Nick Herbert, minister for policing and criminal justice, said it was a "mistake" to believe that success or failure for an independent police commissioner candidate depended on whether they got a free election address.
Speaking to the Today programme, he defended the decision of not offering a state-funded mail-shot to candidates, a move which has prompted independent candidates to claim they are at an unfair disadvantage against candidates representing political parties.
The elections for the 41 commissioners in England and Wales will take place in November.
When pressed by Evan Davis on what would be a satisfactory turnout, Nick Herbert refused to give a figure saying it would be "arbitrary" to be drawn into setting a target or threshold.
"I want the highest possible turnout," he said.
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