It is very likely that the people who know they are casting a negative vote will vote strategically for the opposite of the thing they actually want to happen,

It is very likely that the people who know they are casting a negative vote will vote strategically for the opposite of the thing they actually want to happen, thus turning their negative vote into an anti-negative vote. I don't think that is resolvable unless each vote has an intrinsic auction process wherein each vote is accompanied by a dollar-valued bid, which is what it would cost for you to not vote your shares on that issue. The costs are ordered, and the cost of the lowest N votes are sold to the N anti-shares of open short positions, and so each short pays 1/N of the total cost. Any vote not cast or cast-by-proxy or explicitly cast as "abstain" is intrinsically a $0 bid for not-voting that share. So if there are 10000 real shares in circulation, and 4000 shadow shares, and 4000 shadow anti-shares, then 14000 shares are eligible to vote, but the shadow anti-share holders are also on the hook for collectively buying off the proxy for the 4000 least-interested shareholders, and not-voting those shares. If 2000 people don't vote or fail to assign their proxy, and the next-lowest 2000 bids amount to $80, then each short pays $0.02 per shorted share, and the brokers distribute that to all the low bidders, including those who didn't vote or assign proxy.