The idea is that if I donate $100 to the Democratic Party, and you donate $200 to the Republican party (or to their nominees for President, say), the net marginal effect on the election is very similar to if you'd donated $100 and I've donated nothing; $100 from each of us is being canceled out.

It seems to be implicit in your model that funding for political parties is a negative-sum arms race. This is starkly at odds with much of political thinking, which sees funding for political parties as a positive-sum game. This is expressed by public subsidies for political parties, in such terms as public funding/matching funding/tax deductibility of political donations, depending on where you reside.

Political parties turn funding into votes by getting their message out to voters, so the more funding political parties have, the better informed an electorate we will have. Moreover, to the extent that funding getting your message out becomes less binding of a constraint, then other constraints (such as the persuasiveness of that message) will become more binding - which seems like a good thing.

I guess it just goes to show that one person's public good is another person's public nuisance. In my own view, the most damaging negative-sum arms race is academia. Perhaps you will inspire me to set up my own 501c(3) to allow matching donations to universities to be diverted to political parties.