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 nonmathematician 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.
Michigan
Arkansas
Huntington
Webster
17
7
18
6
• 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, 501503.
• Colloquy in Sociometry: vol 4 (1941) 278-282,
283-298.
Thank you for your attention