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Proportional Representation for the United States?

But that is still a single-winner system.
Ipetrich
Reading through all of the info you have provided is good. Thank you for all of it.
Yet I can't help but notice that you are adverse to a single-winner system.
Why is that? In some systems single-winner is a feature not a bug.
For example a presidential system, like the USA, cannot really use PR to elect a president. There can only be a single winner, which is FPTP by definition.
People bag FPTP (sometimes with good reason) but there are times when it is necessary. If only one person can win then FPTP is necessary. If filling a parliament PR is useful.
FPTP is the absolute worst system for a single winner situation. For instance, under a FPTP system, if Mr Fascist gets 34% of the votes, Mr Moderate 33% and Ms Other 33%, then Mr Fascist wins. This is where a preferential system is very needed. As to filling a parliament, that is just a large number of single winner situations combined, as each electorate/seat is a single winner situation.
Are you most upset about the fact that Mr Fascist won rather than Ms Other? If that be true then it is who is elected rather than how they are elected that bothers you. No voting system can guarantee that your preferred candidate will win (unless you rig it).
To avoid unfounded accusations I would be appalled if a fascist got 34% in any Australian election.
Do I need to remind people that Hitler was SELECTED Chancellor of Germany under a PR system? A PR system does not guarantee good government. It has its good features but of its self it is not a panacea.
Under a PR system the losers can claim that the winning candidate did not get a majority and so does not have a 'mandate'. More arguments.
We need the best way to select the best candidates and make sure that the best candidates are chosen to stand. Worldtraveller noted that in post 115.
Wow, you totally leapt to an unjustified conclusion. I was expecting Mr Moderate to win from runoff votes from Ms Other voters.
Under FPTP system the losers also can claim that the winning candidate did not get a majority - see Donald Trump. As to what you were really claiming- if the system is accepted by all, then there will rarely be claims of winning candidate not getting a majority, except in the rare cases where fraud actually occurs.
FPTP is never the best system, and preferential voting, along with other reforms such as an independent electoral oversight organization to determine electorate borders (in Australia, the Australian Electoral Commission) is much better.
As for selecting best candidates, it is up to the parties to offer better candidates.
In the USA (and elsewhere but especially in the USA) there are often very poor candidates, lots of gerrymandering, massive lying by candidates, and voter suppression.
To fix this, which is difficult against the special interests, one needs something like the AEC I mentioned above, and preferential compulsory voting.
I too am in Australia so are very familiar with the AEC and are quite pleased with it.
In the emboldened bit you merely stated a series of figures without mentioning about run off votes.
I didn't mention runoff votes there, because that example was referring to FPTP situation, where the main vote wins outright even though they don't have a majority (over 50%) of the total votes. The runoff refers to use of preferential system [and I think I actually used the wrong word (runoff) for redistributed votes].
 
I've decided to take on proportional representation for the US Senate. I decided to avoid creating a body as big as the House, so I decided to make the current number of 2 Senators per state an average. States may have more Senators or fewer in proportion to their population.

I used the code in lkpetrich/Proportional-Allocation: For doing proportional allocation and representation though I'll have to upload my Senate version some time.

I used Huntington-Hill as the main allocation or apportionment algorithm, because it's what's used for the House. It's highest-averages with a divisor function D(S) = sqrt(S*(S+1)) for S seats. It's close to Sainte-Laguë, S+1/2.

I used the 2020 US Census data for all the present states, omitting DC and Puerto Rico.

The result; each number of Senators and the states with that number:
  • 10 CA
  • 8 TX
  • 6 FL
  • 5 NY
  • 3 GA IL MI NC NJ OH PA
  • 2 AZ CO IN MA MD MN MO TN VA WA WI
  • 1 AK AL AR CT DE HI IA ID KS KY LA ME MS MT ND NE NH NM NV OK OR RI SC SD UT VT WV WY

To get a semi-proportional result, I decided to take the square roots of the state populations. I also took the square of the Huntington-Hill divisor, and both methods agreed:
  • 5 CA
  • 4 FL NY TX
  • 3 GA IL MI NC NJ OH PA
  • 2 AL AR AZ CO CT IA IN KY LA MA MD MN MO MS NV OK OR SC TN UT VA WA WI
  • 1 AK DE HI ID KS ME MT ND NE NH NM RI SD VT WV WY

I also tried setting an upper limit on the number of Senators for each state.

Max: 8
  • 8 CA TX
  • 6 FL
  • 5 NY
  • 4 IL PA
  • 3 GA MI NC NJ OH
  • 2 AZ CO IN MA MD MN MO TN VA WA WI
  • 1 AK AL AR CT DE HI IA ID KS KY LA ME MS MT ND NE NH NM NV OK OR RI SC SD UT VT WV WY
Max: 6
  • 6 CA FL NY TX
  • 4 IL PA
  • 3 GA MI NC NJ OH VA
  • 2 AL AZ CO IN MA MD MN MO SC TN WA WI
  • 1 AK AR CT DE HI IA ID KS KY LA ME MS MT ND NE NH NM NV OK OR RI SD UT VT WV WY
Max: 4
  • 4 CA FL GA IL NC NY OH PA TX
  • 3 AZ MI NJ VA WA
  • 2 AL CO IN KY LA MA MD MN MO OR SC TN WI
  • 1 AK AR CT DE HI IA ID KS ME MS MT ND NE NH NM NV OK RI SD UT VT WV WY
 
I've decided to take on proportional representation for the US Senate. I decided to avoid creating a body as big as the House, so I decided to make the current number of 2 Senators per state an average. States may have more Senators or fewer in proportion to their population.

I used the code in lkpetrich/Proportional-Allocation: For doing proportional allocation and representation though I'll have to upload my Senate version some time.

I used Huntington-Hill as the main allocation or apportionment algorithm, because it's what's used for the House. It's highest-averages with a divisor function D(S) = sqrt(S*(S+1)) for S seats. It's close to Sainte-Laguë, S+1/2.

I used the 2020 US Census data for all the present states, omitting DC and Puerto Rico.

The result; each number of Senators and the states with that number:
  • 10 CA
  • 8 TX
  • 6 FL
  • 5 NY
  • 3 GA IL MI NC NJ OH PA
  • 2 AZ CO IN MA MD MN MO TN VA WA WI
  • 1 AK AL AR CT DE HI IA ID KS KY LA ME MS MT ND NE NH NM NV OK OR RI SC SD UT VT WV WY

To get a semi-proportional result, I decided to take the square roots of the state populations. I also took the square of the Huntington-Hill divisor, and both methods agreed:
  • 5 CA
  • 4 FL NY TX
  • 3 GA IL MI NC NJ OH PA
  • 2 AL AR AZ CO CT IA IN KY LA MA MD MN MO MS NV OK OR SC TN UT VA WA WI
  • 1 AK DE HI ID KS ME MT ND NE NH NM RI SD VT WV WY

I also tried setting an upper limit on the number of Senators for each state.

Max: 8
  • 8 CA TX
  • 6 FL
  • 5 NY
  • 4 IL PA
  • 3 GA MI NC NJ OH
  • 2 AZ CO IN MA MD MN MO TN VA WA WI
  • 1 AK AL AR CT DE HI IA ID KS KY LA ME MS MT ND NE NH NM NV OK OR RI SC SD UT VT WV WY
Max: 6
  • 6 CA FL NY TX
  • 4 IL PA
  • 3 GA MI NC NJ OH VA
  • 2 AL AZ CO IN MA MD MN MO SC TN WA WI
  • 1 AK AR CT DE HI IA ID KS KY LA ME MS MT ND NE NH NM NV OK OR RI SD UT VT WV WY
Max: 4
  • 4 CA FL GA IL NC NY OH PA TX
  • 3 AZ MI NJ VA WA
  • 2 AL CO IN KY LA MA MD MN MO OR SC TN WI
  • 1 AK AR CT DE HI IA ID KS ME MS MT ND NE NH NM NV OK RI SD UT VT WV WY
Lots of work done. You ought to hire yourself out to your various electoral commisions. I reckon you'd or better than some of teh resuts that have been thrown up. I'll give you a reference.
 
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