Constitutional fractions

In a comment, Jake points out that it’s silly that we can amend the CA constitution with just a simple majority.  A simple majority is the weakest possible condition, but seems too weak.  What’s an appropriate fraction?

The U.S. constitution can be amended by a 2/3 vote in both the House and Senate, together with 3/4 of the states.  2/3 is quite a popular fraction for constitutional amendments or other things you want to make hard to do, but it’s not clear what it has to recommend it besides being a nice round rational number.  I would guess (e – 1) / e would be more likely to be the “right” answer, because e always comes up in these sorts of things.

The most infamous fraction in the U.S. constitution is 3/5 – specifying that each slave counts as 3/5 of a person from the point of view of determining the House of Representatives. 3/5 has even less to recommend it than 2/3, suggesting something fishy.  In fact it was a compromise to balance out the political power of the free and slave states.  Ironically, the South would have preferred for slaves to be on an equal footing in this regard, so the slave states could get more votes in Congress.  Funnily enough, they kept the 3/5 kludge for their own constitution, perhaps, as suggests, to even out representatives among their slave-heavy and slave-light states.


2 Responses to “Constitutional fractions”

  1. Cassandra's boyfriend Says:

    You are pulling your chin about supermajority threshholds. Here’s a survey article on this topic, by a master:

    Naelbuff, Barry, 1995, “An Introduction to Vote Counting Schemes” (with J. Levin), Journal of Economic Perspectives, Vol. 9, No. 1, 3-26.

    If my memory is not failing me, work by Nalebuff (and coauthors) argues that there are economic and mathematical reasons for requiring a 3/5 supermajority in certain contexts.

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