Political parity

This blog will not endorse a candidate in the US presidential election. (That will change if somebody can convince me that one or more of the candidates is particularly good or bad for mathematics.)

There appears to be some confusing mathematics behind the way that delegates in the presidential primaries are allotted, at least when there are more than two candidates getting delegates, which isn't the case in either party any more. (Basically, partial delegates can't be awarded, so how do you handle the rounding if there are, say, 24 delegates to allot and three candidates appear to be entitled to, say, 7.7, 9.7, and 6.6 delegates? You have to round up for two of the three -- but which two? This problem also occurs in congressional reapportionment, and I suspect similar solutions are used.)

Anyway, in a lot of states delegates are apportioned by congressional district; according to Slate, California's Democratic primary is an example, where each congressional district gets between three and six delegates. (Since congressional districts have equal population, I can only assume that the districts with more delegates are the ones with a greater proportion of Democrats. That article says the maximum is seven, but they link to a chart that only goes up to 6.)

There are no rounding problems with two candidates. A district with six delegates, for example, would have two delegates going to Obama if he gets between 1.5/6 and 2.5/6 of the vote; three delegates if he gets between 2.5/6 and 3.5/6 of the vote; four if he gets between 3.5/6 and 4.5/6 of the vote; and so on. (Similarly for Clinton.) So if the district is close, the delegates get split 3-3. In a district with five delegates, by contrast, there can be no tie.

The Slate article that I linked to claims this disenfranchises people in districts with even number of delegates -- which may be true, although I don't have district-level polling data. The state of California as a whole may be close, but that doesn't mean that every district is close. Still, it's interesting to think that the odd-versus-even distinction could have actual ramifications. (In some sense, though, one expects them to all cancel each other out.)

I would argue that perhaps we should do away with this system of having integer numbers of delegates; why can't there be fractional delegates? The mathematics would not be that hard. (Or use larger integers; say each delegate gets an integer number of votes at the convention which is the actual number of people which led to them being seated at the convention. In the end these would be equivalent, because any fractional delegations would almost certainly have sizes which were rational numbers.) I'd make the same statement for electoral votes. I understand that we have to have whole numbers of representatives and senators because no state's going to accept that it gets, say, 2.7 representatives -- but why not give the state that has population 2.7 times that of the average Congressional district 4.7 electoral votes?