Some Things You May Not Have Considered About The Process Of Voting

The hideous Trump vs. Clinton contest has probably made more people feel like not voting than in any time in recent American history. The prospect of choosing their President this time around is rather like voting for a four year dose of haemorrhoids or a four year chronic earache. 

If you are someone to whom the above applies (and ditto the British political equivalent), I have one or two things to say. I've written before (here and here) about how in terms of probability your individual vote in an election or a referendum almost certainly won't make the slightest bit of difference to the outcome.

 

A challenger once tried to prove me wrong by posting a link doing the rounds to a low-turnout local election in which a councillor had won a district seat by two voles. What he should have realised is that the fact that an outcome like this is so newsworthy and shared so many times is all the indication one needs that 99.9999% of the time individual votes (or even a few hundred votes) don't make any difference to the outcome.

 

That doesn't necessarily mean I'm advising everyone not to vote - for some people the experience is worthwhile, and it's not for me to tell people how to behave. When it comes to deciding on whether to vote, people should do whatever is valuable to them. But it's always important to remember that value is measured in a whole range of things, and everything is a trade off. If you get x, you get don’t get y.

If you choose y you get less of z, and so on. One is ill-advised to just think of voting as ‘Well everyone should do it!’. Those for whom voting is a beneficial trade off should do it, and those for whom it’s not, should not. As with most things, it’s easy to plug in the numbers and ascertain probability for whether a trade off is beneficial, to yourself and to the wider population.

 

Here's an illustration to show why it probably isn't worth your while voting. Suppose a single vote costs you £3 of your time. In addition you are made an offer – if you care that much about the outcome you can buy as many additional votes as you like for £50 a vote. In other words, if you want to vote 11 times for your local MP or councillor it’s going to cost you £503 (that’s £500 in cash, and £3 in time).

 

Given the astronomically low chance that your additional 10 votes are going to make any difference to the outcome, I would think that most rational minds would agree that in the trade off – negligible chance of securing a candidate vs. not sacrificing £500 – you’d be ill-advised to waste £500, because in all likelihood your £500 of additional votes is likely to mean that the winning margin will be, say, 6031 instead of 6041 (or reverse that if you vote for the winner).

 

It’s pretty obvious to me that if offered additional votes for money, your individual demand curve for increased probability of outcome is pretty flat, and ditto almost the entire population. Therefore, taken to its rational conclusion, and in full knowledge that almost nobody else is going to change their voting habits based on the above wisdom, you’d be wise to take the logic to its farthest conclusion and trade off the vote that costs £3 of your time.

 

A friend replied with the following comment:

 

"I suppose the exception would be in the cases where the difference in the outcome would be so high that it would offset the negligible probability when working out the expected value. In the recent Scottish Independence referendum, 400,000 votes would have altered the outcome. At £50 a vote that would mean £20million would be the cost of a different outcome - so if you thought Scotland being independent would bring more the £20million in value to you then the £50 investment would be worthwhile (not to mention the £3 of time to vote). Admittedly, this exception would only apply to a very small number of people.

 

Also, there's surely an altruistic implication to this. If the £20million of value wasn't something that I saw for myself but for society as a whole (and people on both sides of debates of these kind are throwing around numbers much larger than £20million), then surely that provides a very compelling reason to vote - I am using my time (or in your hypothetical example, money) to produce a greater expected value for society than the cost I have incurred to do so. It seems to me that the smallness of the odds of an individual vote changing the outcome is mitigated by the largeness of the potential payoff of changing the outcome compared to the cost of casting that vote."

 

My friend is partially right - I could conceive of instances in which that’s the case, yes. However, by equal measure, uncertainty of the ramifications of an outcome has to be factored in too, as does the trivial nature of some outcomes.

 

In the case of the latter, in the grand scheme of things it really makes little difference whether the city councillors for Blackpool south wards are Labour councillors or Lib Dem councillors, so even if a millionaire could affect the outcome by buying £50,000 pounds’ worth of votes, I’d argue there are far better ways he could spend the money.

 

In the case of the former, it’s very difficult to know the exact ramifications of a massive decision like Scottish independence or hard and soft Brexits – much of it is contingent on numerous factors not yet apparent, so you could argue that spending millions of pounds affecting the outcome might be a bit of a blindfold in the dark-type of bet.

 

Finally, sometimes in life we find that even big outcomes could be settled in trivial ways, particularly if the democratic process has primacy, as I argued in this blog post about deciding the Scottish referendum by tossing a coin.