Got a problem? Vote!

We’ll start with a passage from J.E. Littlewood’s celebrated Mathematician’s Miscellany.

“A voting paradox. If a man abstains from voting in a General Election on the ground that the chance of his vote's mattering is negligible, it is common to rebuke him by saying 'suppose everyone acted so’. The unpleasant truth that the rebuke is fallacious in principle is perhaps fortunately hidden from the majority of the human race. Consider, however, the magnitudes involved, where the election and the constituency are reasonably open. The chance that his vote will elect his member by a majority of 1 is of the order of 1 in 5000; there is a further chance of the order of 1 in 50 that this result will cause a change of Government. The total chance for this is no worse than 1 in 250,000. Since there are 30,000,000 voters with similar opportunities it would appear that there is something wrong; the explanation is that when the event happens to one man, 20,000 or so other voters in his constituency are in the same position.”

In principle, the same story holds anywhere in the world: the responsibility of an individual is not as big as we like to make it. Tom Stoppard was pretty clear: It's not the voting that's democracy; it's the counting.

Speaking of counting votes and giving out the MP positions, I was interested to see how it works in Bosnia and Herzegovina. Going through the regulations taught me that B&H uses the Sainte-Lague method. Let me put a quote from the election law here:

Article 9.5

  1. Mandates are allocated in each constituency in the following manner: For each political party and coalition, the total number of valid votes received by that political party or coalition shall be divided by 1, 3, 5, 7, 9, 11, et seq., as long as necessary for the allocation in question. The numbers resulting from this series of divisions shall be the “quotients”. The number of votes for an independent candidate is the quotient for that candidate.

  2. The quotients shall be arranged in order from the highest quotient to the lowest quotient. Mandates shall be distributed, in order, to the highest quotient until all the constituency mandates for the body have been distributed.

  3. Political parties, coalitions, lists of independent candidates and independent candidates cannot participate in the allocation of mandates if they do not win more than 3% of the total number of valid ballots in a constituency.

Unlike B&H, in the neighbouring countries (Serbia, Croatia), they use the D’Hondt method. They differ in terms of coefficients dividing the number of votes. While in Sainte-Lague method, the numbers are divided by 1, 3, 5,... In d’Hondt method they’re divided by 1, 2, 3,... It is not too hard to make an example in which the two methods produce different results: D’Hondt method favours strong parties more than Sainte-Lague.

(The title is an advertisement slogan in Bosnia and Herzegovina.)

This is the last in a series of ten articles written by the author.

Featured Image Courtesy: Shutterstock

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Harun Šiljak

READ:   Handbook of Cubik Math
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