This was inspired by a lunch conversation which I couldn’t let go since yesterday.

I find it difficult to engage in productive debates verbally: I too often find the flow of the conversation jumping around the issue rather than logically follow from one statement to another and the debates fade into discussions instead. The discussions can be insightful, but it is difficult to summarise what exactly happened later on.

Anyway, whilst I was happily chewing on a disgusting piece of sweet potato the discussion’s random walk hit the “you shouldn’t vote since it won’t matter” point. Things were about to get interesting.

I. Ignoring negligible events.

My position on the “you shouldn’t vote since it won’t matter” is that it is true. Of course the huge assumption here is that your only reason for voting is to exert certain influence, not to use voting as an opportunity to learn about different policies, not to have a lovely stroll to a polling station, not to signal to yourself and your peers that you are a good citizen.

My original (and faulty) reasoning for the above was the following: the probability of your vote being pivotal is tiny and people usually ignore events with such probabilities when they decide what to do.

How tiny is tiny? Depends on the election, but googling around yields \( O(10^{-6}) \) chance of swinging a nationwide election.

It is too easy to come up with examples when people partake in negligibly (\( O(10^{-6}) \)) lethal activities for very little benefit and it is also too easy to dismiss same examples by focusing on how beneficial they truly are. And that is exactly what happened yesterday: the discussion digressed into how beneficial a bus ride can be. The least convenient possible world springs to mind: when people dismiss arguments due to a technicality, which isn’t true in the real world but miss the point.

And the point is: a consistent agent won’t vote since he/she neglects tiny probabilities usually and making an exception for voting is inconsistent.

However, whilst consistency is an excellent heuristic to point out when people are acting irrationally, it’s not the goal. Just because I slip up daily and ignore things with negligible probabilities I shouldn’t carry on.

II. If everyone thought this way…?

The usual objection to the “you shouldn’t vote because it won’t matter” is the title of the paragraph.

This is when the game theory kicks in and the dilemma becomes exciting.

It is also interesting how it pays to be a hypocrite here: it is obvious that you should advocate voting so that our government continues to function, but not clear whether you should actually bother going and voting yourself.

Based on the previous polls I know that people do vote. Perhaps they thought about not voting but then the “if everyone thought this way” persuaded them to vote anyway.

So given that I know that most will vote due to “if everyone thought this way” argument, should I bother?

Of course there are people who are thinking just like me: they know all of the above and they are in the dilemma. Let us call the people like this “group X”. And here comes the solution: if there was an argument that was persuasive enough for a person from the group X to go out and vote, he/she should use that argument to convince himself/herself to vote. Then the entirety of the group X votes and it has a great impact. But what I just wrote is that argument. It is amazing that it is self-referencing.

By going and voting not only you are casting your vote, you are casting a vote for the group X: it is as if you are in a simulation with hundreds of clones and they will follow your decision for the exact same reasoning.

III. It boils down to the expectation.

Combining I & II is the final step in deriving the answer. We need to calculate the expectation of the act of voting. The calculation of the probability of a pivotal vote shouldn’t take into account just 1 vote, it should take into account the size of the group X instead. How big is the group X for your candidate of choice? (How many clones do you have?) How many people bother to investigate the issue this way? My guess is not that many, but my preliminary calculation yields an order of magnitude higher chance of a swinging vote: down to \( O(10^{-5}) \). Remark: I am being way too generous here as two major parties won’t have huge groups X: people who think like me aren’t likely to like them.

However, the most pessimistic yet strongest point of view: candidates aren’t different enough when it comes to assessing the benefits.

Can you really say that Britian will benefit under Torries (as opposed to Labour) or vice versa in tens of millions? If yes, then go ahead and cast your vote. But why stop there? If you really believe your estimate, why not persuade a friend or 2 to follow your vote, start a political campaign (be it just on Facebook) or distribute some flyers? Thousands of pounds worth of value are at stake (if your estimate is in hundreds of millions).

IV. Alternative way to make your vote count.

Abstention could be used to indicate that you don’t support the current system altogether. That’s a real vote, arguably worth more than a vote for one of the two leading parties. This is where my current stance is but I am ready to be swayed.

Alternatively, one could cast a vote for a minor party instead in a hope that major parties will examine the election results later on and align their policies with minor parties in order to take the measly 1 or 2% from them in the next election. The borderline 1 or 2% are worth a lot to the major parties and that’s why this works.

V. “This is all very academic…”

That was the phrase which ended the discussion yesterday. I wish we lived in a Tell culture where I didn’t have to guess whether it was a signal to move on from the topic or it meant that my reasoning was useless. Both are reasonable assertions but the latter begets question why. Given the importance of the matter, the decision how to vote shouldn’t be taken lightly.