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WHICH DEMO WON? DEPENDS ON METHOD

With primaries, caucuses, a glut of rules on eligibility, incessant polling, media watches and reams of punditry, the Democratic candidates' spin doctors have ample material from which to fashion an argument that their man is the front-runner.

Further evidence for this came over the weekend in the balloting that took place in Nebrarkamassacalowa.The 55 voting members in this little-known state's caucus ranked the five candidates as follows:

Eighteen members preferred Tsongas to Kerrey to Harkin to Brown to Clinton. Twelve members preferred Clinton to Harkin to Kerrey to Brown to Tsongas. Ten members preferred Brown to Clinton to Harkin to Kerrey to Tsongas. Nine members preferred Kerrey to Brown to Harkin to Clinton to Tsongas. Four members preferred Harkin to Clinton to Kerrey to Brown to Tsongas. And two members preferred Harkin to Brown to Kerrey to Clinton to Tsongas.

To determine the winner, Tsongas supporters argued that the plurality method should be used, whereby the candidate with the most first-place votes wins.

With this method and 18 first-place votes, Tsongas wins easily.

Alert for signs of a comeback, Clinton supporters argued that there should be a runoff between the two candidates receiving the most first-place votes.

Clinton handily beats Tsongas in such a runoff (18 members preferring Tsongas to Clinton but 37 preferring Clinton to Tsongas).

Brown's people had to be a little more ethereal to come up with a winner.

Their suggestion: The candidate with the fewest first-place votes (Harkin in this case) should be eliminated first; then the first-place preferences for the others should be adjusted (still 18 for Tsongas, now 16 for Clinton, now 12 for Brown, still 9 for Kerrey).

Next, the candidate among the remaining four having the fewest first-place votes (Kerrey in this case) should be eliminated and the first-place preferences for the remaining candidates adjusted. (Brown now has 21 first-place votes.)

Winnowing the candidates by removing at each stage the one with the fewest first-place votes is continued.

Using this method, Brown is the winner.

Kerrey's campaign manager remonstrated that more attention should be paid to the overall rankings, not just to the top preferences.

He argued that if first-place votes are each accorded 5 points, second-place votes 4 points, third-place votes 3 points, fourth-place votes 2 points and last-place votes 1 point, then associated with each candidate will be a number that will accurately reflect that candidate's support.

Since Kerrey's count of 191 is higher than anyone else's, he wins.

Finally, Harkin responded that only man-to-man contests should count.

Pitted against any of the other four candidates in a two-person race, he comes out the winner.

For example, he beats Kerrey 28 votes to 27 and Clinton 33 votes to 22.

Harkin says he therefore deserves to be the overall winner.

All the numbers concocted here (and manipulated by drawing upon the work of the American mathematicians William F. Lucas and Joseph Malkevitch and the 18th century philosophers Jean-Charles de Borda and the Marquis de Condorcet) are intended to show how the choice of a voting method can sometimes determine the winner.

(John Allen Paulos, professor of mathematics at Temple University, is the author of "Beyond Numeracy.")