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The Apportionment of the US Congress in the 1920’s—The The Apportionment of the US Congress in the 1920’s—The

The Apportionment of the US Congress in the 1920’s—The - PowerPoint Presentation

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The Apportionment of the US Congress in the 1920’s—The - PPT Presentation

Social Choice in Political Controversies Paul H Edelman Vanderbilt University Problem How to allocate seats among the states to the US House of Representatives Representatives shall be apportioned among the several Statesaccording to their respective numbers The actual Enumerat ID: 165900

huntington method apportionment congress method huntington congress apportionment willcox mathematical difference choice political webster states methods social question webster

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Slide1

The Apportionment of the US Congress in the 1920’s—The Role of Social Choice in Political Controversies

Paul H Edelman

Vanderbilt UniversitySlide2

Problem: How to allocate seats among the states to the US House of Representatives

“Representatives … shall be apportioned among the several States…according to their respective numbers…. The actual Enumeration shall be made…within every subsequent Term of ten Years, in such Manner as they shall by Law direct.”

Article I Section 2 US ConstitutionSlide3

History prior to 1920

1790

Hamilton proposes his method for the first Congressional apportionment. Washington vetoes it, and Jefferson’s method is adopted instead.

1840

Webster’s (Sainte-Laguë) method is adopted because of the bias to large states exhibited by Jefferson.

1850-1900

Hamilton’s method adopted (under the name of Vincent’s method.) Ultimately rejected because of the Alabama Paradox.

1910

Return to Webster’s methodSlide4

Increasing the size of the HouseSlide5

1920- A confluence of problems

Massive demographic shifts from rural to urban centers.

These shifts were exacerbated by movement of population due to WWI.

The 1920 census was taken in January during a particularly rough winter (or so it was alleged.)

Most importantly—House did not want to expand in size.Slide6

The issues in the debateThe size of the House

Punishing the southern states for disfranchising African-Americans

Delegation of authority to apportion to the executive branch

Counting aliens for the purposes of apportionment

The method of apportionmentSlide7

Battle over methodThere was no particular method of apportionment enshrined in law

In 1910 the Webster method had been employed, although not explicitly

At that time, James Hill of the Census Office had proposed a new method based on using a relative rather than absolute measure of difference in allocation of seatsSlide8

Edward V. Huntington (1874-1952)

Professor of Mathematics, Harvard University, 1905-1941

MAA president, 1918

Vice President, AAAS, 1926

Statistics Branch of the General Staff of the War Department, 1918Slide9

Walter F. Willcox (1861-1964)

Professor of Statistics, Cornell University, 1891-1931

American Statistical Association, president, 1912

American Economic Association, president, 1915

Chief Statistician, Bureau of the Census, 1899-1901Slide10

The argumentWillcox advocated for the Webster method, and in fact it was his influence behind the choice in 1910

Huntington developed a mathematical theory of apportionment, inspired by Joseph Hill, and argued in favor of the method he developed (equal proportions).Slide11

The mathematical issues

Relative vs. Absolute Difference– Webster’s method minimizes the pair-wise absolute difference in per capita representation between states. Huntington’s method minimizes the pair-wise relative difference in per capita representation (and most other relative differences, as well.)Slide12

Mathematical Issues, cont.Bias—Since the demise of Jefferson’s method, there was concern that some methods were systematically more favorable for big or small states. Huntington argued that his method was unbiased. Willcox argued that Webster’s method was unbiased. (Willcox was right, Huntington was wrong.)Slide13

The argumentsHuntington was trying to displace Webster’s method and so had to justify that a new method was better. He based that claim on mathematical arguments

Willcox

argued that his method was the better pragmatic choice, in addition to arguing that it was the less biased of the two.Slide14

Huntington“A new mathematical theorem is not a matter for “proponents” and “opponents” to wrangle over as if it were a river-and-harbors bill. A new mathematical theorem has just one essential property: it is either true or false….The new theorem came like an answer to a prayer, supplying precisely the kind of simple and self-explanatory test that Congress had long been seeking.” Slide15

Huntington

“Indeed it is hard to see what light the early history of the Constitution can throw on the present-day problem… The only question is

what method of computation comes nearest to satisfying this requirement of proportionality?

This is a purely mathematical question, important facts about which were not known until 1921. Certainly the "framers of the Constitution" had no idea of the mathematical pitfalls that surround the whole question; and any discussion of methods of apportionment which does not take account of the clarification introduced by the modern theory is futile

. “Slide16

Huntington

“The current debate in Congress turns on a choice between two methods. The role of mathematics in this debate may be summed up as follows:

Theorem 2

. I f Congress desires to equalize the congressional districts as far as possible among the several states, the method of (Huntington) will always give a better result than the older method of (Webster). The method of (Webster) cannot be counted on to equalize the congressional districts on any basis whatever.”Slide17

Willcox

“Perhaps the main difference between Profes

s

or Huntington and me is over the nature of the problem. He treats it as a statistical or “purely mathematical” question which mathematicians and statisticians are to solve, while Congress should accept their solution. I regard it as a political problem in which the scholar should attempt first to find what end the constitution or Congress aims at and then devise or improve a method by which Congress may accomplish that end. The function of mathematicians in the problem is not to choose among ends but merely to determine how some primary end of apportionment can best be secured.”Slide18

Willcox, cont.

“Upon this main difference another depends. Professor Huntington thinks I owe it to the world of scholars to defend my heterodox opinions by publishing them "in some regular journal." My main purpose, however, has been to help Congress out of a dilemma and I am not interested in justifying my course in so doing to my academic colleagues.”Slide19

A broader conceptionPragmatism—Willcox advocated for Webster at least in part because it was the last method to be approved by Congress and hence he thought it would have the best chance of being passed.

Comprehensibility– Willcox viewed Huntington’s method as difficult to sell to Congress because of its difficulty:Slide20

Comprehensibility

One of the main objections to the method of equal proportions (Huntington) is that to the non-mathematician in Congress or out it is almost unintelligible.” (Willcox,

Science

, 1928)

“ This is perhaps the first time in history that advocates of any measure have openly accused the Congress of the United States of being unable to multiply and divide. And yet the ability to follow these most elementary rules of arithmetic is all that is needed to understand the exact meaning of the test (in Huntington’s method.)” (Huntington, Sociometry, 1941)Slide21

What happenedOnly two bills were able to make it out of the House to the Senate—one in 1921 (which the Senate never acted on) and one in 1929.

The latter bill was stalled in the Senate, but Senator Vandenberg managed to tie it to the bill authorizing the census which forced a Senate vote.Slide22

What happened—cont.

Bill of 1929

Census Bureau to produce tables using Huntington’s method, Webster’s method, and the most recently used method.

If Congress fails to act by the end of the term (March 4, 1931) apportionment by most recent method (Webster) goes into effect.

Process repeats every ten years.

Both Webster and Huntington methods give same result for 1930 census, so no further action.Slide23

1941

Huntington and Webster methods produce different results.

Huntington

Webster

Michigan

17

18

Arkansas

7

6

Huntington apportionment adopted for 1940’s

• Automatically used for all future apportionmentsSlide24

Some speculationsMaybe the difference in attitude between Huntington and Willcox was the distinction between a consultant and an advocate?

Maybe the difference was between Cornell and Harvard?

Maybe the difference was just pure personal style?Slide25

Speculations, cont.Maybe this was a question of the right level of abstraction:

Huntington took the mathematical approach of extracting the apportionment of the House from its political context.

Willcox, the “statist,” thought it important to consider the question in the political context in which it arose.Slide26

Speculations, cont.Is one approach clearly better than the other?

Willcox is more highly regarded, but that may be because he is now viewed as correct on the merits. (But he changed his mind later!)

Huntington ultimately won, but that was because of the politics of apportionment, not on the basis of his mathematical arguments!Slide27

Was the mathematical debate helpful?For social choice theorists probably, Yes

For the political process probably, No

No one in Congress understood

The truth was easy to misrepresent

It gave objective cover and credibility to those opposed to reapportionment.

The real social problem was never adequately addressed by apportionment anyway!Slide28

Social choice and political turmoil

When political salience is high

technical social choice arguments are at their least persuasive

they will mostly be employed as an objective cover for a position adopted for other reasons

When political salience is low

it will be difficult to get groups to care about changing social choice methods

it will also make less of a difference in the outcomeSlide29

CourtsPerhaps one way around this if courts get involved:

In the US, courts have required IRV and cumulative voting in VRA cases

In Switzerland with the reforms introduced by Balinski and Pukelsheim

But this might require a more aggressive judiciary than many places haveSlide30

SwedenWhy the concern now?Is the concern about the system or about the outcome?

Would any electoral reform address the underlying political stress?Slide31

Final points

Advocates for change in social choice methods should be pragmatic in making their case

It would be unusual for a purely technical argument to be dispositive

Purely technical arguments can confuse as easily as they can illuminate

Sometimes the perfect is the enemy of the good

The less politically salient the situation the easier it will be to make the caseSlide32

Bibliographical NotesM. Balinski & H. P. Young, Fair Representation: Meeting the Ideal of One Man, One Vote, 2

nd

ed., Brookings Inst. Press, 2001

Thomas L. Bartlow,

Mathematics and Politics: Edward V. Huntington and Apportionment of the United States Congress,

Proceedings of the Canadian Society for History and Philosophy of Mathematics

19

(2006), 29-54.

----------------------,

The Mathematical Life of Edward V. Huntington

, preprint.Slide33

Notes, cont.Colloquy between Willcox and Huntington in

Science

: vol 67 (1928) 509-510, 581-582; vol 68 (1928) 579-582;vol 69 (1929) 163-165, 272, 357-358, 471-473; vol 95 (1942) 477-478, 501-503.

Colloquy in

Sociometry

: vol 4 (1941) 278-282, 283-298. Slide34

Thank you for your attention