They're entirely RIGHT to be cynical. I've NEVER seen the introduction of a new tax to cover something previously covered by general funds to result in the reduction of general taxes. The old money just goes to something else, and some politician will claim that the million dollars that is no longer taken from the general fund is "money he saved the taxpayers" even though in reality they're now paying twice as much.
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Work: the 8 hours that separates bike rides.