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Math Experts Find the Formula for Electoral Chaos
By Amanda Onion  Fox News
What do a patch of warm water in the Pacific and a White House intern have in common?

Sorry, no punch line — this is actually a mathematical question. According to a study published recently in the Physical Review Letters, El Niño and Monica Lewinsky do share a quality: both exist in chaotic — or unpredictable, sometimes illogical — systems, and, so, have the potential to effect enormous change.

The idea that El Niño makes the weather do strange things, and that the Lewinsky affair has precipitated great political turmoil, may be obvious.

But the explanation hasnít always been so clear to mathematicians. For those who scrutinize daily events and search for abstract truths that can be expressed in numbers and symbols, there was little to explain how a factor like a White House intern could alter the course of political history.

Now there is: S[f_p] = log \Lambda_{f_p}

Or, put differently, factors like Monica Lewinsky are significant because decision-making settings like elections are inconsistent and therefore vulnerable to outside factors which, over time, greatly affect the outcome of future voting.

"A small change in the order — a change in who the candidates are in a given year — can make a big difference down the line," said David Meyer, co-author of the study and a mathematician at the University of California at San Diego. "Over five to six elections, the results are going to diverge further and further with this small difference in the beginning."


Consider, for example, the 2000 elections.

If given a choice between Al Gore and Texas Governor George Bush, Jr., the majority may choose Bush. But, Meyer explains, if the Lewinsky scandal favors a candidate who stresses morality issues, like, for example, Pat Robertson, the majority may opt for Gore.

In the next election, however, a candidate who might have beaten Bush in a future election — say, Dick Gephardt — will instead lose to an incumbent Gore in the primary and never have the opportunity to run against Bush and win in an election — all because of Monica Lewinsky.

Over time, itís the chronological order in which choices appear to voters that determines whether or not a candidate wins a majority vote.

To demonstrate that decision-making processes like voting and polling are highly unpredictable, Meyer and his colleague Thad Brown, a political scientist at the University of Missouri, first studied the 24-year-old General Impossibility Theorem by Kenneth Arrow. Arrowís theorem states when some groups vote among three or more choices, the majority consensus will forever cycle from one choice to another.

Taking that concept further, Meyer and Brown then applied and measured for the chaos theory: a relatively new concept which says that, in unstable systems, one small factor can lead to enormous changes down the line. They found voting systems measured a high degree of chaos.

"Chaos — the incredible complexity that comes about from minor disturbances — exists in voting systems," said Brown. "So that which was a purely physical phenomenon also relates straight to politics."

The fact that results vary, depending on when issues or candidates are brought to the ballot, also means that the setter of the agenda — whether a random factor like Lewinsky or a rules committee in the House — has the power to influence the outcome of any vote.

While political scientists have long sensed that agenda is somehow linked to the voting outcomes, there was no precise proof to explain that connection.

"The person who sets the agenda — the chairman — can determine the outcome by changing the order of the alternatives," said Meyer.

One of the most common examples of a chaotic system is the weather. To predict weather patterns, meteorologists must take into account myriad factors from around the globe, since one small change, such as the warming of a patch of water in the Pacific, can influence the weather thousands of miles away.

Meyer believes there may be a lesson in the way meteorologists predict the weather only by probability. Since itís impossible to predict when a chaotic factor like El Niño may turn up, meteorologists always predict the weather as a percentage chance.

Likewise, that practice would work well in predicting any kind of election, poll or Congressional vote outcome. "Meteorologists never tell you itís definitely going to rain," he said. "Weíre showing that in decision making, the best you should expect to do is to give statistical predictions."

In other words, you never know when a new scandal may be around the corner.

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