it's hard to cheat on paid advertising as it has to be visible
"it is not worth it for a candidate to spend money even if they can buy 10% of the vote for $1 (which is absurdly unrealistically high)."
So what is a realistic price / 'exchange rate' for this example, in your opinion?
I provided a coefficient of '1' spelled out in the line below that, it could be '10' or '100', etc.
"Sure, and my proposal of Votes / (10X + Y) would imply that the first candidate wins."
Which invariant(s) would you construe this as maintaining? Why not just add a constant coefficient? This is more efficient to compute, and the average price is already too high, that's 'half the point'.
"No way is the relationship between money and outcome linear"
What do you claim is the relationship?
"Well, 201 > 200, right? If you think voters have free will, and are competent to vote, and each vote is equal in strength, then clearly candidate 2 has the support of the majority."
By this logic, payola makes music sound good, which we know is not true. Is it possible that the additional spending is what affected the result, rather than the truth about people's preferences. If not, why would the right have become obsessed with freedom of speech to preserve citizen's united?
"Is the will of the people expressed in voting, or is it not?"
False binary, this is a comparative question between two voting systems (in an infinite space) and the question is which system expresses the will of the people better, and the new system does so better by controlling for the confound of payola in measuring preference.
"Look, I'm sympathetic to playing with non-democratic election and decision systems. I'm strongly suspicious that one-person-one-vote is suboptimal (even aside from FPTP winner). I wish there were some sort of directed voting where more informed, smarter, less selfish, voters had more strength than the median citizen. But I strongly expect any change in that direction will immediately be Goodharted away, and the legitimacy conferred by "everyone is equal" is not something to mess with."
I am proposing a change in the opposite direction from what you propose. One person, one vote, is, let's say, the ideal, (why say this? considering Condorcet's jury theorem, in the context of general elections, we have an education system tasked with making voters better than chance so that the conditions of Condorcet's jury theorem are met, making voter turnout an epistemic virtue--with these conditions provided, one person, one vote is the ideal)
BUT, the extreme fungibility of both attention and money means that one person, one vote, is 'drowned out' by the one person, many dollars system of capitalist inequality, which progressively undermines democracy (one person, one vote) as it in increases in size, as votes are easy to buy. In this context 'money' is the 'noise' and 'preference' is the 'signal':
'Getting the money out of politics' has been a bugbear of many an idealist in the anglosphere (and I presume elsewhere) and I propose to simply divide it out mathematically by law.
"votes-per-dollar" IS a formula -- aka v/d -- 'per' means division -- spelling out the coefficient we have:
1*v/d where 'undefined' is ranked last and infinity is not a return value
OR
1*v/(1+d) where 1/0 approached from the right is +inf
(there are no negative votes -- if dollars are negative eg a campaign turns a profit we could take abs(1+d) or abs(d) as the denominator)
v = total votes for the candidate
d = total dollars spent by the candidate
But here's a basic unit test, riddle me this:
If one candidate gets 200 votes and spends 200 dollars, and candidate 2 gets 201 votes and spends two MILLION dollars, who has the strongest mandate, in the sense that the representative actually represents the will of the people when wealth differences are ignored?
This counterproposal has a data dependency where we need to know averages from the past, and also will still present a spending barrier for dirt-poor candidates if the average happens to be large (it is).
What I meant in response to your original comment is that whether it's 'worth it' depends on the current 'effective exchange rate' between votes and dollars, which is represented by a coefficient of '1' in this first approximation. There should presumably be an update rule for 'learning' the 'correct' coefficient....
These are all problems with the existing system as well so they are irrelevant for A-B testing the two options.
It's no more impossible to enforce than existing campaign spending limits.
what coefficient in the numerator would change your conclusion?
Then you're against the electoral college?