Delete/undelete reversal cycles can be prolonged (and the ultimate outcome altered) by double voting, in which users undo the defeat of their earlier votes by casting the same vote a second time.
For example, on this famous question that at one time generated all the Reversal badges, the recent cycle of deletion and undeletion was a repetition of the same tug-of-war that had previously been settled with an undeletion, after one double-voter helped push the question back toward deletion, and two voters he had reversed replied with undelete votes. There was no substantial change to the question, only a minor edit to change a tag:
The purpose of this meta question is to determine whether there exists support for the idea of
not casting the same vote twice (in the same direction, consecutively) on a question
Alternation such as delete/undelete/delete would not be a problem, in the sense that it does not increase an individual's total voting power, and also because people sometimes do reverse their opinion of a question after edits.
To be very clear, the question is whether there is a general preference (or a "social norm", whatever that could mean here) that double-voting be voluntarily avoided, although SE has made it possible, or whether it is viewed as (e.g.) a beneficial capability. It is not proposed that there be any kind of "policy" or enforcement mechanism to try to prevent or punish such actions, which are individual voting decisions that happen to be permitted by the software.
It is currently possible to re-vote accidentally, by not remembering an earlier vote, and it might be justifiable to re-vote in order to reverse the effect of another user's double vote, but those would be practical exceptions that do not contradict the principle of not deliberately initiating a double-vote.
the point pertains primarily to questions that essentially retain their identity, if they are edited. For questions that bear no relation to the previous versions after an edit or receive drastic changes (such as defacement, spam, or asking a completely new question in the same posting) the preferred response would include a rolling back of the edit, so it is still not clear in that situation whether a repeat vote would ever be in order.
Correction of earlier version of question (discussing edits and open/close): for delete/undelete, edits play no role, SE does not check for double votes. For close/reopen votes there is a hard limit of one close and one re-open vote per user, per question, so there is no possibility to multiple vote.