Jason Brennan argues that it's impermissible to vote 'badly' (i.e., voting without sufficient reason for harmful or unjust policies -- but misleading evidence may be exculpatory here). As he puts it in the abstract for his 'Polluting the Polls' paper, "This duty to avoid voting badly is grounded in a general duty not to engage in collectively harmful activities when the personal cost of restraint is low." (Basing the duty on the collective harm done is necessary for Jason, as he takes the expected impact of an individual vote to be negligible -- easily outweighed by any warm fuzzies the bad voter might get from voting.) But I wonder whether this principle might "prove too much", by equally establishing a duty to vote well rather than abstain (whereas Jason considers the latter to be perfectly permissible).
Consider an election between two fellows with the apt names 'Good' and 'Bad'. Suppose that voter turnout is low, but Bad is winning by a sizeable margin. One Ms. Voter is walking by the voting booth. Suppose she knows that Good's policies would better promote the common good, but she just doesn't like the guy and so isn't very motivated to vote for him. What are her permissible options? According to Jason, she may not vote for Bad. For though her individual vote is negligible, she would be part of a collective (namely, the Bad-voters) who bring about significant harm that they could have avoided at low personal cost.
Okay, let's consider abstaining then. Can't the same thing be said of this? By this (in)action, Voter would be part of a collective (namely, 'the abstainers' -- or, more broadly, 'those who failed to vote for Good') who collectively bring about significant harm that they could have prevented at low personal cost. The members of this collective could have voted for Good (at minimal personal cost), and thereby collectively prevented Bad's election and subsequent bad policies.
Perhaps one could escape this argument by appealing to the doing/allowing distinction. The initial principle invoked the idea of 'collectively harmful activities', and you might think that abstaining or failing to vote is not a (positive) activity, but rather a failure to engage in an activity. And maybe it's okay (on this view) to be part of a collective failure to act, even if this collective failure is harmful. This all sounds rather dubious to me, but then so did the original principle, so I'd welcome any responses from those more sympathetic to the Collective Harm principle as to whether they would be inclined to interpret it in this more limited way.