The poor man's paradox and the vocal minorities

Philosophical concepts are often deemed exotic and purely academical, but today I would like to discuss two of them which not only are relevant for everyday life but very salient in the current US election cycle. The poor man's paradox (also know as sorites paradox) can be formulated as:

1. A person who has one million dollars is rich.
2. A person who has zero dollars is poor.
3. Giving a poor person one dollar does not make them rich.

This is paradoxical because, of course, if you repeat the one-dollar donation often enough, you eventually reach the one million border. So the paradox is only apparent if we formulate number 3 correctly: Giving a poor person one dollar does not make them rich unless they already have 999,999 dollars.

How is this relevant, you may ask? The fact is that the same principle can be applied to voting:

1. Half of the votes plus one is a majority.
2. Zero votes is a minority.
3. Adding a vote to a minority does not turn it into a majority (unless you are at exactly half of the votes).
   

This reasoning is repeated time and time again every time there is an election, and also quite often when there is a vote in a legislative chamber: in a heavily partisan vote, where two sides have fervent group of supporters that do not configure a majority, the result of the vote is essentially dictated by the undecided members. Consider a chamber of 15, with seven decided supporters of party A, six decided supporters of party B and members c and d which are not aligned. It is easy to see how the possible outcomes play out:

• If both c and d abstain, A wins with 7 votes out of 13
• If one of them abstains, B cannot win, because it can reach at most 7 votes (same as A)
  
• If c or d vote for A, A wins with 8 votes regardless of what the other one votes
• Only if both c and d vote for B, B wins with 8 votes out of 15

That is why, on every single campaign, candidates focus on bringing voters to the polls in the hope that they vote for them: every non-partisan vote that a candidate gets is like a lottery ticket to win the election. 

Photo: Alisdare Hickson

The question now is, how are non-aligned voters (or legislative representatives) moved to vote in one direction or the other? That is where the vocal minorities come into play. As Richard Nixon said repeatedly, the opinion of the silent majority can easily be silenced by the noise created by a small minority if they are outspoken enough. The sub-text to this vocal minority is clear: a (barely) veiled threat of causing unrest or even tearing down the society if their demands are not met. It is remarkable how this is actually an appeal for "qualified vote" in the sense that this group, which admits to be a minority, should still be heeded and their wishes imposed to the society at large only because the damage they can cause to society. How is this fair?

This is precisely why it is important that all citizens play an active part in the forming of the opinion of the society, discussing their beliefs in their social circles, attending (or even organizing) demonstrations to support their causes. In sum, letting themselves be heard, because otherwise those who are more vocal will hijack the democratic arena to an unfair result. I hope you have a nice evening.