General discussion about Congressional Apportionment

[Antonio the Sixth]

But we're not considering how to allocate 435 seats, but rather how to allocate 385 seats.

Even so, the least populous States (Wyoming) deserves 0.67 seats, enough to secure it.

[Kevinstat]

The House of Representatives is intended to represent the people, not the States.  The d'Hondt seat allocation method (equivilent to Jefferson's method) badly under-represents the people of the very smallest states those who vote for smaller parties.  If you have one state party with 121,000 22,355 votes and another with 59,000 11,087 votes, or barely over a 2:1 vote ratio in population, it produces a 4:1 ratio in representation.

See the West Belfast 1996 Forum election for a real example of this.  I crossed off the badly in jimrtex's post because I actually like d'Hondt as a seat-allocation method for parties if a list method is going to be used, since, to use the West Belfast 1996 example, if (Provisional) Sinn Féin in West Belfast had divided into two parties with half of the voters who voted for Sinn Féin in real life voting for each party, and all else being equal, each of those two parties would have bet the Social Democratic and Labour Party out for a second seat, and those voters, as crazy as they were for voting for SF, shouldn't be penalized for their consolidation.

Interestingly enough, the one successful SDLP candidate in that election, Joe Hendron, was the MP for West Belfast at the time, although redistricting had occured since his election as an MP and he had only won narrowly and because of Unionist tactical anti-SF voting.  Sinn Féin leader Gerry Adams, whom Hendron had unseated in 1992, defeated Hendron in 1997 and has been elected as West Belfast's MP (although he has never taken his seat in Westminster as that would require taking an oath to the Queen) in every election since.

[Antonio the Sixth]

I've always wondered where the idea that "it's fair and normal to under-represent small party in proportional elections". The voice of a person who votes for a small party has to be heard as well as the one those who chose large parties. The D'Hondt method is hardly proportional, just as the Jefferson method of Apportioning Congress would be blatantly unfair, hadn't the Senate existed to compensate it.

[Kevinstat]

I've always wondered where the idea that "it's fair and normal to under-represent small party in proportional elections". The voice of a person who votes for a small party has to be heard as well as the one those who chose large parties. The D'Hondt method is hardly proportional, just as the Jefferson method of Apportioning Congress would be blatantly unfair, hadn't the Senate existed to compensate it.

Well, the Jefferson or d'Hondt method (I think I goofed by capitalizing the first letter d earlier; I've fixed that now) minimizes the largest (best) level of representation per capita or per voter, respectively, of any two or more states or parties, respectively, given the total number of seats awarded to those states or parties, except where overriden in the Jefferson apportionment method, as it would have to be practiced in the U.S., by every state having to have at least one seat in the governing body for which the seats are apportioned.  Said another way, the Jefferson or d'Hondt method maximizes the smallest (best) number of people or votes, respectively, per seat of any two or more states or parties, respectively, given the total number of seats awarded to those states or parties, except where overriden in the Jefferson apportionment method, as it would have to be practiced in the U.S., by every state having to have at least one seat in the governing body for which the seats are apportioned.

The d'Hondt method could thus be said to minimize the greatest "fat rat effect" benefitting the voters of any party among two or more parties given the total number of seats awarded to those parties, as long as that "fat rat effect" is measured in either absolute terms (seats per vote or votes per seat, not compared to any other party or parties (or slate or slates of candidates, including "slates" of only one candidate)) OR is measured in comparison to all parties or slates of candidates combined (i.e. how a the largest number of seats per vote or the smallest number of votes per seat, repsectively, among a given set of two or more parties compares to the total number of seats divided by the total number of votes, or vice versa, for the governing body being elected).

If you're more concerned about parties making out like fat rats than about parties being greatly underrepresented (and there will likely be slates of candidates receiving no seats anyway, and comparing the underrepresentation of voters for any slate receiveing no seats is like comparing the underrepresentation of voters who voted in 2008 for John McCain to that of those who voted for Chuck Baldwin - both were 100% unrepresented in terms of the number of Presidential and Vice Presidential seats awarded), than d'Hondt is your method.  Practically every elected official in a non-proportional election will talk about how he or she represents all his or her constituents, not only those who voted for him or her.  While a lot of that is just talk, I think it's reasonable for someone who to be more concerned about minimizing underepresentation in terms of voters having someone representing them who they get to vote for or against, while being more concerned about limiting the "fat rat effect" when it comes to the partisan or ideological makeup of the governing body in question.

It just so happens that, everything else being equal, larger parties will fare the same or better, while smaller parties or states will fare the same or worse, under a method (d'Hondt or Jefferson) that minimizes the "fat rat effect" than under one which minimizes the worst case of underrepresentation (the smallest divisors or Adams method), absolute difference in votes per representative (harmonic mean) or representation per voter (major fractions, Webster or Sainte-Laguë) between any two parties given the number of seats between them, relative (percentage) difference either in votes per representative or representation per capita/voter (equal proportions) between any two parties given the number of seats between them, or one which minimizes the number of ill-assigned seats (largest remainders or Hamilton).

[Antonio the Sixth]

Sure, every method have advantages and drawbacks. But in such case, wouldn't the best solution be the one situated right in the middle of the two...
The Adams method is undoubtedly the silliest, and the one that creates the biggest distortion. A party could theoretically ge a seat with 1 vote ! On the other hand, the d'Hondt divisors method is quite excessive too, since, as Jim pointed out, a 2/1 difference in votes may create a 4/1 distortion... Not to mention the fact that the State which deserves 0.99 seats gets no one while one deserving 1.01 gets one. Both method have great odds to violate the fairness rule.
The Sainte Laguë method avoids both extremities. It is situated "right in the middle" between Adams' and Jefferson"s (while the geometric and harmonic means are closer to Adams method). Also, the number of ill-assigned seats is extremely close to the minimum reached with the Strongest Reminders. So, I view it as the best possible compromise.

[jimrtex]

Sure, every method have advantages and drawbacks. But in such case, wouldn't the best solution be the one situated right in the middle of the two...
The Adams method is undoubtedly the silliest, and the one that creates the biggest distortion. A party could theoretically ge a seat with 1 vote ! On the other hand, the d'Hondt divisors method is quite excessive too, since, as Jim pointed out, a 2/1 difference in votes may create a 4/1 distortion... Not to mention the fact that the State which deserves 0.99 seats gets no one while one deserving 1.01 gets one. Both method have great odds to violate the fairness rule.
The Sainte Laguë method avoids both extremities. It is situated "right in the middle" between Adams' and Jefferson"s (while the geometric and harmonic means are closer to Adams method). Also, the number of ill-assigned seats is extremely close to the minimum reached with the Strongest Reminders. So, I view it as the best possible compromise.

So for 2010 we find that the average workload for a Representative is 708,000 persons, and that a representative can do an adequate job working an 8-hour day.    But if you use Ste. Lague to assign the representation tasks, you can end up with some representatives having to work 12 hours.  They may be tired, so they actually don't represent any of their constituents as well, despite spending 50% more time each day.  And for why?  So some big state representative can knock off a few minutes early.  Hardly fair at all.

But let consider Adams.  We set a maximum representation load of 748,000.  So some representative might have to work 8 hours and 27 minutes.  Hardly overworked.  And if the workload for some state runs over 748,000 per representative, you hire another representative.    Sure a few representatives might get a cushy job and not have to work 8 hours.  But isn't that acceptable considering the alternative.

St.Lague is only the middle ground if we consider D'Hondt at all acceptable.  But if we would use D'Hondt, we might as well bring back child labor with 8-years olds working from dawn to dusk picking clinkers out at the coal mine, sleeping on a hard board and being fed thin gruel twice a day.

[Antonio the Sixth]

Sure, every method have advantages and drawbacks. But in such case, wouldn't the best solution be the one situated right in the middle of the two...
The Adams method is undoubtedly the silliest, and the one that creates the biggest distortion. A party could theoretically ge a seat with 1 vote ! On the other hand, the d'Hondt divisors method is quite excessive too, since, as Jim pointed out, a 2/1 difference in votes may create a 4/1 distortion... Not to mention the fact that the State which deserves 0.99 seats gets no one while one deserving 1.01 gets one. Both method have great odds to violate the fairness rule.
The Sainte Laguë method avoids both extremities. It is situated "right in the middle" between Adams' and Jefferson"s (while the geometric and harmonic means are closer to Adams method). Also, the number of ill-assigned seats is extremely close to the minimum reached with the Strongest Reminders. So, I view it as the best possible compromise.

So for 2010 we find that the average workload for a Representative is 708,000 persons, and that a representative can do an adequate job working an 8-hour day.    But if you use Ste. Lague to assign the representation tasks, you can end up with some representatives having to work 12 hours.  They may be tired, so they actually don't represent any of their constituents as well, despite spending 50% more time each day.  And for why?  So some big state representative can knock off a few minutes early.  Hardly fair at all.

But let consider Adams.  We set a maximum representation load of 748,000.  So some representative might have to work 8 hours and 27 minutes.  Hardly overworked.  And if the workload for some state runs over 748,000 per representative, you hire another representative.    Sure a few representatives might get a cushy job and not have to work 8 hours.  But isn't that acceptable considering the alternative.

St.Lague is only the middle ground if we consider D'Hondt at all acceptable.  But if we would use D'Hondt, we might as well bring back child labor with 8-years olds working from dawn to dusk picking clinkers out at the coal mine, sleeping on a hard board and being fed thin gruel twice a day.

I think this argument is really too pragmatic to be considered for apportionment. We don't have to forget that it's about apportioning Representatives to States according to which deserves a Rep the most.
And Jim, remind that differences between all those members remain marginal enough to avoid too overworked Representatives. I'm not worried about that.

[Kevinstat]

Sure, every method have advantages and drawbacks. But in such case, wouldn't the best solution be the one situated right in the middle of the two...
The Adams method is undoubtedly the silliest, and the one that creates the biggest distortion. A party could theoretically ge a seat with 1 vote ! On the other hand, the d'Hondt divisors method is quite excessive too, since, as Jim pointed out, a 2/1 difference in votes may create a 4/1 distortion... Not to mention the fact that the State which deserves 0.99 seats gets no one while one deserving 1.01 gets one. Both method have great odds to violate the fairness rule.
The Sainte Laguë method avoids both extremities. It is situated "right in the middle" between Adams' and Jefferson"s (while the geometric and harmonic means are closer to Adams method). Also, the number of ill-assigned seats is extremely close to the minimum reached with the Strongest Reminders. So, I view it as the best possible compromise.

So for 2010 we find that the average workload for a Representative is 708,000 persons, and that a representative can do an adequate job working an 8-hour day.    But if you use Ste. Lague to assign the representation tasks, you can end up with some representatives having to work 12 hours.  They may be tired, so they actually don't represent any of their constituents as well, despite spending 50% more time each day.  And for why?  So some big state representative can knock off a few minutes early.  Hardly fair at all.

But let consider Adams.  We set a maximum representation load of 748,000.  So some representative might have to work 8 hours and 27 minutes.  Hardly overworked.  And if the workload for some state runs over 748,000 per representative, you hire another representative.    Sure a few representatives might get a cushy job and not have to work 8 hours.  But isn't that acceptable considering the alternative.

St.Lague is only the middle ground if we consider D'Hondt at all acceptable.  But if we would use D'Hondt, we might as well bring back child labor with 8-years olds working from dawn to dusk picking clinkers out at the coal mine, sleeping on a hard board and being fed thin gruel twice a day.

Just to be clear, I do not support D'Hondt for a seat apportionment method for a regional unit of voters (such as a state).  My favorite method there would probably be major fractions (Sainte Laguë), but with the current apportionment method (geometric mean or equal proportions) a close second, harmonic mean third, the paradoxical strongest remainders/Hamilton method fourth and even smallest divisors/Adams ahead of greatest divisors/Jefferson, but not by much.  But when you consider that one of congresswoman Allison Shwartz (D-PA-13)'s constituents is or has been Keystone Phil and one of congressman Geoff Davis (R-KY-4) constituents is Bandit3, you can see how representation by someone you get to vote for or against is different from representation by someone you actually voted for.  Currently, if Keystone Phil still lives in PA-13 and Bandit3 still lives in KY-4, I doubt either one has any representative in the U.S. House of Representatives (and Bandit3 in the U.S. Congress period; I'm not sure if Keystone Phile voted for Specter in the 2004 general election) whom they voted for.  That's democracy (or the democratic aspects of our republic) for you.  If that's okay than having D'Hondt (which can't be any less proportional than winner-take all) for multi-winner elections should be okay too.

[Antonio the Sixth]

Well, my ranking is :

Webster/Sainte-Laguë method, corrected with the fairness rule
Hamilton/Strongest remainder method
Huntington-Hill method, corrected with fairness rule
Webster/Sainte-Laguë method
Huntington-Hill method
Hamronic mean method, corrected with the fairness rule
Hamronic mean method
Jefferson method, corrected with the fairness rule
Adams method, corrected with the fairness rule
Jefferson method
Adams method

This ranking is a generic one. In the case of US Congress apportionment, I'd rank Jefferson method higher (because of the Senate). In the case of a voting system, I'd exclude Adams, Huntington-Hill and harmonic mean, because this would give 1 seat to every party.

[Antonio the Sixth]

I'm bumping this so that we can use this thread to comment the recent apportionment numbers.