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« Voting while Republican in NYC | Home | Super Tuesday in NYC »

February 05, 2008

The mathematics of complex voting schemes

Discussion on my email list. (I don't think anyone read Jay Cost before talking about this, but he discusses the same problems here.)

Jim:

.....But it's not as though it's in the Dems' interest to have Republicans voting in their primary--presumably the opposite is true.

Ben:

Mathematically, it would be very much in their interest, although neither side chooses to think mathematically. (mostly because to be in politics you have to get so psychologically vested in "your guy".)

THe problem is this: Republican primary voters are a subset, Democrat primary voters are a subset. Performance in a vote among a non-random subset does not predict performace in the general vote. A mathematician named Kenneth Arrow actually won a Nobel for figuring out, basically, that no election system is perfect, and all can give skewed results.

For example, let's assume an election in which all 100% of the people will vote in both elections, and in the primary, 50% will vote in the Republican Primary and 50% in the Democrat primary. Let us assume also that even though this is the case, people may switch parties and vote for the opposite in the General election, if it is a preferred candidate.

Let us assume 4 candidates:

A and B face off in the Democrat Primary, C and D in the Republican.

A is acceptable to 80% of Democrat Primary Voters and 0% of Republican Voters
B is acceptable to 60% of Democrat Primary Voters and 30% of Republican Voters
C is acceptable to 40% of Democrate Primary Voters and 50% of Republicans.
D is acceptable to 0% of Democrats and 70% of Republicans.

In this scenario, A and D win the primary, and then A wins the general... BUT... had their been no primary, B and C would have been closely matched, with A and D being less popular in a 4-way election. B would beat candidate D in a general election, and C would beat A. Logically, it is in the republicans best interest to nominate C, and the democrats B, in the primaries!

The only way to do this is to get the other side to vote in your primary.

Arrow showed that any system can lead to paradox results, where the winner is someone the majority of voters would not prefer. (A McCain victory in the primary would be exactly that). He went on to suggest a few interesting alternates to our way of voting, including the idea of having everyone allocate points to any and all candidates they liked, with the winner being the one with the highest point score. The paradox there was that the overall winner could be someone whom no one ranked "best"- simply being "good enough" to enough people would win.

Jim:

There's thinking mathematically, and there's also thinking strategically. The scenario I had in mind was Republicans maliciously voting for the less electable Democrat, or vice versa. So in your example, Dems might vote for B because he's more electable, but Republicans would cross over and vote for A, giving A the nomination but assuring a Republican winner in the general election.

Mary:

Just imagine the worst possible results if both sides did that - instead of Mc Cain vs. Obama, or Romney vs. Clinton we'd have Ron Paul vs. Dennis Kucinich. Everybody loses.

The tactic of "maliciously voting" is a perfect example of how an organized campaign of rabid partisanship could destroy a democracy - or at least cripple it for four years.

Ezzie:

More likely, we'd end up with an Independent like Bloomberg.

Jim:

Just to be clear, I wasn't advocating that tactic, just explaining why I thought Democrats wouldn't necessarily want Republicans voting in their primary. But I wouldn't be so alarmist about it--attempts at collective voting are pretty tough to pull off.

Mary:

Sure. But I was just going to say that I didn't think Jim was trying to advocate the tactic of 'maliciously voting'. If he was, he probably wouldn't have called it 'maliciously voting' :-)

Ezzie's idea that rabid partisanship, taken to extremes, could empower an independent candidate is appealing.

Rich:

I am not sure but some leftist group tried to do this earlier this year. They were encouraging Democrats to switch and vote in the Republican primary for Romney to take votes from McCain who they saw as there biggest threat against Hillary

Judith:

That's funny. Some Republicans in states where their vote wouldn't make a difference advocated voting for Hillary, because they see her as easier to beat than Obama.

Does anybody remember all the vote-swapping schemes of 2000? And then there are the people living in their own reality-bubble who think voting in Hillary or Obama for four years will somehow disgust the electorate enough so they will want a conservative the next time around, or it will have a salutory effect on the conservative movement for some reason. As one commenter pointed out, Jimmy Carter only served one term and we are still trying to clean up the messes he made.

The problem with this stuff is that you can't predict its effects that far out. I think you need chaos theory to deal with it, which will only tell you that you can't predict this stuff that far out.

Now I remember why I stopped blogging. I am doing this instead of my Hebrew homework.

Judith | 02/05/08 at 06:12 PM | Categories: - GOTV '06 to '08

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