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PR vs. gerrymandering

I was at an anarchism reading discussion last night, and afterwards talking with a fellow social democrat about election reform. He didn't see why I said proportional representation solves gerrymandering, and I didn't have a fluent explanation at the time. Thus this post.

Of course, if you do PR from a single district, or pre-existing districts like US states, then there's nothing to gerrymander, so we assume multiple districts are drawn, for locality or to limit ballot size, with some number n of delegates being elected from each.

If n=1, almost half of the votes in a district can be wasted. (Or more, with more than two candidates and plurality voting, but let's assume optimal competition instead.)

With n=2, almost 1/3 of the votes can be waste: two candidates with a bit over 1/3 each, and the rest for someone else.

With n=3, almost 1/4. The pattern should be obvious. Bigger (or rather, higher n) districts mean there's less room for throwing votes away.

But I think it's more useful to look at minimal votes need to capture a legislature. With single-member, n=1, like the House, you in theory need bit over 25% of the votes to control the body. (Or less, with plurality...) With half the seats, with half the votes in each of those districts, and no votes anywhere else. Yes, that's absurdly fine tuned, but it's *possible*.

For n=2, you need a bit over 2/3 of the vote in half the districts, for 1/3 of the total vote.

N=3, 3/4 in half, for 3/8. Or half (to get two seats) in 3/4 of the districts, for 3/8 -- comes out the same.

N=10, need 10/11 in half the districts for 5/11 of the total vote, or some other arrangement that I'm fairly sure will come out the same.

Once you have any number of districts greater than 1 (or maybe 2) there's some potential for getting a majority of seats with a minority of votes, but the threshold needed approaches 1/2 as the number of seats in a district rises.

And, of course, bigger districts means fewer districts, which I think reduces the flexibility of gerrymandering.

(Even in a single district, there may be potential to get a majority without a majority of votes if lots of small parties don't make the cut to get any seats, especially if there's an artificially higher threshold. This is the equivalent of more than two parties running for a plurality seat, and not so much 'potential' as "happens all the time".)

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Damien Sullivan

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