[openasocket]

OT, but there's another really interesting, related problem at the intersection of mathematics and politics, which is apportionment (https://en.wikipedia.org/wiki/United_States_congressional_ap...). The US House of Representatives has a certain number of seats (currently 435) and, based on the results of the census, those seats are assigned to the 50 states according to their populations. But the proportions don't always divide evenly, and you can't give a state 7.35 representative seats, so you need a method for determining the fairest division of representatives. And it turns out there is no optimal solution in the general case (https://en.wikipedia.org/wiki/Apportionment_paradox).

I point out this problem because it is one of the few times you will find Supreme Court cases and writings by the Founders on what algorithm to use. A bill changing the apportionment algorithm was subject to the very first presidential veto. The first proposed amendment to the Constitution (https://en.wikipedia.org/wiki/Congressional_Apportionment_Am...) was on the subject of apportionment. When else will you find the highest levels of government debating the merits of algorithms and mathematics?

[taoistextremist]

It's actually one topic I've grown to agree with my extremely conservative father on, that they should have never fixed the seats at 435. This was done long after the founding of the country (relative to the age of the country, that is), but if we had kept the original apportionment we'd have one of the largest legislatures in the world. It wouldn't solve the apportionment problem, but it would make the unfairness of any given solution much less consequential and also it would make gerrymandering harder (though still not impossible).

[specialist]

I think of it as a scale problem. A Representative's front office is basically a call center & triage operation. The embodiment of the Politics of Attention (squeaky wheel gets the grease).

What's the ideal size for a constituency? To maximize responsiveness, accountability, effectiveness? 100k? 200k? 400k?

I don't know, but I'd like to find out.

[itsameta4]

The Republic of Ireland's constitution guarantees a member of the Dáil (Lower Parliamentary house; similar to the US House of Representatives) for every 20-30,000 people, and districts are redrawn and reapportioned frequently.

This seems to be a pretty ideal number to me - it's about the size of the township I grew up in. Many people in their district would have personal ties to their representative, as a further detriment to attempts at lobbying/corruption.

The US constitution used to have a similar provision, but this was abandoned by the ammendment process in the late 1920's.

[squiggleblaz]

Apparently largest assembly sizes are normally fall somewhere around the cube root of the population. Obviously you don't want so many electorates that the house becomes unmanageable, nor so few the voters can't make an effective choice. See some political scientist's thoughts here: https://fruitsandvotes.wordpress.com/category/electoral-rule...

I have no idea if that's the ideal rule or how you might determine that.

[taoistextremist]

Around the founding of the country, there were arguments of some range between 30k to 40k. Obviously that wouldn't be practical nowadays, that would create 10k representatives and the ability of the government to respond to an urgent issue like war or economic depression would be severely diminished. It could also decrease public turnout because they feel like not just their vote, but their representative can't make a difference.

But yeah, I think at a few hundred thousand, though that would likely mean over one thousand representatives, could probably work.