Re: mathematical curiosity known as Benford's law

[ivan.meek@xxxxxxxxx]

Hi,

"...mathematical curiosity known as Benford's law."

It is actually very logical if you think about it.  And Cary suggested, it is a
pretty weak way to detect election fraud.  Our emphasis should be on preventing
fraud (with robust voting methods) rather than focusing on detecting fraud. 
IMHO.

-ivan




Quoting Margit Johansson <margitjo@xxxxxxxxx>:

> Political science
> Election forensics
>
> Feb 22nd 2007 | SAN FRANCISCO
> From *The Economist* print edition
> How to detect voting fiddles
>
> A WEEK is a long time in politics. And a decade is a long time in political
> science. Ten years ago, bright young academics would probably have thought
> that analysing the impact of ballot formats and comparing the merits of
> voting machines was unworthy of intellectual pursuit. The 2000 presidential
> election in America, with its butterfly ballots and controversial outcome,
> changed all that and spurred a more scientific approach to studying voting
> and how it might be subverted.
>
> One way to detect fraud is to use statistics. Walter Mebane and his team at
> Cornell University have devised a new method of doing so, which they
> described to the American Association for the Advancement of Science. It is
> similar to that of a mathematical curiosity known as Benford's law. This law
> states that in certain long lists of numbers, such as tables of logarithms
> or the lengths of rivers, the first digit of each number is unevenly
> distributed between one and nine. Instead, there are far more numbers
> beginning with one?about a third of the total?and far fewer starting with
> nine. For example, a 2km stream is twice as long as a 1km stream; by
> contrast, a 10km stream is only 11% longer than a 9km stream. So you will
> find more streams measuring between 1km and 2km than between 9km and 10km.
>      [image: Click Here!]
>
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>
> The pattern that Dr Mebane has detected concerns not the first but the
> second digit of lists of election results from different precincts of a
> constituency, where he also observes a non-uniform distribution of possible
> digits. The effect is far more subtle, with zero occurring about 12% of the
> time and nine turning up on 9% of occasions. Dr Mebane has observed this
> pattern with great consistency for voting results from precincts across the
> United States in recent elections. The cases where there are significant
> deviations from the pattern correlate well with places where there have been
> known problems of election rigging.
>
> In contrast with more sophisticated statistical analyses, which require
> laborious research to correlate voting patterns with variables such as race,
> wealth or historical precedent, Dr Mebane's test can be applied to data
> without further ado. It is a very simple test for fraud.
>
> Dr Mebane is careful to point out that the test is not foolproof. It
> sometimes fails to detect a discrepancy in a vote that is known to have been
> problematic, and occasionally detects fiddling where there was none.
> However, he has managed to develop a mathematical model that explains the
> distribution of the second digits, putting what might appear to be a
> statistical oddity on a more solid footing. He has also had some encouraging
> success using it in practice.
>
> One example concerns an analysis of the last three elections in Bangladesh.
> The 1991 election showed no strange results. For the 1996 election some 2%
> of results were problematic. And fully 9% of the results in 2001 failed the
> test. The 2001 election was fiercely contested. Yet monitors from the Carter
> Centre and the European Union found the election to be acceptably, if not
> entirely, free and fair. Tests like Dr Mebane's one could provide monitors
> with quantitative estimates of exactly how free and fair an election has
> been, on which to base their qualitative judgment of whether that is indeed
> acceptable.
>
> As Jasjeet Sekhon of the University of California, Berkeley, points out, the
> emerging field of election forensics presents opportunities as well as
> risks. In the best cases, it is encouraging political scientists to team up
> in an interdisciplinary way with statisticians, economists, psychologists
> and even software engineers, to understand the complex interplay between
> human and technological factors that can influence an election. These
> collaborations force political scientists to question some of their
> cherished assumptions in the light of insights that experts from other
> disciplines bring to the problem.
>
> On the downside, the excitement surrounding this sort of research can
> attract self-appointed experts with a limited knowledge of the realities of
> voting. For example, statistical discrepancies between exit polls and actual
> votes cast have been used by some to deduce widespread fraud on statistical
> grounds. In fact, it has long been known that exit polls, though they may
> claim to be based on random samples, suffer from biases in the way that they
> are conducted. In America these tend to skew the results towards the
> Democrats.
>
> Dr Sekhon notes that, thanks to Karl Rove, the mastermind of George Bush's
> election victories in 2000 and 2004, the Republicans have been far more
> effective at exploiting new scientific information about voting and
> elections. Indeed, several of his colleagues have been surprised to receive
> hand-written notes from Mr Rove pointing out minor blemishes in their
> academic articles. "In contrast, the Democrats have had faith-based
> electioneering tactics," says Dr Sekhon. The party often engages in
> activities such as contacting people who have voted in the primaries, which
> can be shown to be a waste of time and money. In 2008 its workers would do
> well to consult the latest scientific literature instead.
>
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> »<http://www.economist.com/science/displaystory.cfm?story_id=8733747#top>
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>  Related Items More articles about...
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statistics<http://www.economist.com/research/articlesBySubject/display.cfm?id=348972>
>
> Websites
>
> Dr Mebane posts research papers <http://macht.arts.cornell.edu/> on his
> home-page.
>
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