Ha ha. That sounds a little like preemptive aggression than a proactive measure, but might work. Not sure I would take that route.
Maybe you should be proactive and accuse them of harboring voles that are messing up your wood chips...
You said the other adjacent neighbors lawns were unaffected by voles, this is good evidence that they aren't originating from your chips.
Dan Vorhis wrote:Voles eat mostly grasses, roots, tubers. So I think they aren't getting much nutrition from your mulch-covered yard. But they might be using it for cover. And voles hate to be caught out in the open. They hate running across gravel and pavement. If voles are using your mulch for cover, you could dig a trench maybe 12" deep, 12" wide between your yard and your neighbor's, and fill it with pea gravel. The round gravel collapses into vole burrows, so voles don't like it. And they don't like to cross over the top. Makes a good-looking, inexpensive, and permanent vole barrier. And happy neighbors are better than unhappy neighbors!