**The Apportionment of the US Congress in the 1920’s—The** Role of 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 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 Constitution

**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 method

**Increasing the size of the House**

**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.

**The issues in the debate** • The 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 apportionment

**Battle over method** • There 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 seats

**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, 1918

**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, 1899-1901

**The argument** • Willcox 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).

**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.)

**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.)

**The arguments** • Huntington 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.

**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.”

**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. “

**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.”

**Willcox** • “Perhaps the main difference between Professor 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.”

**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.”

**A broader conception** • Pragmatism—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:

**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)

**What happened** • Only 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.

**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.

**1941** • Huntington and Webster methods produce different results. •Huntington apportionment adopted for 1940’s • Automatically used for all future apportionments

**Some speculations** • Maybe 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?

**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.

**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!

**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!

**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 outcome

**Courts** Perhaps 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 have

**Sweden** • Why the concern now? • Is the concern about the system or about the outcome? • Would any electoral reform address the underlying political stress?

**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 case

**Bibliographical Notes** • M. Balinski & H. P. Young, Fair Representation: Meeting the Ideal of One Man, One Vote, 2nd 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.

**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.

**Thank you for your attention**