[This is an automatic translation of the original post in Spanish and has not been edited yet.]

Last week I did a survey about the preference that there was for the candidates for the first presidential round in Colombia this year. Those who took the survey could organize the five candidates, plus the blank vote, according to their preference, from what they considered to be the best option (and assigned a value of 1) to the worst of all (to which they assigned the value 6). The following image shows two examples of how it could be answered.

In the example on the left, the preference was for Petro, who was followed by Fajardo, the blank vote, Vargas Lleras, De La Calle and the last Duke. In the example on the right, the preference was for Duque, followed by Vargas Lleras, the blank vote, De La Calle, Fajardo and last Petro. To make it easier to read in this post, I’m going to use the nomenclature “So-and-so> Mengano” to say that So and so is preferred over Mengano. Thus, the example on the left of the previous image can be written as follows:

Petro> Fajardo> Blank> Vargas Lleras> Street> Duque,

and the example on the right can be written like this:

Duque> Vargas Lleras> Blank> Street> Fajardo> Petro.

The survey was answered by 252 people who saw the survey on my Facebook profile or on one of my friends who were kind enough to share it (thank you very much!). I knew that the sample was going to be too small and biased to make predictions of what was going to happen on May 27, but this did not matter to me because what I wanted to do was something different. My intention with this poll was to do a first experiment of what kind of results we can get when we incorporate the spectrum of our political preferences in elections.

The simplicity of our choices hides the great complexity that is generated in a society whose individuals do not see politics in black and white but in a range of colors. Regardless of whether you support Petro or Duque, the way in which someone perceives the rest of the candidates can offer very valuable clues about the type of society in which you want to live. Compare, for example, the example on the right I gave earlier (Duque> Vargas Lleras> Blank> De La Calle> Fajardo> Petro), with the following order of preferences that someone else might have:

Duque> Fajardo> Street> Vargas Lleras> Petro> Blank.

Both people support Duque, but can you feel that there is something different between them? Can you identify the kind of desires and fears that one or the other may have? Can you imagine what these two people are like? Do you know them perhaps? Tell me what you think of these two people in the comments section.

A basic math exercise shows that there are hundreds of these chains when there are six candidates (extra point to those who say the exact number) but before doing the survey I thought that in real life people would only have preference for a few of these. The surprise came when I told that between 252 people 86 different preference chains were formed, many of them marked by just one or two people.

Now comes the million-dollar question: How can we make sense of all this information? The key here is to find some way to group the different responses together to get a picture of the set of voters. Here are some options:

• Let’s start with the system we use in our elections, in which each person only gives one candidate one vote. We can replicate this using preference chains, taking only the first one, giving the latter one vote and ruling out the rest of the candidates (what a waste of information!). We add up all the votes that each candidate obtained and we order them from highest to lowest. The technical name of this method of choice is plurality system. By doing this, the candidates in my survey were arranged as follows:

Duque> Petro> Fajardo> Street> Vargas Lleras> Blank

• What if we try to incorporate the information of the second preferred candidate? We could recognize its value by rewarding it in some way, for example, we could give the first candidate of our preference two votes, and the second candidate one vote. To calculate the totals, we add all the votes obtained by each candidate and order them from highest to lowest (of course, now it will appear that there are more votes than voters but that does not matter, the only thing that matters is the way they are ordered at the end The candidates). When I do this in my survey results, I now get the following order:

Duque> Fajardo> Petro> Street> Vargas Lleras> Blank

       Petro and Fajardo have swapped positions!

• What would happen if we incorporated the third preferred candidate? We can give, for example, three votes to the first candidate of our preference, two to the second, and one vote to the third. The photo we get again is different:

Fajardo> Duque> Petro> Street> Vargas Lleras> Blank

• Since we are in those, why not then do we give the first five candidates of our preference, from highest to lowest, five, four, three, two and one vote respectively, but none to the sixth? This way of allocating votes is known as Reda Borda and what we get now is again a different order:

Fajardo> Street> Vargas Lleras> Duque> Blank> Petro

• One last: If instead of rewarding the candidate we most prefer, do we penalize the one we most detest? So what we do is give a vote to the least preferred candidate, we add all the votes that each one obtained, but we order them from the smallest number of votes to the largest number of votes. Although it may seem strange, this is a respectable electoral system known as the anti-plurality method and by doing this I get the following order:

Vargas Lleras> Blank> Street> Fajardo> Petro> Duque

I hope that the reader who has come this far is feeling a bit of discomfort with all these results. We start with the illusion of being able to incorporate a broader spectrum of preferences than we currently have, but what we get is that the results fluctuate depending on the weight we give to each of the candidates. How can we interpret all these results? Who should go to the second round? Which of all these results is correct?

The answer is that all of these results are correct. No one can claim to be more natural than the other. They are all equally arbitrary, including our current plurality system. It is puzzling and I will have to explain this in detail, but it will be something that will have to wait for the next entry.