Chance News 47

Quotations

It is remarkable that a science which began with the consideration of games of
chance should have become the most important object of human knowledge.

Pierre Simon Laplace
Théorie Analytique des Probabilités, 1812,

Elections

Andrew Gelman has an interesting article regarding the statistics of elections. He starts with

“Presidential elections have been closer in the past few decades than they were for most of American history. Here's a list of all the U.S. presidential elections that were decided by less than 1% of the vote:

1880
1884
1888
1960
1968
2000

Funny, huh? Other close ones were 1844 (decided by 1.5% of the vote), 1876 (3%), 1916 (3%), 1976 (2%), 2004 (2.5%).

Four straight close elections in the 1870s-80s, five close elections since 1960, and almost none at any other time.”

Perhaps more interesting is his take on House and Senate elections:

http://www.dartmouth.edu/~chance/forwiki/elections1.gif

In the companion piece written with Nate Silver, the graphic concerning the House is made more evident here:

http://www.dartmouth.edu/~chance/forwiki/elections2.gif

From the graph, “the rate of close elections in the House has declined steadily over the century. If you count closeness in terms of absolute votes rather than percentages, then close elections become even rarer, due to the increasing population. In the first few decades of the twentieth century, there were typically over thirty House seats each election year that were decided by less than 1000 votes; in recent decades it's only been about five in each election year.”

Another way of putting it: “Consider that, in the past decade, there were 2,175 elections to the United States House of Representatives held on Election Days 2000, 2002, 2004, 2006 and 2008. Among these, there were 41 instances — about 1.9 percent — in which the Democratic and Republican candidates each received 49 percent to 51 percent of the vote (our calculations exclude votes cast for minor parties). In the 1990s, by contrast, there were 65 such close elections. And their number increases the further one goes back in time: 88 examples in the 1950s, 108 in the 1930s, 129 in the 1910s.”

Discussion

1. A contention mentioned in the NYT article for this bifurcation of opinion is: “as the economy has become more virtual, individuals can now choose where to live on an ideological rather than an occupational basis: a liberal computer programmer in Texas can settle in blue Austin, and a conservative one in the ruby-red suburbs of Houston.” Argue for and against this assertion of coupling ideology and occupational mobility.

2. Gelman and Silver end their NYT article with “Elections like those in New York’s 20th district or in Minnesota, as contentious as they are, actually hark back to a less divisive era in American politics.” Explain the seeming paradox of a close race indicating less divisiveness.

3. As of this posting, the Minnesota senate seat is unfilled despite a manual recount, a canvassing board followed by a so-called election contest and awaits the results of the appeal to the Minnesota Supreme Court—possibly further. See When Does ‘Close Become Too-Close-to-Call? for an analysis of error rates and how likely it is that the real winner would be Norm Coleman instead of Al Franken who currently leads by 312 votes out of about 2.9 million cast. The Minnesota Supreme Court will hear oral arguments on June 1, 2009.

Submitted by Paul Alper