Those who appeal to the Common Man Argument, CMA, must also demonstrate that these laymen don't believe, along with libertarian free will, that God determines, causes, plans, ordains all events whatever.
I have found that the majority of laymen are what we'd call 'Calminians.'
They appeal to "mystery" or "paradox" or "antinomy," to hold that both LFW and exhaustive determinism are true.
If the proponent wants to push CMA to its limited limits, they must demonstrate those these same people do not hold to exhaustive determinism.
But it has been my expereince that they do not disbelieve exhaustive determinism. Those who doubt it are usually those who have reflected on the debate and so are disqualified as subjects for the statistical question since intuitions are pre-reflective.
Since I take it that the above is a likely scenario with "many people" (cf. Olson, Arminian Theology, pp. 67-69), the argument has now been rendered a non-Starter. If one sees this kind of thing in non-laymen libertarians, how much more will they see it in laymen? For an example of the former, see Witherington, The Acts of the Apostles: A Socio-Rhetorical Commentary, Eerdmans, 1998, 202.
CMA, at best, is seen to prove both libertarianism and determinism. So we're back at ground zero and must toss this argument in the trash where it belongs.