Analysis: After a weekend of intense number-crunching and computer simulations, these researchers have an answer.

By Pádraig MacCarron and Paul Maher, University of Limerick

With an election coming around fast, the age-old debate of how far down the ballot paper you should cast your vote is once again doing the rounds on social media. Like many, we have always been told you should always vote all the way down so you can be sure the candidate at the bottom will never get your vote. Someone will always counter this with "if you don’t put them down at all, they also can’t get your vote". Some even suggest that giving your last choice to a candidate you oppose is better than voting for all others and simply stopping. This is a moot point: your vote will never transfer to the bottom ranked candidate, so putting them last or leaving them blank makes no difference.

So how far down the ballot should you go? We have never been fully satisfied with the many convoluted explanations received, but we’ve also never been convinced not to go all the way down either. I usually vote for my preferred two or three candidates and put the ones I don’t want to get in at the bottom of the ballot paper. I put the ones I haven’t heard about in the middle in a semi-random order which generally tends to be influenced by how close their address is to mine, how nice their candidate photo is and how much I like the sound of their name.

When this question arose in work last week, my colleague asked how easy would it be to write a computer programme to simulate this. I confidently answered that it shouldn’t be too hard. Shortly afterwards, I realised that I really did not understand the single transferable vote system and its intricacies particularly well.

From RTÉ Radio 1's History Show, Elaine Callinan and David Farrell on how and why Ireland embraced the single transferable vote system

Not only is it difficult to write a script to simulate the real-world situation, but one has to run thousands of simulations with different choices to get accurate results because of the many parameters and scenarios involved. However, after a weekend of workstation number-crunching, I can now say I have an answer I am satisfied with. Spoiler alert: halfway down the ballot paper is sufficient.

I tested multiple situations, each running 100,000 simulations with 50,000 voters, 10 candidates and 4 seats. There are two broad categories of simulations which decide how people vote. I purposefully first chose an unrealistic situation where people inherently vote completely at random. In this case, each candidate is just assigned a probability from a uniform distribution to receive a vote. In the second case, I chose a more realistic situation, where some candidates have a high probability to receive a vote, but most have a low one. 

In both cases the candidates are ordered in terms of the assigned probability and I test to see how likely a low probability candidate is to get elected in various conditions. If everybody votes randomly, there is around a 2% chance a candidate outside of the 4 most likely candidates will get in regardless of how far down the ballot voters go.

From RTÉ News & Current Affairs, what is proportional representation?

In those situations where the distribution is not uniformly random, and some candidates have a high probability of getting a vote but most register lower preferences, the chances of a candidate outside the top four getting in is now 4.3%. If they have to rank their preferences to the exact number of seats, the chances remain at 4.3%. However, if they only have to go at least halfway down the ballot paper, this probability now rises to 6.5%. If everyone has to go all the way down the ballot, this number stays the same.

So what does all of this mean? If all voters go at least halfway down the ballot, candidates who would normally be unlikely to win have a 2% higher chance of getting elected. When all voters go all the way down the ballot, this probability remains the same.

This happens for two reasons. There is almost zero probability that a vote will transfer beyond the fifth rank so it will almost always be counted even if it goes to the surplus as long as your vote goes that far. The second reason is that if a candidate who has a high probability of receiving a vote is either ranked at the end, or not named, that vote will always go to another candidate they are competing with for that seat. To reiterate, you do not need to go all the way down the paper as at least halfway down is enough.

From RTÉ Archives, Tim Sexton from the Department of the Environment discusses the proportional representation voting system with RTÉ News' reporter Linda Sherlock in 1987

The next question; should you vote at least halfway down? There’s a small chance that your vote will not be transferred to anyone if it is in the surplus and you don't go far enough down. However, if your preferred candidates are either voted in or eliminated, then it probably doesn’t matter to you.

What happens if you really don’t want someone to get in? By putting many other candidates down, not only are you not voting for that person, but you’re also increasing the chance of one of their competitors getting in by giving them that vote. You only need to go far down the list if you are in strong opposition to certain candidates who you fear may be elected.

Dr Pádraig MacCarron and Dr Paul Maher are postdoctoral researchers working on the DAFINET project based in the Centre for Social Issues Research and MACSI (Mathematics Applications Consortium for Science and Industry (MACSI) at the University of Limerick

The views expressed here are those of the author and do not represent or reflect the views of RTÉ