Something called the "Alabama paradox."





This site was super helpful at explaining the history and math of apportionment. As always though, verify the specifics of the data yourself (but all the general points are definitely correct).

https://www.maa.org/press/periodicals/co...troduction

CORRECTIONS
- He didn't bother showing him locking cell references in the animations. Things like "=B4/B2" should have been "=B4/$B$2" so he could drag the formula down. We took that out in the interest of clarity.
- Yes, at 13:20 he s"the divisor ceases to lose some of its strict meaning" which is the opposite of what he meant! The sentence needs but the one negative. Either of these would work: "the divisor loses some of its strict meaning" OR "the divisor ceases to have some of its strict meaning".
- Sorry, at 16:47 column D is wrong. These are different numbers using 880 but the values over in E use the correct 930. It's just a display issue and does not change the results (despite being a bit confusing!). Spotted by a few people.

(06-07-2022 01:13 AM)GoodOwl Wrote:  Something called the "Alabama paradox."





This site was super helpful at explaining the history and math of apportionment. As always though, verify the specifics of the data yourself (but all the general points are definitely correct).

https://www.maa.org/press/periodicals/co...troduction

CORRECTIONS
- He didn't bother showing him locking cell references in the animations. Things like "=B4/B2" should have been "=B4/$B$2" so he could drag the formula down. We took that out in the interest of clarity.
- Yes, at 13:20 he s"the divisor ceases to lose some of its strict meaning" which is the opposite of what he meant! The sentence needs but the one negative. Either of these would work: "the divisor loses some of its strict meaning" OR "the divisor ceases to have some of its strict meaning".
- Sorry, at 16:47 column D is wrong. These are different numbers using 880 but the values over in E use the correct 930. It's just a display issue and does not change the results (despite being a bit confusing!). Spotted by a few people.

Math makes my eyes cross. But the problem with "fair share" is that it is subjective. BTW, same problem with "common sense" solutions.

That was fun.
But I must say, the Illinois accent early in the video is a bit off -- it was not a Midwestern twang at all.

The only way for a republican form of government to apportion fairly would be to adopt a legislature system that has all legal voting citizens in it. But then, that would not be a republican form of government at that point.

(06-07-2022 02:56 PM)tanqtonic Wrote:  The only way for a republican form of government to apportion fairly would be to adopt a legislature system that has all legal voting citizens in it. But then, that would not be a republican form of government at that point.

I disagree, as follows: the video outlines three ways of proportioning -- Hamilton, Jefferson, and Adams -- all of which seem fully "fair" to me, in the sense that they are procedurally just, non-arbitrary, and ultimately reasonable.

What they don't do is produce numerically perfect outcomes. The flaw is in the belief that fairness necessarily requires numerical perfection.

(06-07-2022 09:34 PM)georgewebb Wrote:  

(06-07-2022 02:56 PM)tanqtonic Wrote:  The only way for a republican form of government to apportion fairly would be to adopt a legislature system that has all legal voting citizens in it. But then, that would not be a republican form of government at that point.

I disagree, as follows: the video outlines three ways of proportioning -- Hamilton, Jefferson, and Adams -- all of which seem fully "fair" to me, in the sense that they are procedurally just, non-arbitrary, and ultimately reasonable.

What they don't do is produce numerically perfect outcomes. The flaw is in the belief that fairness necessarily requires numerical perfection.

Each noted detracts from some, and buttresses others. That outcome is endemic when engaging in a system that requires whole integer outcomes to a proportional representation.

The only way that a republican system can typically achieve an ‘only integers’ accurate representation that neither detracts nor adds to an outcome is when the number of representatives equals the population size. That is just raw number theory. Political science dictates that a form of government where the representatives are each and every individual in a population is not republican in nature.

(06-07-2022 10:20 PM)tanqtonic Wrote:  

(06-07-2022 09:34 PM)georgewebb Wrote:  

(06-07-2022 02:56 PM)tanqtonic Wrote:  The only way for a republican form of government to apportion fairly would be to adopt a legislature system that has all legal voting citizens in it. But then, that would not be a republican form of government at that point.

I disagree, as follows: the video outlines three ways of proportioning -- Hamilton, Jefferson, and Adams -- all of which seem fully "fair" to me, in the sense that they are procedurally just, non-arbitrary, and ultimately reasonable.

What they don't do is produce numerically perfect outcomes. The flaw is in the belief that fairness necessarily requires numerical perfection.

Each noted detracts from some, and buttresses others. That outcome is endemic when engaging in a system that requires whole integer outcomes to a proportional representation.

I agree of course -- I just don't think that those outcomes are "unfair", as I mentioned.

(06-07-2022 10:20 PM)tanqtonic Wrote:  The only way that a republican system can typically achieve an ‘only integers’ accurate representation that neither detracts nor adds to an outcome is when the number of representatives equals the population size. That is just raw number theory. Political science dictates that a form of government where the representatives are each and every individual in a population is not republican in nature.

There is no small irony in the fact that integer-ness is required for representatives, even though integrity is not. :)

(06-07-2022 11:27 PM)georgewebb Wrote:  

(06-07-2022 10:20 PM)tanqtonic Wrote:  

(06-07-2022 09:34 PM)georgewebb Wrote:  

(06-07-2022 02:56 PM)tanqtonic Wrote:  The only way for a republican form of government to apportion fairly would be to adopt a legislature system that has all legal voting citizens in it. But then, that would not be a republican form of government at that point.

I disagree, as follows: the video outlines three ways of proportioning -- Hamilton, Jefferson, and Adams -- all of which seem fully "fair" to me, in the sense that they are procedurally just, non-arbitrary, and ultimately reasonable.

What they don't do is produce numerically perfect outcomes. The flaw is in the belief that fairness necessarily requires numerical perfection.

Each noted detracts from some, and buttresses others. That outcome is endemic when engaging in a system that requires whole integer outcomes to a proportional representation.

I agree of course -- I just don't think that those outcomes are "unfair", as I mentioned.

On this side, I would characterize someone 'getting an extra quarter' while a few swallow the cost at a nickel each as an inherent unfairness --' but one do minute as to not get lathered up about. And as an unfairness necessitated by the requirement of the requirement of forcing integer number of representatives onto sets of non-uniform sized voting populations and justified by number theory.