To try and understand how/why adding additional seats to Congress would be a positive change (or really, ANY proposal) - take the most extreme ends of the spectrum:
With 1 single seat, 50.1% of voters would get 100% of the representation.
With 1 seat for every voter, 50.1% of voters would get 50.1% of the representation.
Obviously, not EVERY single person can be a congressman - so the goal should be to find the minimum number of representatives required to optimally represent the populace.
Always nice to look at edge cases, but the 1 seat per voter is never going to happen, not least because that’d be direct democracy, not representative democracy.
For any realistically-sized constituency, as long as the election remains first-past-the-post, if the votes are evenly split among districts, 50.1% of the voters would still get 100% of the representation.
In addition, gerrymandering will still be possible.
As for proportional representation (upthread), it can also lead to antidemocratic anomalies, as can every electoral system. That’s because they all have to meet requirements that are sometimes logically contradictory. In existing systems that approximate PR, coalition governments are common, and centrist parties have disproportionate power since they’re the difference between a coalition with a majority and one without. So the centrists end up perpetually in government and often prevent the larger parties from meeting their manifesto commitments.
Let’s say you have 1 district. 50.1% wins, provided you have only 2 parties. If you have more than two, you could win with as little as 34% in FPTP.
Let’s say you have 3 districts. You need 2 districts to be in control. Each of those two need 50.1% of one third of the population for 2 parties, or about 34% of the vote. If there are more than two parties and FPTP, you could win majority with as little as 2/9, or 22% of the popular vote.
The more districts you add, the fewer people you need to win a simple majority in FPTP.
Those are ideal numbers, but so is the 50.1% you submitted.
My math is exactly correct. Note the assumptions “for any reasonably-sized constituency” and “if the votes are evenly split among districts.” That’s the very well-known mathematical practice of freezing or bounding certain variables in order to focus on the effect of others.
Let’s say a reasonably-sized constituency has more than a few hundred voters. Then the anomalies you’d see with 1-person districts won’t happen. First simplifying assumption.
In that scenario, with votes evenly distributed, 50.1% for Party A in each district leads to Party A controlling 100% of the seats, as I said. And if there are more than two parties, as long as the vote is evenly split among districts and Party A is the leading party, Party A will still get 100% of the seats. You can keep arbitrarily adding parties to show the same effect with even smaller vote shares.
Your observation that even smaller vote shares can still control a legislature is correct, but requires multiple parties with roughly similar vote shares, or votes to be distributed unevenly to the parties among the districts. That’s a bit closer to how real elections work, but in practice, most uneven distributions cancel out each other’s effects, and only relatively few of such patterns can lead to the extreme cases you describe. And there are seldom many parties that gain over 10% of the vote. Those things can happen, but it’s putting you a few sigma out on the tail of the curve. Though in the UK, recent governments have had parliamentary majorites won by parties that got 35-40% of the vote. FPTP with multiple parties can cause that. Changing constituency sizes wouldn’t have any effect on that kind of outcome.
Your match is correct to get 100% of the districts, but a party only needs to get between 50 and 75% of the seats to have uncontested control of the legislative body, depending on their particular laws, meaning that above that threshold the rest are poorly represented, if at all. Hence, as little as 25% of the popular vote, even with only 2 parties. Yes, without perfect gerrymandering, you won’t reach those numbers, but minimums and maximums don’t care about sigmas.
Actually, thinking about this, if you have one person per district, direct democracy, you need 50.1% to win a simple majority. If you have one district with 2 parties and FPTP, you need 50.1%. But overall, you need about half the votes per district and about half the districts for a simple majority, which means for most values of districts and people per district, you need about 25% of the vote. Near the extremes of number of districts and the number of people per district, you can see fluctuations up to just over 50% and a fair amount below 25%.
To try and understand how/why adding additional seats to Congress would be a positive change (or really, ANY proposal) - take the most extreme ends of the spectrum:
With 1 single seat, 50.1% of voters would get 100% of the representation.
With 1 seat for every voter, 50.1% of voters would get 50.1% of the representation.
Obviously, not EVERY single person can be a congressman - so the goal should be to find the minimum number of representatives required to optimally represent the populace.
Always nice to look at edge cases, but the 1 seat per voter is never going to happen, not least because that’d be direct democracy, not representative democracy.
For any realistically-sized constituency, as long as the election remains first-past-the-post, if the votes are evenly split among districts, 50.1% of the voters would still get 100% of the representation.
In addition, gerrymandering will still be possible.
As for proportional representation (upthread), it can also lead to antidemocratic anomalies, as can every electoral system. That’s because they all have to meet requirements that are sometimes logically contradictory. In existing systems that approximate PR, coalition governments are common, and centrist parties have disproportionate power since they’re the difference between a coalition with a majority and one without. So the centrists end up perpetually in government and often prevent the larger parties from meeting their manifesto commitments.
Your math is wrong.
Let’s say you have 1 district. 50.1% wins, provided you have only 2 parties. If you have more than two, you could win with as little as 34% in FPTP.
Let’s say you have 3 districts. You need 2 districts to be in control. Each of those two need 50.1% of one third of the population for 2 parties, or about 34% of the vote. If there are more than two parties and FPTP, you could win majority with as little as 2/9, or 22% of the popular vote.
The more districts you add, the fewer people you need to win a simple majority in FPTP.
Those are ideal numbers, but so is the 50.1% you submitted.
My math is exactly correct. Note the assumptions “for any reasonably-sized constituency” and “if the votes are evenly split among districts.” That’s the very well-known mathematical practice of freezing or bounding certain variables in order to focus on the effect of others.
Let’s say a reasonably-sized constituency has more than a few hundred voters. Then the anomalies you’d see with 1-person districts won’t happen. First simplifying assumption.
In that scenario, with votes evenly distributed, 50.1% for Party A in each district leads to Party A controlling 100% of the seats, as I said. And if there are more than two parties, as long as the vote is evenly split among districts and Party A is the leading party, Party A will still get 100% of the seats. You can keep arbitrarily adding parties to show the same effect with even smaller vote shares.
Your observation that even smaller vote shares can still control a legislature is correct, but requires multiple parties with roughly similar vote shares, or votes to be distributed unevenly to the parties among the districts. That’s a bit closer to how real elections work, but in practice, most uneven distributions cancel out each other’s effects, and only relatively few of such patterns can lead to the extreme cases you describe. And there are seldom many parties that gain over 10% of the vote. Those things can happen, but it’s putting you a few sigma out on the tail of the curve. Though in the UK, recent governments have had parliamentary majorites won by parties that got 35-40% of the vote. FPTP with multiple parties can cause that. Changing constituency sizes wouldn’t have any effect on that kind of outcome.
Your match is correct to get 100% of the districts, but a party only needs to get between 50 and 75% of the seats to have uncontested control of the legislative body, depending on their particular laws, meaning that above that threshold the rest are poorly represented, if at all. Hence, as little as 25% of the popular vote, even with only 2 parties. Yes, without perfect gerrymandering, you won’t reach those numbers, but minimums and maximums don’t care about sigmas.
Actually, thinking about this, if you have one person per district, direct democracy, you need 50.1% to win a simple majority. If you have one district with 2 parties and FPTP, you need 50.1%. But overall, you need about half the votes per district and about half the districts for a simple majority, which means for most values of districts and people per district, you need about 25% of the vote. Near the extremes of number of districts and the number of people per district, you can see fluctuations up to just over 50% and a fair amount below 25%.