In terms of the present argument, they should each be able to spend roughly the same amount on it. That suggests a system based on individual contributions - no union, corporate or government money - and individual contribution limits, much as we have now.
How each chooses to participate, however, should be up to the individual. In particular, whether he chooses to contribute to a political party, or to an advocacy group, or to spend his money directly, it should be no business of the state. Rather than have one system of contribution limits for political parties and another for advocacy groups or individuals, that suggests they should all come under the same umbrella: a global, annual ceiling of, say, $10,000, on the amount an individual could spend on political advocacy - through whatever vehicle. Ideally, you'd donate via the income tax return; even more ideally, anonymously.
I would argue a cap of this form amounts to institutionalizing unfair advantage toward the wealthy. This system wouldn't be an extension of "one person, one vote", it would create tiers, in that those with resources could exact influence on our system, which others simply couldn't leverage in the same capacity. A $10000 cap gives advantage to the wealthy, those without sufficient disposable income simply don't have the luxury to maximize their political contribution under this system. Rather than achieving the fairness sought, what is created is a regime which marginalizes some, at the same time providing disproportionate influence to the affluent.
The libertarian notion strikes me as the ideal, like most tenets within that philosophy it offers simplistic solutions, but in the practical world, becomes so bastardized and exploited, the initial spirit buried to the point of unrecognizable. Coyne tries to square this libertarian want with the other extreme, a total ban on many forms of monetary expression, but the compromise doesn't find equality, it finds more room for uneven influence over our political process.
I see the evolution of political contributions, third party input, leading to one educated place, a learned political existence. A total ban on all third party players, a hard cap on individual donations set at a rate which strives for optimal inclusively, complete disclosure of donors, transparency and heavily scrutinized. Coyne mentions the situation in Ontario, where certain groups have gone after the Progressive Conservatives, I would support a total ban on these activities, no matter your partisan persuasion, set limits from the parties themselves and no augmentation from any third party. It sounds draconian, perhaps it does, perhaps it steps all over individual liberty and free expression, but a full on ban and strict regimes are the only way to ENSURE the true equality other models try to achieve.
Human beings cheat, not all of us live under equal terms, this circumstance leads to certain advantages. As soon as money is allowed into a process- beyond campaign limits, moderate individual contributions- the notion of voter equality is undermined, eroded by those with greater means, creating an uneven discussion and debate. Under the Coyne model, you would have a circumstance wherein ten people could have the power of another hundred, thousand, unless the cap is quite low, you are left with money as power, a situation which ultimately betrays the notion of equality for all, "one person, one vote". The only way to ensure this equality is to effectively ban many activities, in so doing you limit personal expression on a monetary front, but you protect a certain sanctity, no influence equates to equal influence, we are all left to individually express ourselves with nothing than our our commitments, opinions, drive. You care about an issue, you get out and fight for that cause, influence a byproduct of participation in a sense that goes beyond how deep your pockets, but left to the realm of intellectual persuasion. Rather than being shutdown by absurd constraints, we are all created equal in this formula, our words and deeds can extract influence, rather than factors which we can't control.
As soon as you create a system that handicaps participation from any societal subset, you have strayed from the ideal of individual freedoms, which is why the only solution is to eliminate any potential advantage altogether, create a system which favours no one and puts our political debate outside of financial considerations. This system isn't pretty, perhaps it is at odds with individual liberties, but it is fair in it's universal restraint, the field is even for all, it is the only compromise which truly respects "one person, one vote", or at least strives to protect that core political tenet.