow members of the working class, either voting is unimportant or they consider it a sacrosanct activity. So abstentionist outreach will be either boring & irrelevant or an outrageous affront to them. At this moment, there are much more important messages to convey.
For my part, I've been careful to focus my fire on electioneering — the organized work, money, and resources dedicated to campaigns — not the act of voting itself.
"Instead of 'a socialist in every office,' a much more interesting and urgent call-to-action would be a union in every workplace (and prison!). A tenant union in every apartment building. A student union in every school..." https://blackrosefed.org/socialist-dog-catchers-wont-save-us/
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