The Math of Voting

The Math Of Voting
The Math Of Voting

The House of Representatives in the United States Congress is responsible for creating laws that, if they get through the Senate and the President, become, well, law. the House has 435 members. The British House of Commons has 650 lawmakers. Even the Australian House of Representatives has 150 members.


Democratic countries deliberately choose to have their laws created by large groups of people. The idea is that special interest groups will not be able to have too much influence on the passage of laws, and so the government will truly be a government representative of the people.

Is it possible, then, that an entire democratic country could be run by as few as two individuals? Let’s see what the math says…

Suppose lawmakers are debating some law. The final version of the law is put to the House of Representatives for a vote. Hands are raised or lowered, and the House Speaker announces the result of the vote – “The Ayes have it!” and the law is passed. Surely, all 435 or 650 or whatever number of these lawmakers have had their say? Surely the result is truly representative of (these Representatives of) the people?

The math says “no!”

Imagine that 218 of these 435 people get together and make a pact. They meet elsewhere in the government building before the main vote, and hold their own vote on the issue at hand. They agree that when they meet with the other 217 members in the House, the pact members will all vote according to what they decided beforehand. Then, the 217 notice something very strange – they become completely powerless to influence the course of the nation. Yes, they can make speeches – blustering and filibustering until they are red in the face. But when it comes to the crunch – to the crucial vote that decides what is law, the 218 can do whatever they want. It’s a travesty of democracy! The House of Representatives becomes Half a House of Representatives, Half a House Paid Powerless Politicians.

We have a name for this downgrading of democracy – we call it “political parties”. The United States founding fathers were surprised that political parties formed. Unfortunately, in hindsight, it’s surprising that anyone would find it surprising.

But still, 218 is a good number of representatives, isn’t it? It might not be as good as 435, but surely the 218 from the Party in Power can be trusted to look out for the interests of the common man? Unfortunately, no. Imagine that 110 of these 218 gang together, and before each Party Room vote, they decide amongst themselves which way they will push the Party. Then, in the Party Room, these 110 all vote the same way, and the remaining 108 have absolutely no sway over the course the Party adopts. Then, the opinion of this group of 110 representatives is imposed on the whole group of 435, and the whole nation.

Could this really happen? Well, we have a name for this phenomenon too – it’s called “factions”. Since we have a name for it, it probably happens quite a lot.

But what about factions within the faction? Could a small power-hungry clique (see, we have a word for this, too) of 56 sway the vote of the 110? If they were united, yes – and these 56 could be dominated by an inner circle (another word) of 29. Once the inner circle is established, all their decisions could be swayed by a small group of 15 people – or 8, or 5, or 3 or finally 2 uber-powerful individuals who hold (between them) the helm of the entire nation. These two dominate the third person of their triumvirate, just by agreeing in advance to always agree. The triumvirate dominates the council of 5, which in turn dominates the band of 8. Then the 15, the 29, the 56, the 110, 218 and 435 members of the House of Representatives all follow like puppies every whim of the powerful two. All that’s required is that every smaller circle remains united against the rest.

So the math says that it’s possible, perhaps even easy, for an entire nation of millions to fall under the dominance of a mere two individuals.

Can we expect these two people to vote in line with the interests of the common man? Will these people – these politically savvy, immensely powerful people, who fought tooth and nail to gain their position of absolute sovereignty, and must carefully and continually balance alliances and enmities to maintain it – will these two people look out for the interests of the common man?

The math doesn’t tell us that, but I think you can guess!