It seems there are some potential participants in the vote who are: in favour of an open ballot, indifferent to the type of ballot, and against an open ballot and want a secret ballot.
So, if the poll is a 'secret ballot' that is then likely to disaffect those who would prefer an open ballot, and vice versa* .....
Suggestions?
(*Should the ballot be 'secret' then one answer is for those who wanted an open ballot to say that they will now refrain from voting. But that would be childish, eh.)