Earlier quoted context omitted.
> which I believe has strong empirical support What is that strong support? We routinely see very well-moneyed campaigns lose. In the very last election in the US the losing candidate outspent the winning one - if you look at Super-PAC spending (which is the one considered most "dark and dangerous", right?) the losing campaign had gathered 3x from the winning one ($189.4M against $59.3M). Somehow turned out having mo…
As you noted, it's a complicated relationship [1], consequently the only place we'd be likely to see a reliable result is in aggregate. Correlation is not causation, but congressional campaigns in 2012 that outspent their opponent won 91% of the time [2]. One of the clearer links is to voter turnout. I've read it takes between $5-20 to reliably motivate a voter to vote. Sans this minimum level of funding, your suppor…
Ah, of course, you have the minimum funding to get your message out, I do not doubt that for a minute. There's a minimum level beyond which you can not mount a successful campaign. But beyond that level, the link between dollars and votes becomes much less direct and obvious.
> general consensus is that the difference in funding was largely erased by media time
Yeah, of course, Trump used this trick. But the next one might use another trick. The common thread is that there are many ways to conduct the campaign, and dollars alone do not mean victory.
> we're in an era where we actually don't know how much "money with intent of political influence" is being spent.
Not exactly, but organizations with influence on national scale are not exactly invisible, and their ad spending is not secret too. I mean, you can't exactly hide a public electoral ad, right? And knowing how much ads were run (public info) and what is a typical spot price for an ad (public info), and the same for rallies, etc. one can estimate the spending if not entirely accurately, then with enough accuracy to be able to reason about it, I think. Of course, this does not account for things like free airtime given by networks to a popular entertaining personality or other ways to buy exposure for cheap, but this only underlines the point that dollars is not everything.